{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Last Updated On: 2023-02-11 15:55:10.378740\n" ] } ], "source": [ "from datetime import datetime\n", "print('Last Updated On: ', datetime.now())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# M62_TP1 EDO : calcul approché VS formel." ] }, { "cell_type": "markdown", "metadata": { "toc": true }, "source": [ "

\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## ✨ Calcul approché avec la fonction `odeint` du module `SciPy`\n", "--- " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "L'ECUE M62 n'est qu'une introduction aux méthodes numériques d'approximation d'EDO en utilisant Python comme langage commun de programmation. \n", "Nous allons étudier, programmer et tester plusieurs méthodes numériques.\n", "\n", "Cependant toutes ces méthodes (et bien plus) se trouvent déjà dans le module `SciPy`. \n", "Bien sûr vous devez toujours faire un peu de programmation avec Python pour les utiliser et une compréhension des fondements de la méthode numérique que vous utilisez est toujours indispensables. \n", "\n", "Voyons sur trois exemples comment utiliser la fonction `odeint` du module `SciPy` pour approcher la solution d'abord d'une EDO ensuite d'un système d'EDO (ce qui inclut les équations différentielles d'ordre 2 ou plus)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Principe d'utilisation de `odeint`\n", "\n", "Le principe d’utilisation de `odeint` (pour intégrer numériquement des équations différentielles) est le suivant: pour avoir une estimation numérique de la solution du problème de \n", " $$\\begin{cases}\n", " \\mathbf{y}'(t)=\\boldsymbol{\\varphi}(t,\\mathbf{y}(t)),\\\\\n", " \\mathbf{y}(t_0)=\\mathbf{y}_0\n", " \\end{cases}$$\n", "avec $\\mathbf{y}(t)=(y_1(t),y_2(t),\\dots,y_n(t))$ le vecteur des fonctions recherchées, dépendant de la variable $t$ et $\\boldsymbol{\\varphi}=(\\varphi_1,\\varphi_2,\\dots,\\varphi_n)$ une fonction de forme quelconque, on donne comme argument la fonction $\\boldsymbol{\\varphi}$ (qui doit avoir deux paramètres, même dans le cas autonome), la condition initiale $\\mathbf{y}_0$ et les points de l'interval de temps où approcher la solution (qui commence à $t_0$). Elle retourne un tableau `Numpy` (même si $t$ était une liste).\n", "\n", "\n", "Cf. https://docs.scipy.org/doc/scipy-1.2.1/reference/generated/scipy.integrate.odeint.html\n", "\n", "Par défaut, l'ordre requis des deux premiers arguments de `func` est dans l'ordre inverse de celui classique. Pour utiliser une fonction avec la signature `func(t, y, ...)`, c'est-à-dire d'abord $t$ puis $y$, l'argument `tfirst` doit être défini à `True`.\n", "\n", "**Remarque:** la résolution de $y''(t)=F(t,y(t),y'(t))$ passera par celle du système différentiel\n", "$$\\begin{cases}\n", "y_1'(t)=y_2(t),\\\\\n", "y_2'(t)=F(t,y_1(t),y_2(t))\n", "\\end{cases}$$\n", "avec \n", "$y(t)=y_1(t)$, \n", "$y'(t)=y_1'(t)=y_2(t)$ \n", "et \n", "$\\varphi_1(t,y_1(t),y_2(t))=y_2(t)$, \n", "$\\varphi_2(t,y_1(t),y_2(t))=F(t,y_1(t),y_2(t))$. \n", "\n", "**Remarque:** SciPy propose une interface plus récente et plus personnalisable pour résoudre un problème de Cauchy, il s'agit de `solve_ivp`. L'avantage principal est que `solve_ivp` offre plusieurs méthodes pour résoudre les équations différentielles alors qu'`odeint` est limité à une seule. Cependant, la prise en main de `odeint` est plus simple et suffisante pour les objectifs de ce cours. \n", "\n", "Cf. https://docs.scipy.org/doc/scipy-1.2.1/reference/generated/scipy.integrate.solve_ivp.html\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exemple de résolution approchée d’une équation différentielle d'ordre 1\n", "\n", "En guise d’exemple, considérons le problème de Cauchy $y(0)=1$ et une équation logistique simple de la forme\n", "$$\n", "y'(t)=\\frac{3}{2} y(t) \\left( 1-\\frac{y(t)}{6} \\right). \n", "$$\n", "On crée alors la fonction $\\varphi$" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "%reset -f\n", "%matplotlib inline\n", "from matplotlib.pylab import * # importe aussi numpy sans alias\n", "# rcdefaults()\n", "rcParams.update({'font.size': 16})\n", "from scipy.integrate import odeint" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "La fonction `odeint` peut être appelée avec au minimum trois arguments: \n", "- `func`: la fonction $\\varphi$, \n", "- `y0`: la valeur $y(t_0)$, \n", "- `t`: le vecteur (qui commence à $t_0$) où la fonction $y$ sera évaluée.\n", "\n", "Elle renvoi un vecteur `sol` contenant l'évaluation de la solution en les points du vecteur $t$.\n", "\n", "Nota bene: par défaut la fonction $\\varphi$ doit avoir $t$ comme deuxième variable, mais on retrouve l'ordre usuel avec le paramètre `tfirst=True`." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# def phi(t,y):\n", "# return 1.5*y*(1-y/6)\n", "# ou \n", "\n", "phi = lambda t,y : 1.5*y*(1-y/6)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "t0 = 0\n", "y0 = 1\n", "tt = linspace(t0,5,201)\n", "# sol = odeint(func=phi,y0=y0,t=tt,tfirst=True) # Appel avec arguments nommés: 4 paramètres, passées dans n'importe quel ordre\n", "sol = odeint(phi,y0,tt,tfirst=True) # Appel classique: 4 paramètres, passées selon l'ordre" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "La solution peut alors être tracée simplement " ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "figure(figsize=(10,7))\n", "plot(tt,sol)\n", "xlabel('t')\n", "ylabel('y')\n", "grid();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "NB: le nombre de points en lesquels les résultats sont évalués n’est pas (du moins directement) relié à la précision des calculs internes (ne pas imaginer que cela fixe le pas de la méthode, en particulier)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Champ de vecteurs et lignes de courant\n", "\n", "Bien qu'il soit trés rare que l'on puisse résoudre explicitement une équation différentielle donnée, on peut souvent avoir une idée de l’allure des graphes des solutions en observant le champs de vecteurs associé. \n", "En effet le graphe d'une solution de l'équation $y'(t)=\\varphi(t,y(t))$ est par définition tangent à son vecteur vitesse $(1,y'(t))$ et donc au vecteur $(1, \\varphi(t,y(t))$. \n", "La connaissance de la fonction $\\varphi$ en chaque point $(t,y)$ permet donc de représenter facilement ces vecteurs tangents même si l'on ne connait pas les solutions. \n", "Et si l'on en trace un grand nombre, uniformément répartis dans le plan $(t, y)$, on obtient une représentation\n", "du champ de vecteurs associé à l'équation différentielle qui permet souvent de deviner les graphes des solutions puisqu'il s'agit des courbes qui sont tangentes en tous leurs points aux vecteurs de ce champs de vecteurs. \n", "Il est alors intéressant d'y superposer la solution numérique obtenue avec `odeint`.\n", "\n", "La fonction `quiver` du module `matplotlib` permet de tracer un champ de vecteurs. La fonction `streamplot` permet de tracer des lignes de courant.\n", "Utilisons-les pour obtenir les tracés associés à notre équation différentielle.\n", "La courbe rouge est la solution déterminée par `odeint`. " ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# define a grid \n", "g1 = linspace(0,5,21)\n", "g2 = linspace(0,8,21)\n", "T,Y = meshgrid(g1,g2) # create a grid\n", "\n", "# compute direction at each point\n", "DT, DY = 1, phi(T,Y) # compute growth rate on the grid\n", "M = sqrt(DT**2+DY**2) # norm growth rate \n", "M[ M==0 ] = 1 # avoid zero division errors \n", "\n", "\n", "figure(figsize=(20,7))\n", "\n", "# Champ des pentes\n", "subplot(1,2,1)\n", "quiver(T,Y, DT/M, DY/M, M, pivot='mid')\n", "plot(tt,sol,'r')\n", "grid()\n", "xlabel('t')\n", "ylabel('y')\n", "title('Champ des pentes');\n", "\n", "# Lignes de courant\n", "subplot(1,2,2)\n", "streamplot(T,Y, DT/M, DY/M, color=M)\n", "plot(tt,sol,'r')\n", "grid()\n", "xlabel('t')\n", "ylabel('y')\n", "title('Lignes de courant');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exemple de résolution approchée d’un système d'équations différentielles d'ordre 1\n", "\n", "Considérons deux espèces: une proie (des lièvres par exemple) et un prédateur (des lynx par exemple). \n", "Ces deux populations sont représentées par $y_1(t)$ et $y_2(t)$ des fonctions continues du temps $t$. \n", "Si on suppose qu’il n’y a aucune autre intervention extérieur, une modélisation possible pour ce genre de système a été proposée indépendamment par Alfred James Lotka en 1925 et Vito Volterra en 1926:\n", "$$\n", "\\begin{cases}\n", "y_1'(t) = y_1(t)(a-by_2(t)) &[\\stackrel{\\text{déf}}{=}\\varphi_1(y_1(t),y_2(t),t)] \\quad\\text{équation équation des proies}\\\\\n", "y_2'(t) =-y_2(t)(c-dy_1(t)) &[\\stackrel{\\text{déf}}{=}\\varphi_2(y_1(t),y_2(t),t)] \\quad\\text{équation équation des prédateurs}\n", "\\end{cases}\n", "$$\n", "soit encore, en notation matricielle, \n", "\n", "$$\\begin{pmatrix}\n", " y_1\\\\\n", " y_2\n", " \\end{pmatrix}'(t)\n", " =\n", " \\begin{pmatrix}\n", " \\varphi_1(y_1(t),y_2(t),t)\\\\\n", " \\varphi_2(y_1(t),y_2(t),t)\n", " \\end{pmatrix}.$$\n", "\n", "On suppose qu’à ce jour il y a $y_1(0)=2$ unités de proies (une unités = $1000$ animaux) et $y_2(0)=1$ unités de prédateurs et on se demande comment vont évoluer les populations de ces deux espèces. \n", "Pour les simulations on prendra $a=2$, $b=1$, $c=1$ et $d=0.3$. \n", "\n", "Soit $\\mathbf{y}(t)\\stackrel{\\text{déf}}{=}(y_1(t),y_2(t))$ le vecteur des deux fonctions inconnues. \n", "On commence par créer la fonction vectorielle \n", "$$\n", "\\boldsymbol{\\varphi}(\\mathbf{y},t)=(\\varphi_1(\\mathbf{y},t),\\varphi_2(\\mathbf{y},t))\n", "$$" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "%reset -f\n", "%matplotlib inline\n", "from matplotlib.pylab import * # importe aussi numpy sans alias\n", "# rcdefaults()\n", "rcParams.update({'font.size': 16})\n", "from scipy.integrate import odeint" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "# yy est une liste a deux composantes\n", "pphi = lambda t,yy : [ yy[0]*(2-yy[1]) , -yy[1]*(1-0.3*yy[0]) ]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "En faisant varier le temps sur l'intervalle $[0;20]$ et en prenant comme condition initiale le vecteur $\\mathbf{y}_0=(2,1)$ on écrit" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "t0 = 0\n", "yy0 = [2,1]\n", "tt = linspace(t0,20,201)\n", "\n", "# V1\n", "# odeint revoie une matrice, la colonne j contient l'approximation de la j-ème composante de la fonction inconnue\n", "sol = odeint(pphi,yy0,tt,tfirst=True)\n", "sol_1 = sol[:,0] # [y_1(t) for t in tt]\n", "sol_2 = sol[:,1] # [y_2(t) for t in tt]\n", "\n", "# V2\n", "# Pour que odeint renvoit séparément les valeurs de la solution, il faut rajouter .T à la fin\n", "sol_1,sol_2 = odeint(pphi,yy0,tt,tfirst=True).T" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Le tracé des évolutions de $y_1$ et $y_2$ en fonction du temps $t$ peut être obtenu par " ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "figure(figsize=(10,7))\n", "plot(tt,sol_1,tt,sol_2)\n", "grid()\n", "xlabel('t')\n", "ylabel('y')\n", "legend([r\"$y_1(t)$ proies\",\"$y_2(t)$ prédateurs\"]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Le tracé des évolutions de $y_2$ en fonction de $y_1$ peut être obtenu par" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "figure(figsize=(10,7))\n", "plot(sol_1,sol_2)\n", "grid()\n", "xlabel(r'$y_1$')\n", "ylabel(r'$y_2$');" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "Y1,Y2 = meshgrid(linspace(min(sol_1),max(sol_1),21),linspace(min(sol_2),max(sol_2),21))\n", "V1,V2 = pphi(tt,[Y1,Y2]) \n", "r1=sqrt(1+V1**2)\n", "r2=sqrt(1+V2**2)\n", "\n", "figure(figsize=(10,7))\n", "quiver(Y1, Y2, V1/r1, V2/r2) \n", "plot(sol_1,sol_2)\n", "grid()\n", "xlabel(r'$y_1$')\n", "ylabel(r'$y_2$');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Considérons la fonction\n", "$$\n", "E(t)=dy_1(t)+by_2(t)-c\\ln(y_1(t))-a\\ln(y_2(t))\n", "$$\n", "Vérifions analytiquement que la fonction $E$ est une intégrale première du système, c’est-à-dire que si $(y_1, y_2)$ est une solution alors l’application $E$ est constante:\n", "\\begin{align}\n", "E'(t)\n", "&=dy_1'(t)+by_2'(t)-\\frac{c}{y_1(t)}y_1'(t)-\\frac{a}{y_2(t)}y_2'(t)\n", "\\\\\n", "&=\\left(d-\\frac{c}{y_1(t)}\\right)y_1'(t)+\\left(b-\\frac{a}{y_2(t)}\\right)y_2'(t)\n", "\\\\\n", "&=\\left(d-\\frac{c}{y_1(t)}\\right)y_1(t)(a-by_2(t))-\\left(b-\\frac{a}{y_2(t)}\\right)y_2(t)(c-dy_1(t))\n", "\\\\\n", "&=(dy_1(t)- c)(a-by_2(t))-(by_2(t)-a)(c-dy_1(t))\n", "\\\\\n", "&=(dy_1(t)- c)(a-by_2(t))-(a-by_2(t))(dy_1(t)- c)\n", "=0.\n", "\\end{align}\n", "Vérifions cette propriété numériquement:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "7.942278004158254e-07\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "figure(figsize=(10,7))\n", "# valeur pour t=0\n", "E0 = 0.3*yy0[0]+yy0[1]-log(yy0[0])-2*log(yy0[1])\n", "plot([tt[0],tt[-1]],[E0,E0])\n", "\n", "EE = 0.3*sol_1+sol_2-log(sol_1)-2*log(sol_2)\n", "print(max(abs(EE-E0)))\n", "plot(tt,EE)\n", "xlabel('t')\n", "ylabel('E')\n", "grid();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exemple de résolution approchée d’une équation différentielle d'ordre 2\n", "\n", "Considérons l'EDO $y''(t)=-\\sin(y(t))$ qui décrit le mouvement d'un pendule non amorti, équivalente au système différentiel\n", "$$\n", "\\begin{cases}\n", "y_1'(t)=y_2(t),\\\\\n", "y_2'(t)=-\\sin(y_1(t))\n", "\\end{cases}\n", "$$\n", "avec $y(0)=0$ et $y'(0)=1$. " ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "%reset -f\n", "%matplotlib inline\n", "from matplotlib.pylab import * # importe aussi numpy sans alias\n", "# rcdefaults()\n", "rcParams.update({'font.size': 16})\n", "from scipy.integrate import odeint" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pphi = lambda t,yy : [ yy[1], -sin(yy[0]) ]\n", "\n", "t0 = 0\n", "yy0 = [0,1]\n", "tt = linspace(t0,10,1001)\n", "sol_1, sol_2 = odeint(pphi,yy0,tt,tfirst=True).T\n", "\n", "figure(figsize=(18,7))\n", "\n", "subplot(1,2,1)\n", "plot(tt,sol_1,tt,sol_2)\n", "xlabel('t')\n", "ylabel('y')\n", "grid()\n", "\n", "subplot(1,2,2)\n", "plot(sol_1,sol_2)\n", "xlabel(r'$y_1$')\n", "ylabel(r'$y_2$')\n", "grid()\n", "axis('equal');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Considérons l'énergie suivante (somme de l'énergie potentielle et de l'énergie cinétique):\n", "$$\n", "E(t)=-\\cos(y_1(t))+\\frac{1}{2}(y_2(t))^2\n", "$$\n", "Vérifions analytiquement que la fonction $E$ est conservée au cours du temps:\n", "\\begin{align}\n", "E'(t)\n", "&=\\sin(y_1(t))y_1'(t)+y_2(t)y_2'(t)\n", "\\\\\n", "&=-y_2'(t)y_1'(t)+y_1'(t)y_2'(t)\n", "=0.\n", "\\end{align}\n", "Vérifions cette propriété numériquement:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "9.448590565508397e-08\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "figure(figsize=(10,7))\n", "# valeur pour t=0\n", "E0 = -cos(yy0[0])+yy0[1]**2/2\n", "plot([tt[0],tt[-1]],[E0,E0])\n", "\n", "EE = -cos(sol_1)+sol_2**2/2\n", "print(max(abs(EE-E0)))\n", "plot(tt,EE)\n", "xlabel('t')\n", "ylabel('E')\n", "grid(); " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 🐍 Calcul analytique avec le module `sympy`\n", "--- \n", "https://docs.sympy.org/latest/modules/solvers/ode.html" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "%reset -f\n", "%matplotlib inline\n", "\n", "import sympy as sym\n", "sym.init_printing()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exemple de résolution analytique d’une équation différentielle d'ordre 1\n", "\n", "Considérons le problème de Cauchy\n", "$$\\begin{cases}\n", "u'(x)=-3x^2u(x)+6x^2,\\\\\n", "u(0)=4.\n", "\\end{cases}$$" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\frac{d}{d x} u{\\left(x \\right)} = - 3 x^{2} u{\\left(x \\right)} + 6 x^{2}$" ], "text/plain": [ "d 2 2\n", "──(u(x)) = - 3⋅x ⋅u(x) + 6⋅x \n", "dx " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = sym.Symbol('x')\n", "u = sym.Function('u')\n", "left = sym.diff(u(x),x)\n", "right = 6*x**2-3*x**2*u(x)\n", "edo = sym.Eq( left , right )\n", "display(edo)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle u{\\left(x \\right)} = C_{1} e^{- x^{3}} + 2$" ], "text/plain": [ " 3 \n", " -x \n", "u(x) = C₁⋅ℯ + 2" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "solgen = sym.dsolve(edo,u(x))\n", "display(solgen)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Prise en compte des conditions initiales:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\left\\{ C_{1} : 2\\right\\}$" ], "text/plain": [ "{C₁: 2}" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x0 = 0\n", "u0 = 4\n", "consts = sym.solve( sym.Eq( u0, solgen.rhs.subs(x,x0)) , dict=True)[0]\n", "consts" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle u{\\left(x \\right)} = 2 + 2 e^{- x^{3}}$" ], "text/plain": [ " 3\n", " -x \n", "u(x) = 2 + 2⋅ℯ " ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solpar = solgen.subs(consts)\n", "solpar" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On transforme le résultat en une fonction vectorisée :" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "func = sym.lambdify(x,solpar.rhs,'numpy')" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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KeZJU/D7jV986gp37D3Dfm5833UFERCROKeRJ0hnaswMXju7LjOISVmza63U5IiIiEaGQJ0npppMGkZ2ewp3/XKKbMEREJCEp5ElS6pyVxo0nHcZ7K7fz2pLNXpcjIiISdgp5krQuGt2XQbnt+eUrSymvrPa6HBERkbBSyJOkleL3cfsZQ1m/o4xH9SQMERFJMAp5ktTGD+zClGG5PDBnFZt2l3tdjoiISNgo5EnS++lpQ6l2jrv/vczrUkRERMJGIU+SXp+cTKYd258XP/mSBSU7vS5HREQkLBTyRIDrCgfQtX06v35lmaZUERGRhKCQJwJkpafw3yceyvySnbyxVFOqiIhI/FPIEwn6bkEf+nfN4p5Xl1NVXeN1OSIiIm2ikCcSlOL38aMpg1m1dR/PLtjgdTkiIiJtopAnUseUYbmMzOvMfW98zv4DVV6XIyIi0moKeSJ1mBm3njKYLXsr+Mu7a7wuR0REpNUU8kRCFOTnMHloLn+eu5rtpRVelyMiItIqCnki9fjRyYMpq6zm/tkrvS5FRESkVRTyROoxsFs25xX04ckPSyjZvs/rckRERFpMIU+kAT848VD8PuP/3vzC61JERERaTCFPpAHdOmRwydh8XvxkIyu37PW6HBERkRZRyBNpxDXH9Scj1c99OponIiJxRiFPpBGHZKdz+fh8/vXpVyz7ao/X5YiIiDSbQp5IE64+tj/t01O4743PvS5FRESk2aIa8sxsipnNNrNNZlZhZhvM7BkzG9qMvq6B15Eh7XxmdquZrTWzcjNbZGbfidhGScLrlJnGVcf25/Wlm/lsw26vyxEREWmWaB/JywEWANcDk4FbgWFAsZnlNaP/48DYkFfo4ZVfAHcAfwROAYqBZ83s1LaXL8nqign5dMpM5X/fWOF1KSIiIs2SEs2VOeeeAp6qu8zM5gHLgXOAe5v4io3OueKGPjSzbsDNwN3Oud8FF88xs4HA3cArra1dklv7jFSmHdef37y6ggUlOxmZ19nrkkRERBoVC9fkbQ++V4bhu6YAacDMkOUzgSPMrF8Y1iFJ6tKx+RySlaajeSIiEhc8CXlm5jezNDM7FHgI2ATMakbX64LX8u0PXtt3bMjnw4AKIPRZVEuC701e+yfSkKz0FK4rHMB7K7dTvHp70x1EREQ8ZM656K/UbD4wMvjrSuBM59yyJvrMAP4JfAnkAT8kENpOcs4VBds8HPyu7iF9BwJfAJc452Y08P3TgGkAubm5I2fNak7mbL3S0lKys7Mjuo5kE40xPVDt+OHbZfTKNn50TLuIrstr2kfDT2MaXhrP8NOYhle0xnPSpEkLnHMFocujek1eHVOBDkB/AtfQvWFmE5xzaxvq4JybWufXd8zsJWAxcBcwIbjcgPpSqzVVkHPuYeBhgIKCAldYWNj0VrRBUVERkV5HsonWmJakruaXryyjfb8RCX1tnvbR8NOYhpfGM/w0puHl9Xh6crrWObfMOfdh8EaME4Bs4JYWfsde4F/AMXUW7wA6m1loqOtc53ORNrloTF86Z6Zy/2w9BUNERGKX5zdeOOd2EThlO7AV3UOP3C0B0oEBIe1qr8Vb2op1iHxDZloKVx3bn6IVWzVvnoiIxCzPQ56Z5QKDgVUt7NcBOA34sM7iV4EDwEUhzS8GFjvn1rShVJH/uGRsHh0yUnQ0T0REYlZUr8kzs78DC4FPgT3AYcAPgCqCc+QFJ0VeBdzpnLszuOxmYBAwh69vvLgZ6E6dQOec22Jm9wG3mtne4Lq+CxwPnBWFTZQk0T4jlcvG9+MPb33B8k17GNy9g9cliYiIfEO0j+QVA2cD0wlcT3cjMBc40jlX++QKA/whta0gcMr1D8AbwP8Ca4AJzrl3QtZxG4GbMW4AXgPGA+c55/4Rge2RJHbF+Hyy0vz8cXbojD0iIiLei/YTL+4B7mmizVpC7oYNBrRmhTTnXDWBkHdX66oUaZ5OmWlMHZvPQ2+v4gdbSxnQVdMOiIhI7PD8mjyReHbVsf1IT/HxwBwdzRMRkdiikCfSBl2y07lodB4vffIl67bv97ocERGR/1DIE2mjacf1x2/Gn99u0Q3iIiIiEaWQJ9JGuR0y+M7I3jy3YANb9pZ7XY6IiAigkCcSFtOO609ldQ2Pv7fW61JEREQAhTyRsOjXJYtTDu/OjOIS9pZXel2OiIiIQp5IuFw7cQB7y6v424frvC5FREREIU8kXIb37sT4gYfw2LtrqKiq9rocERFJcgp5ImF07cQBbNlbwYsfb/S6FBERSXIKeSJhNGFgF4b17MBDb6+mpsZ5XY6IiCQxhTyRMDIzrp04gNVb9/H60s1elyMiIklMIU8kzE45vDt9czJ5cO4qnNPRPBER8YZCnkiYpfh9TDuuP4vW76J49Q6vyxERkSSlkCcSAeeM7E2X7DQe1qPORETEIwp5IhGQkepn6ph85qzYysote70uR0REkpBCnkiEXDymL+kpPh57d43XpYiISBJSyBOJkEOy0/nOyN48v3Aj20orvC5HRESSjEKeSARdOaEfB6pqmPFBideliIhIklHIE4mgAV2zOXFIN2YUl1BeqUediYhI9CjkiUTYlRP6s2PfAV5YqEediYhI9CjkiUTYmP45HN6rA4+9q0ediYhI9CjkiUSYmXH1sf1ZtXUfRZ9v8bocERFJEgp5IlFw6hE96NExg0fe1nQqIiISHQp5IlGQ6vdx+fh8Pli9ncUbd3tdjoiIJAGFPJEoOX9UX7LS/Dz6zmqvSxERkSSgkCcSJR0yUjnvmD7867Ov2LKn3OtyREQkwSnkiUTRZePyqapxzCzW5MgiIhJZCnkiUZR3SBYnDM7lyQ/XaXJkERGJKIU8kSi7Ynw+2/cd4OVFX3pdioiIJDCFPJEoGzvgEAZ3b89f3l2Dc5ocWUREIiOqIc/MppjZbDPbZGYVZrbBzJ4xs6FN9Csws4fNbLmZ7TezdWb2pJn1q6ftWjNz9bzOjtiGibSAmXH5+HyWb9rLB6u3e12OiIgkqGgfycsBFgDXA5OBW4FhQLGZ5TXS7/xguz8ApwC3AEcD882sTz3tXwPGhrzmhmkbRNrsrCN7kZOVxl/fW+t1KSIikqBSorky59xTwFN1l5nZPGA5cA5wbwNd73HObQ3p9x6wBrgauD2k/TbnXHFYihaJgIxUPxeO6ssDRSsp2b6PvEOyvC5JREQSTCxck1d7vqqyoQahAS+4rATYCvSKUF0iETV1bB5+M6a/r+lUREQk/DwJeWbmN7M0MzsUeAjYBMxq4XcMAboBy+r5+IzgtXsVZlas6/EkFuV2yOC04T14Zv569pY3+DeOiIhIq5gXd/eZ2XxgZPDXlcCZzrn6wlpD/VOAt4AhwCDn3M46n90PfETgVG4ugev/JgJTnXMzG/nOacA0gNzc3JGzZrUoc7ZYaWkp2dnZEV1HsonHMV29q5o7i8u5cHAak/NTvS7nG+JxPGOdxjS8NJ7hpzENr2iN56RJkxY45wpCl3sV8oYAHYD+wM0EwtgE59zaZvb/M3AlcJpz7vUm2vqBYqC7c66+mzQOUlBQ4ObPn9+cpq1WVFREYWFhRNeRbOJ1TL/9p/fYse8As28qxOczr8v5j3gdz1imMQ0vjWf4aUzDK1rjaWb1hjxPTtc655Y55z4M3ohxApBN4I7ZJpnZrwkccbuiqYAXXFc18CzQ28x6tKFskYi4bHw/1m7fz9zPD7r0VEREpNU8v/HCObeLwCnbgU21NbPbCITBG5xzM1qwmtrDI5p5VmLOKYd3p1v7dB5/f63XpYiISALxPOSZWS4wGFjVRLv/Au4CbnPO3d+C708BzgXWOec2taVWkUhI9fu4aHQecz/fyqqtpV6XIyIiCSLaT7z4u5n9j5mdZWaTzOwaApMUVxGcI8/M8sysysxur9PvfOD3wKvAbDMbU+c1tE67C8xslpldEvz+84E5BG7y+HH0tlSkZS4Y3YdUvzHjA02nIiIi4RHVyZAJ3ABxHnATkAasB4qAX9e56cIAP98MoCcHl58cfNU1FygM/ryGwLQqvyXwdI39BO60Pdk591pYt0QkjLq1z+C0I3rw3IIN3DxlENnp0f6fpoiIJJpoP/HiHuCeJtqs5etr6GqXXQZc1ozvLwaOb3WBIh66dFw+L37yJc8v2MCl4/K9LkdEROKc59fkiUjAUX07M6J3R6Z/sJaaGt0jJCIibaOQJxJDLhufz+qt+3h35TavSxERkTinkCcSQ049ogddstOYrulURESkjRTyRGJIeoqfC0f1ZfaKLazbvt/rckREJI4p5InEmIvG5OE344kP1npdioiIxDGFPJEYk9shg5MP784z89ez/0CV1+WIiEicUsgTiUGXjstnT3kVL33ypdeliIhInFLIE4lBBXmdGdy9PU98UIJzmk5FRERaTiFPJAaZGZeMzWfZV3uYX7LT63JERCQOKeSJxKizj+pJ+4wUntDzbEVEpBUU8kRiVGZaCueO7MO/P/uKLXvKvS5HRETijEKeSAybOjaPqhrHU/PWe12KiIjEGYU8kRjWr0sWxx3WlSc/LKGyusbrckREJI4o5InEuEvH5rFlbwWvL9nsdSkiIhJHFPJEYlzhoG707tyO6XoChoiItIBCnkiM8/uMi8fkMW/NDpZv2uN1OSIiEicU8kTiwHcL+pCe4tN0KiIi0mwKeSJxoHNWGmeM6MmLH29kT3ml1+WIiEgcUMgTiROXjM1j/4FqXliwwetSREQkDijkicSJ4b07MaJPJ2YU63m2IiLSNIU8kTgydUweq7bu44NV270uRUREYpxCnkgcOX14DzpnpuoGDBERaZJCnkgcyUj1c94xfXhj2Wa+2l3mdTkiIhLDFPJE4szFo/OocY6nPlzndSkiIhLDFPJE4kyfnEwmDerG3+at50CVnmcrIiL1U8gTiUNTx+axrbSC15Zs8roUERGJUQp5InFo4qFd6ZuTyQzdgCEiIg1QyBOJQz6fcfGYvsxbq+fZiohI/RTyROLUecHn2eponoiI1EchTyROdcpM48wRPfn7xxvZq+fZiohIiKiGPDObYmazzWyTmVWY2QYze8bMhjajb4aZ/dbMvjKzMjP7wMyOq6edz8xuNbO1ZlZuZovM7DuR2SIRb02tfZ7two1elyIiIjEm2kfycoAFwPXAZOBWYBhQbGZ5TfR9DLgauB04HfgKeM3Mjgxp9wvgDuCPwClAMfCsmZ0ank0QiR16nq2IiDQkqiHPOfeUc+6HzrnnnHNznXMzgG8D7YFzGupnZiOAC4EfOOcecc69BZwHrAPurNOuG3AzcLdz7nfOuTnOuWuAOcDdkdsyEe9MHZPHyi2lfLBaz7MVEZGvxcI1ebX/MjV2UdGZwc+frl3gnKsCZgFTzCw9uHgKkAbMDOk/EzjCzPqFpWKRGHL68B50ykzVDRgiIvINnoQ8M/ObWZqZHQo8BGwiENgaMgxY45zbH7J8CYFQN7BOuwpgZT3tAJq89k8k3mSk+vluQR9eX7qZTbvLvS5HRERiREpLGpvZ7CaaOOfcCc34qg+BkcGfVwLHO+e2NNI+B9hZz/IddT6vfd/lDr44KbSdSEK5eEweD7+zmr/NW8eNJx3mdTkiIhIDWhTyCBz5Cw1QhwCDgK3A5838nqlAB6A/gWvo3jCzCc65tQ20t3rWW7u8Ne0ObmA2DZgGkJubS1FRUVNd2qS0tDTi60g2yT6mw7v4mf7uSob7N5Lia3KXb1Kyj2ckaEzDS+MZfhrT8PJ6PFsU8pxzhfUtN7MBwIvAr5r5PcuCP35oZv8G1gK3ANc20GUH0Lee5Z3rfF773tnMLORoXmi7+mp6GHgYoKCgwBUWFjaxFW1TVFREpNeRbJJ9TF33LVz++EeUdxnE6cN7tvn7kn08I0FjGl4az/DTmIaX1+MZlmvynHOrCNy9+ttW9N1F4JTtwEaaLQH6mVlmyPKhwAG+vgZvCZAODKinHcDSltYnEi8mHtaVPjnteEI3YIiICOG98WIr0OKLgcwsFxgMrGqk2ctAKnBunX4pwHeB151zFcHFrxIIfReF9L8YWOycW9PS+kTihc9nXDw6j3lrdrBi016vyxEREY+FJeSZWQ5wI40HNczs72b2P2Z2lplNMrNrgLlAFXBvsE2emVWZ2e21/ZxznxCYPuX3ZnaVmZ1A4G7cfsDP6rTbAtwH3GpmN5pZoZk9CBwP/CQc2yoSy84r6ENaio8ZxWu9LkVERDzW0rtr13DwjQ1pQG7w56YeH1ZMYBLjm4L91gNFwK/r3HRhgJ+DA+jlwC+Bu4BOwCLgZOfcwpB2twGlwA1Ad2AFcJ5z7h9N1CYS9zpnpXHG8J78feFGfnzyYNpnpHpdkoiIeKSld9fO5eCQVw6UAM8Gr81rkHPuHuCeJtqspZ67YZ1zZQSOFt7YRP9qAkHwrsbaiSSqS8bm8fzCDbywcCOXjsv3uhwREfFIS++uvSxCdYhImIzo04kRvTsyo7iES8bmYdb26VRERCT+xMJjzUQkzC4Zmx94nu0qPc9WRCRZKeSJJKDThvcgJytN06mIiCQxhTyRBJSR6ue8gj68vnQTX+4q87ocERHxgEKeSIK6aHRfHPC3D9d5XYqIiHhAIU8kQfXJyeSEwbnM+mgdFVXVXpcjIiJRppAnksAuGZvHttIDvLp4k9eliIhIlCnkiSSwCQO70K9Llm7AEBFJQgp5IgnM5zMuHpPHgpKdLN642+tyREQkihTyRBLcOSN70y7VzwwdzRMRSSoKeSIJrmO7VM4+qhcvLdrIrv0HvC5HRESiRCFPJAlcMjaP8soanpm/3utSREQkShTyRJLAkB4dGNUvhxnFJVTXOK/LERGRKFDIE0kSl43LZ/2OMuYs3+J1KSIiEgUKeSJJYvLQXHp0zGD6B2u9LkVERKJAIU8kSaT4fVw0ui/vfLGNlVtKvS5HREQiTCFPJImcP6ovaX4fM3Q0T0Qk4SnkiSSRLtnpnD6iB88t2MDe8kqvyxERkQhSyBNJMpeOzWffgWqeX7DB61JERCSCFPJEksyIPp04sk8nnvighBpNpyIikrAU8kSS0KXj8li9bR/vrtzmdSkiIhIhCnkiSejUI3rQJTuN6e+v9boUERGJEIU8kSSUnuLnwlF9mb1iCyXb93ldjoiIRIBCnkiSumhMHn4zpr9f4nUpIiISAQp5Ikkqt0MGpx7Rg2fnr6e0osrrckREJMwU8kSS2OXj89lbUaXpVEREEpBCnkgSO6pvZ47s04nH31+r6VRERBKMQp5Ikrt8fD5rtu1j7udbvS5FRETCSCFPJMmdekQPcjuk85f31nhdioiIhJFCnkiSS/X7uHh0Hu98sY2VW/Z6XY6IiISJQp6IcOHovqSl+HhckyOLiCSMqIY8MzvHzJ43sxIzKzOzFWb2azNr30S/O8zMNfAqD2m7toF2Z0d040Ti2CHZ6Zw1oifPL9jI7v2VXpcjIiJhEO0jeTcD1cBPgJOBB4HrgDfMrLFaHgXGhrxOBKqAl+tp/1o97eeGZxNEEtPl4/tRVlnN0/PXeV2KiIiEQUqU13eGc67uLXxzzWwHMB0oBGbX18k5twH4xkReZjaVQP3T6+myzTlXHJaKRZLE0J4dGN0vh+nvl3DF+H5elyMiIm0U1SN5IQGv1kfB914t/LpLgc0EjtqJSBhcPr4fG3eV8cbSzV6XIiIibRQLN15MDL4va24HM+sNTAKedM7V9zymM8xsv5lVmFmxrscTaZ6ThubSJ6cdj72r6VREROKdOefdLPdm1gv4GFjknDupBf1uBX4FjHDOfRry2f0Ejg6uAXKB6wkEyanOuZmNfOc0YBpAbm7uyFmzZrVwa1qmtLSU7OzsiK4j2WhMw+ONtZU8ufwAN49wHN5D4xlO2kfDS+MZfhrT8IrWeE6aNGmBc64gdLlnIc/MsoEioCcwKnjdXXP7LgPKnHNHN6OtHygGujvn+jTn+wsKCtz8+fObW06rFBUVUVhYGNF1JBuNaXiUVlQx9tdvMaST45n/PtnrchKK9tHw0niGn8Y0vKI1nmZWb8jz5HStmWUQuCu2PzClhQFvFDCY+m+4OIhzrhp4FuhtZj1aUa5IUslOT+HCUX2Zv7maDTv3e12OiIi0UtRDnpmlAs8Do4BTnXOftfArLiUwdcrfWrLa4LuewC7SDJeOywdguiZHFhGJW9GeDNkHPAmcAJzV0mlOzCwNOB94pYE7devrkwKcC6xzzm1qYckiSalnp3aM6u5n1rz17C3X5MgiIvEo2kfyHiAQuH4H7DOzMXVevQHMLM/Mqszs9nr6nw7k0MCpWjO7wMxmmdklZjbJzM4H5gAjgR9HZItEEtSU/FT2VlTxzPxmX00hIiIxJNoh75Tg+23AByGvq4KfGeBvoLZLgR3APxv4/jVAN+C3wOvAQ0AFcLJzLrK3y4okmH4d/YzKz+Gv762hqrrG63JERKSFovrEC+dcfjParOXra+hCPzurib7FwPGtqU1EDnblsf24ZsYCXl+6mVOP0H1LIiLxJBYmQxaRGHXikFzyDsnk0XdWe12KiIi0kEKeiDTI7zOuGN+Phet2saBkp9fliIhICyjkiUijzi3oTafMVB6au8rrUkREpAUU8kSkUZlpKVwyJo83lm1m5ZZSr8sREZFmUsgTkSZdMi6fNL9P1+aJiMQRhTwRaVKX7HTOLejNCws3smVPudfliIhIMyjkiUizXDWhP1U1NfxVjzoTEYkLCnki0iz5XbI45fAezCwu0aPORETigEKeiDTbtOP6s7e8ilnz1ntdioiINEEhT0SabUSfToztfwiPvbuGA1V61JmISCxTyBORFrlmYn827Snn5UVfel2KiIg0QiFPRFpk4mFdGdy9PQ+/vYqaGud1OSIi0gCFPBFpETPjmon9+XxzKbOXb/G6HBERaYBCnoi02OnDe9K7czseKFqJczqaJyISixTyRKTFUv0+rpk4gI/X7eKDVdu9LkdEROqhkCcirXLuyN50a5/OH+es9LoUERGph0KeiLRKRqqfq4/tz/urtrNw3U6vyxERkRAKeSLSaheO7kunzFQemK2jeSIisUYhT0RaLSs9hSvG9+Ot5VtY8uVur8sREZE6FPJEpE0uHZtPdnoKf5qzyutSRESkDoU8EWmTjpmpTB2bxyuLv2LlllKvyxERkSCFPBFpsysn9CM9xceDRTqaJyISKxTyRKTNumSnc/4xfXnxk42s37Hf63JERASFPBEJk2sm9sdn8CcdzRMRiQkKeSISFj06tuP8Y/ry7Pz1OponIhIDFPJEJGy+N2kAPjP+qHnzREQ8p5AnImHTo2M7Lhzdl+cWbmDddh3NExHxkkKeiITVdYUDSPEZ98/+wutSRESSmkKeiIRVbocMLhzdlxc+3sjabfu8LkdEJGkp5IlI2F1XOIBUv/EHHc0TEfFMVEOemZ1jZs+bWYmZlZnZCjP7tZm1b0Zf18DryJB2PjO71czWmlm5mS0ys+9EbKNE5CDd2mdw8eg8Xvx4I6u36ikYIiJeiPaRvJuBauAnwMnAg8B1wBtm1pxaHgfGhrw+D2nzC+AO4I/AKUAx8KyZndr28kWkua6ZOID0FD9/eEtH80REvJAS5fWd4ZzbWuf3uWa2A5gOFAKzm+i/0TlX3NCHZtaNQJC82zn3u+DiOWY2ELgbeKXVlYtIi3Rtn84lY/N45J3VXH/8oQzslu11SSIiSSWqR/JCAl6tj4LvvcKwiilAGjAzZPlM4Agz6xeGdYhIM007rj8ZqX7ueyP0gLuIiERaLNx4MTH4vqwZba8zswoz229ms83s2JDPhwEVQOhMrEuC70PbUKeItNAh2elcNaEf//rsKz7dsMvrckREkoo557xbuVkv4GNgkXPupCbazgD+CXwJ5AE/JBDaTnLOFQXbPAyc6ZzrHtJ3IPAFcIlzbkYD3z8NmAaQm5s7ctasWW3YsqaVlpaSna3TV+GkMQ2vcI1nWZXjR3P306eDjx8d0y4MlcUv7aPhpfEMP41peEVrPCdNmrTAOVcQujza1+T9h5llAy8BVcDlTbV3zk2t8+s7ZvYSsBi4C5hQ+7VAfanVmvH9DwMPAxQUFLjCwsKmurRJUVERkV5HstGYhlc4x/PLjDX84p9L8fcaxrGHdg3Ld8Yj7aPhpfEMP41peHk9np6crjWzDOBloD8wxTm3oaXf4ZzbC/wLOKbO4h1AZzMLDXWd63wuIlF28Zi+9OrUjt+8uoKaGu/OHoiIJJOohzwzSwWeB0YBpzrnPmvL1/HNI3dLgHRgQEi72mvxlrZhXSLSSukpfm486TA+27ibVxZ/5XU5IiJJIdqTIfuAJ4ETgLMamw6lGd/VATgN+LDO4leBA8BFIc0vBhY759a0dn0i0jZnH9WLQbnt+d1rK6isrvG6HBGRhBftI3kPAOcCvwP2mdmYOq/eAGaWZ2ZVZnZ7bSczu9nMHjGzC82s0MwuBd4DugM/rW3nnNsC3AfcamY3Bts+CBxPYAJmEfGI32f86ORBrN2+n6c/Wu91OSIiCS/aN16cEny/Lfiq6+cEnlRhgJ9vBtAVwLeCr47AHgIh70rn3LyQ77kNKAVuIBACVwDnOef+EbatEJFWOX5wN47J78z/vfUF3z66F5lpnt37JSKS8KL6/7DOufxmtFlLyN2wwYDWrJDmnKsmcMftXS2vUEQiycz48cmDOefPH/CXd9dw/fGHel2SiEjCioXJkEUkiRTk5zB5aC4PFq1iy55yr8sREUlYCnkiEnU/OXUIB6pr+N3rK7wuRUQkYSnkiUjU5XfJ4vLx/Xh2wQYWb9ztdTkiIglJIU9EPHH98QPJyUzjzn8uxcvHK4qIJCqFPBHxRIeMVG6cfBjz1uzg1cWbvC5HRCThKOSJiGe+W9CHwd3b86t/L6O8strrckREEopCnoh4JsXv439OH8r6HWX89b21XpcjIpJQFPJExFPjB3bhxCG5PDBnJVv2akoVEZFwUcgTEc/ddtoQKqqq+e2rmlJFRCRcFPJExHP9umRxRXBKlflrd3hdjohIQlDIE5GY8F8nHErPjhn89MXFVFbXeF2OiEjcU8gTkZiQlZ7Cz84cxvJNe3lcN2GIiLSZQp6IxIzJQ3M5YXA37nvzc77cVeZ1OSIicU0hT0Rihplxx5nDqHGOO/+x1OtyRETimkKeiMSUPjmZ/L/jD+XVJZuYs3yL1+WIiMQthTwRiTlXH9ufAV2zuP3lxZQd0JMwRERaQyFPRGJOWoqPX5x9OOt3lPHHOV94XY6ISFxSyBORmDRuQBe+fXQvHpq7msUbd3tdjohI3FHIE5GYdfvpQ+mclcYPn/uUA1WaO09EpCUU8kQkZnXKTONX3zqCZV/t4U9FK70uR0QkrijkiUhMO2loLmcf2ZM/zl7J0i/3eF2OiEjcUMgTkZj3szOG0SkzjR8+t0iPPBMRaSaFPBGJeZ2z0rjr7MNZ8uUe/ly0yutyRETigkKeiMSFkw/vzhkjevKH2V+wfJNO24qINEUhT0Tixs/PHEaHjFRuemYRFVWaJFlEpDEKeSISN3Ky0rjnO8NZ8uUefvvqCq/LERGJaQp5IhJXThyayyVj83j03TUUrdCzbUVEGqKQJyJx5yenDmFQbntufnYRW/dWeF2OiEhMUsgTkbiTkern/guPYm95FTc9u4iaGud1SSIiMUchT0Ti0mG57fnp6UN5+/Ot/OW9NV6XIyISc6Ia8szsHDN73sxKzKzMzFaY2a/NrH0T/QrM7GEzW25m+81snZk9aWb96mm71sxcPa+zI7ZhIuKJi0f3ZfLQXO55dTmfbdjtdTkiIjEl2kfybgaqgZ8AJwMPAtcBb5hZY7WcDwwD/gCcAtwCHA3MN7M+9bR/DRgb8pobpm0QkRhhZtzzneEckpXO/3tqIbvLKr0uSUQkZqREeX1nOOe21vl9rpntAKYDhcDsBvrdE9IPM3sPWANcDdwe0n6bc644PCWLSCzrnJXG/RcexQUPF/ODpz/h0UsK8PnM67JERDwX1SN5oUEt6KPge6+W9HPOlQBbG+snIsnhmPwcfnbGUGYv38Lv3/rC63JERGJCLNx4MTH4vqwlncxsCNCtgX5nBK/dqzCzYl2PJ5L4Lh6Tx7kje/OHt77g9SWbvC5HRMRz5px3Uw+YWS/gY2CRc+6kFvRLAd4ChgCDnHM763x2P4Gjg2uAXOB6AkFyqnNuZiPfOQ2YBpCbmzty1qxZLd+gFigtLSU7Ozui60g2GtPwisfxPFDt+PWH5Xy1r4bbx7ajZ3Ys/B37tXgc01im8Qw/jWl4RWs8J02atMA5VxC63LOQZ2bZQBHQExjlnNvQgr5/Bq4ETnPOvd5EWz9QDHR3ztV3k8ZBCgoK3Pz585tbTqsUFRVRWFgY0XUkG41peMXreH65q4wz7n+XjpmpvPT98bTPSPW6pP+I1zGNVRrP8NOYhle0xtPM6g15nvyZa2YZwMtAf2BKCwPerwkccbuiqYAH4JyrBp4FeptZj1aWLCJxomendjxw0dGUbN/PD55eRLUmShaRJBX1kGdmqcDzwCjgVOfcZy3oexuB6VNucM7NaMlqg+/6f3uRJDCm/yHcfvpQ3ly2mV/8cyleXpYiIuKVqE6hEpwL70ngBAKnWps9zYmZ/RdwF3Cbc+7+FvRLAc4F1jnndDW2SJK4dFw+63bs57F319CrUzuuPq6/1yWJiERVtOfJe4BA4PolsM/MxtT5bINzboOZ5QGrgDudc3cCmNn5wO+BV4HZIf32OOeWBttdAJwFvAKsJ3DjxfeBkcAFkdwwEYk9t506hE27y/nlK8vI7ZjBmSN6el2SiEjURDvknRJ8vy34quvnwB0ETq36+eap5JODy08OvuqaS2AiZQjcUdsN+C2QA+wncKftyc6518KxASISP3w+497zRrBlbzk3P7OIbu3TGdP/EK/LEhGJiqiGPOdcfjParOXra+hql10GXNaMvsXA8a0qTkQSUkaqn0cuKeA7D77PtCfm89x14zgst9HHZYuIJITYmkRKRCQCOmWm8fjlo0hP9XPZX+axfsd+r0sSEYk4hTwRSQp9cjJ5/PJjKK2o4oJHitmwU0FPRBKbQp6IJI1hPTvy5FVj2F1WyQWPFPPlrjKvSxIRiRiFPBFJKkf07siMK0eza18g6G3aXe51SSIiEaGQJyJJ58g+nZh+5Si2lx7ggkeK2bxHQU9EEo9CnogkpaP7dmb6FcewZU+5Tt2KSEJSyBORpDUyL4fHrxjF1j0VfPtP77Ni016vSxIRCRuFPBFJasfk5/DMtWOpcY5z//w+H67e7nVJIiJhoZAnIklvSI8OvPC9cXRpn87Uv8zj1cV6zLWIxD+FPBERoHfnTJ6/dhzDenbge08uYEZxidcliYi0iUKeiEhQ56w0/nbVGCYN6sb/vLiYn720mMrqGq/LEhFpFYU8EZE62qX5eWjqSK6a0I/pH5Rw4SPFbNmrKVZEJP4o5ImIhEjx+/jp6UP5wwVHsXjjHk7/w7ssKNnpdVkiIi2ikCci0oAzR/Tkhe+NIyPVz/kPf8DM4hKcc16XJSLSLAp5IiKNGNKjA/+4fgLjB3bhpy8u5rqZC9mx74DXZYmINEkhT0SkCR0zU3ns0mO45ZTBvLV8M5Pve5u3lm32uiwRkUYp5ImINIPfZ1w7cQAvXz+BLtlpXDl9Prc8/ymlFVVelyYiUi+FPBGRFhjSowMvXT+eaycO4On56znl/95m7udbvS5LROQgCnkiIi2UnuLnllMG88w1Y0nx+bj0L/O4dsYCNuzc73VpIiL/oZAnItJKx+Tn8Op/H8sPpwyi6PMtnPi/c7n/rS8or6z2ujQREYU8EZG2SE/x8/1JA3nrpkImDerGvW98zpTfv82/Pv2KmhpNtyIi3lHIExEJg16d2vHgxSOZceUoUv0+vv+3hZx2/7u8sXSz5tYTEU8o5ImIhNGxh3bltf8+jvu+O4KyA1Vc/cR8zn7gPYpWbFHYE5GoSvG6ABGRROP3Gd86qjdnDO/JCws38n9vfcFlf/2IvA4+dnTYwOkjepCe4ve6TBFJcDqSJyISISl+H+cd04c5Nxdy97ePoLLGcdOzixh/9xx+/+bnbN1b4XWJIpLAdCRPRCTC0lJ8nD+qL7n7VpHS+3D++t5afv/mF/xpziomD8vlO0f35thDu5Di19/dIhI+CnkiIlFiZhx7aFeOPbQrq7eW8sQHJbz0yUb++elXdMlO46wje/Hto3sxtEcHzMzrckUkzinkiYh4oH/XbO44cxg/OXUIRSu28MLCjTzxwVoee3cN/btkceLQXE4amsvRfTvj9ynwiUjLKeSJiHgoLcXH5GHdmTysOzv3HeBfn33Fa0s28df31vDw26vJyUrj+MHdKBzUlTH9D6FLdrrXJYtInFDIExGJEZ2z0rh4TB4Xj8ljT3klb3++lTeWbub1JZt4bsEGAA7LzWZM/0MY2/8QjumXo9AnIg2Kasgzs3OAC4ACoBuwDngB+JVzbm8TfTOAXwAXA52AT4AfO+feDmnnA34MXAN0B1YAdzrnng/ntoiIRFKHjFROH96T04f3pKq6hs827uaD1dspXr2D5xZs4IkPSoDAJMwj+nRkeO9ODO/dkWE9O9KxXarH1YtILIj2kbybCQS7nwAbgKOAO4BJZjbOOVfTSN/HgNOAHwKrge8Dr5nZWOfcJ3Xa/SK4ntuABcD5wLNmdrpz7pXwbo6ISOSl+H0c1bczR/XtzPcKobK6hk837GJhyS4WbdjFpxt288pnm/7TvnuHDA7Nzeaw3PYclpvNwG7Z9M3Jokt2mm7oEEki0Q55Zzjnttb5fa6Z7QCmA4XA7Po6mdkI4ELgCufcX4PL5gJLgDuBM4PLuhEIeHc7534X7D7HzAYCdwMKeSIS91L9Pkbm5TAyL+c/y3buO8CnG3ez9Ms9fLF5L59v2cuTH5ZQXvn1386ZaX765mTSNyeTPjmZ9OiYQfeOGXTvEHjv1j6DtBRN4yKSKKIa8kICXq2Pgu+9Gul6JlAJPF3nu6rMbBZwi5mlO+cqgClAGjAzpP9M4C9m1s85t6bVGyAiEqM6Z6Ux8bCuTDys63+WVdc4Nuzcz6qtpazbvp+SHftZt30/a7bt4+0vtn4jANbq2C6VQ7LT6JKVTk5WGjnZaXRql0rHdql0CL53bJdKVnoK2en+4HsKWWkp+HQXsEhMiYUbLyYG35c10mYYsMY5tz9k+RICoW5g8OdhQAWwsp52AEMBhTwRSQp+n5F3SBZ5h2Qd9Jlzjj1lVXy1p4xNu8sDrz3l7Nh3gO37DrC9tILV20r5aO0BdpdVUlXT9HN301N8tEvz0y418MpI9ZOe6iM9xUdaij/47iPN7yPVb6T6fcGXkeL3keIz/L7Acr/P8Jvh8xl+C2yLr3ZZcPmKjZXs+ngjZuAz+/odCJyVDiwL/P718sCywAe1nwVaf632rLbVWfr1sroNm/ffwprZ0Ouz6ct3VJOxeru3RSSQ5TuqGVdV49kRck9Dnpn1InC69U3n3PxGmuYAO+tZvqPO57Xvu9zBTwEPbSciktTMjI6ZqXTMTGVw9w6NtnXOsf9ANbvLKv/z2ldRRWlFFfsqqv/zc3llNWWV1ZQd+Pr9QHUNFVU17C6r5EBVDRVV1VRW11BV7aisruFAVQ2V1Y7qGkdVTQ3NyJLf9NknrR4DacC8Yq8rSCjnTK707C54z0KemWUDLwFVwOVNNQfq+59+6N88zW1XXz3TgGkAubm5FBUVNdWlTUpLSyO+jmSjMQ0vjWf4JdKY+oGOwRcAqcFXs9Qe1fAf9EmNc9Q4qK6BGqDG1X05XHCZc1C6bz/tMjP/EwydC/wD4AgE09p/DGr/7K/9DPfNn+u8fUPdZQcdOmigT33q6xurysrKaNeunddlJIyysjI+mfc+KR5dyuBJyAtOh/Iy0B+Y6Jzb0ESXHUDfepZ3rvN57XtnM7OQo3mh7Q7inHsYeBigoKDAFRYWNlFS2xQVFRHpdSQbjWl4aTzDT2MaXhrP8NOYhpfX4xn1k8Rmlgo8D4wCTnXOfdaMbkuAfmaWGbJ8KHCAr6/BWwKkAwPqaQewtFVFi4iIiMSZqIa84ETFTwInAGc555p74v9lAicCzq3zXSnAd4HXg3fWArxKIPRdFNL/YmCx7qwVERGRZBHt07UPEAhqvwT2mdmYOp9tcM5tMLM8YBWBp1TcCeCc+8TMngZ+HzwSuAa4DuhHnUDnnNtiZvcBt5rZXmAhgSB4PHBW5DdPREREJDZEO+SdEny/Lfiq6+cEnn5hBK7GDT3KeDmBcHgXgceaLQJOds4tDGl3G1AK3MDXjzU7zzn3j7BsgYiIiEgciPZkyPnNaLOWeu6Gdc6VATcGX431ryYQBO9qVZEiIiIiCUDPrxERERFJQAp5IiIiIglIIU9EREQkASnkiYiIiCQghTwRERGRBKSQJyIiIpKAFPJEREREEpBCnoiIiEgCUsgTERERSUAKeSIiIiIJyJxzXtcQc8xsK1AS4dV0AbZFeB3JRmMaXhrP8NOYhpfGM/w0puEVrfHMc851DV2okOcRM5vvnCvwuo5EojENL41n+GlMw0vjGX4a0/Dyejx1ulZEREQkASnkiYiIiCQghTzvPOx1AQlIYxpeGs/w05iGl8Yz/DSm4eXpeOqaPBEREZEEpCN5IiIiIglIIU9EREQkASnkhZGZ9TGz58xst5ntMbMXzKxvM/tmmNlvzewrMyszsw/M7LhI1xzr2jimroHXkREuO2aZWW8zuz+4f+0Pjkd+M/tqH61HG8dU+2gIMzvHzJ43s5LgfrbCzH5tZu2b0Vf7aIg2jqf2z3qY2RQzm21mm8yswsw2mNkzZja0GX2juo/qmrwwMbNMYBFQAfwUcMBdQCYw3Dm3r4n+TwKnAT8EVgPfB04BxjrnPolc5bErDGPqgMeBh0I++tQ5tz/sBccBMysEngYWAH5gMtDPObe2GX21j9ajjWOqfTSEmRUD64CXgA3AUcAdwHJgnHOuppG+2kdDtHE8tX/Ww8wuAI4GPgS2An2BW4A+wBHOuQYfphD1fdQ5p1cYXsANQDUwsM6yfkAVcGMTfUcQCDCX11mWAqwAXvZ62+JxTINtHXCX19sRSy/AV+fnq4JjlN+MftpHwzymwfbaRw8ek671LLskOFbHN9JP+2gYxzPYTvtn88d5UHC8bmqkTdT3UZ2uDZ8zgWLn3MraBc65NcB7wFnN6FtJ4GhAbd8qYBYwxczSw19uXGjLmEo9XCN/tTdB+2gD2jCmUg/n3NZ6Fn8UfO/VSFfto/Vow3hKy2wPvlc20ibq+6hCXvgMAxbXs3wJ0NR5+mHAGnfw4e8lQBowsO3lxaW2jGmt64LXTOwPXkNxbPjKSyraRyNH+2jTJgbflzXSRvto8zVnPGtp/2yAmfnNLM3MDiVwSnsTgcDWkKjvowp54ZMD7Kxn+Q6gcxv61n6ejNoypgAzge8BJwLTgEOA2cFrqKRltI9GhvbRJphZL+BO4E3n3PxGmmofbYYWjCdo/2zKhwSuGf8cGE7g9PeWRtpHfR9NCfcXJrn67mKxZvSzNvRNdK0eF+fc1Dq/vmNmLxE4MngXMCEMtSUT7aMRoH20cWaWTeCGgSrg8qaao320US0cT+2fTZsKdAD6AzcDb5jZBNfwTVdR30d1JC98dlJ/Cu9M/cm9rh2N9K39PBm1ZUwP4pzbC/wLOKaNdSUj7aNRoH30a2aWAbxM4B/QKc65DU100T7aiFaM50G0f36Tc26Zc+5D59xTwAlANoG7bBsS9X1UIS98lhA43x5qKLC0GX37BacMCe17AFh5cJek0JYxbUhDf0lJ47SPRk/S76Nmlgo8D4wCTnXOfdaMbtpHG9DK8Wzw60jy/bM+zrldBPaxxq6ri/o+qpAXPi8DY8ysf+2C4ISo44OfNdU3FTi3Tt8U4LvA6865irBXGx/aMqYHMbMOBOYn+jBcBSYR7aNRoH0UzMwHPEngyMhZzrniZnbVPlqPNoxnfd+V9PtnQ8wsFxgMrGqkWdT3UV2TFz6PANcDL5lZ7cS9vwDWU2ciSTPLI7AT3OmcuxPAOfeJmT0N/D74F9ca4DoCc8JdFNWtiC2tHlMzu5nAvEVzgC+BPALXTHQnuccUMzsn+OPI4PspZrYV2Oqcm6t9tOVaM6baRxv0AIF/BH8J7DOzMXU+2+Cc26B9tEVaNZ7aPxtmZn8HFgKfAnuAw4AfELjW8d5gm9jYR72eQDCRXgRmvX4++B99L/AiIZOiAvkEwsodIcvbAf9L4BbscgJ/KRV6vU1ev1o7psAZBObT20ZgXqLtBP6KGuX1Nnn9Co5Vfa+ihsYzuFz7aBjHVPtog2O5tpHxvKOh8Qwu1z4apvHU/tnomP6YwBNudgH7CUxm/FDdf5tiZR/VY81EREREEpCuyRMRERFJQAp5IiIiIglIIU9EREQkASnkiYiIiCQghTwRERGRBKSQJyIiIpKAFPJEREREEpBCnoiIiEgCUsgTERERSUAKeSIiEWBmWWa23MzmBZ9TWbt8spnVmNn3vaxPRBKfHmsmIhIhZnYUUAzc55y7xcy6EXio+Tzn3JneViciiU4hT0QkgszsB8C9wGTgZuAIYIRzbpunhYlIwlPIExGJIDMz4F/A8UAacJJz7i1vqxKRZKBr8kREIsgF/pKeAaQDixTwRCRaFPJERCLIzLoDvwcWAiPM7AZvKxKRZKGQJyISIcFTtdOBA8BJBMLePWY23Mu6RCQ56Jo8EZEIMbObgN8Axzvn5ppZGoG7bdOBAudcmacFikhC05E8EZEICE6f8ivg1865uQDOuQPABUA+8L/eVSciyUBH8kREREQSkI7kiYiIiCQghTwRERGRBKSQJyIiIpKAFPJEREREEpBCnoiIiEgCUsgTERERSUAKeSIiIiIJSCFPREREJAH9fxzlpkvi2Q1uAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from matplotlib.pylab import *\n", "# rcdefaults()\n", "rcParams.update({'font.size': 16})\n", "figure(figsize=(10,7))\n", "xx=linspace(0,3,101)\n", "yy=func(xx)\n", "plot(xx,yy)\n", "xlabel('x')\n", "ylabel('u')\n", "grid();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exemple de résolution analytique d’un système d'équations différentielles d'ordre 1\n", "\n", "$$\n", " \\begin{pmatrix}\n", " y_1\\\\\n", " y_2\n", " \\end{pmatrix}'(t)\n", " =\n", " \\begin{pmatrix}\n", " \\varphi_1(t, y_1(t),y_2(t))\\\\\n", " \\varphi_2(t, y_1(t),y_2(t))\n", " \\end{pmatrix}\n", " =\n", " \\begin{pmatrix}\n", " y_1(t)-y_2(t)\\\\\n", " y_2(t)-y_1(t)\n", " \\end{pmatrix}.\n", "$$\n", "avec $t\\in[0;10]$ et en prenant comme condition initiale le vecteur $\\mathbf{y}_0=(2,1)$." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\frac{d}{d t} \\operatorname{y_{1}}{\\left(t \\right)} = \\operatorname{y_{1}}{\\left(t \\right)} - \\operatorname{y_{2}}{\\left(t \\right)}$" ], "text/plain": [ "d \n", "──(y₁(t)) = y₁(t) - y₂(t)\n", "dt " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\frac{d}{d t} \\operatorname{y_{2}}{\\left(t \\right)} = - \\operatorname{y_{1}}{\\left(t \\right)} + \\operatorname{y_{2}}{\\left(t \\right)}$" ], "text/plain": [ "d \n", "──(y₂(t)) = -y₁(t) + y₂(t)\n", "dt " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\left[ \\operatorname{y_{1}}{\\left(t \\right)} = C_{1} - C_{2} e^{2 t}, \\ \\operatorname{y_{2}}{\\left(t \\right)} = C_{1} + C_{2} e^{2 t}\\right]$" ], "text/plain": [ "⎡ 2⋅t 2⋅t⎤\n", "⎣y₁(t) = C₁ - C₂⋅ℯ , y₂(t) = C₁ + C₂⋅ℯ ⎦" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%reset -f\n", "%matplotlib inline\n", "\n", "import sympy as sym\n", "sym.init_printing()\n", "\n", "t = sym.Symbol('t')\n", "\n", "y1 = sym.Function('y1')\n", "y2 = sym.Function('y2')\n", "\n", "right1 = y1(t)-y2(t)\n", "right2 = y2(t)-y1(t)\n", "\n", "edo1 = sym.Eq( sym.diff(y1(t),t) , right1 )\n", "edo2 = sym.Eq( sym.diff(y2(t),t) , right2 )\n", "display(edo1)\n", "display(edo2)\n", "\n", "solgen = sym.dsolve([edo1,edo2],[y1(t),y2(t)])\n", "display(solgen)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\left\\{ C_{1} : \\frac{3}{2}, \\ C_{2} : - \\frac{1}{2}\\right\\}$" ], "text/plain": [ "{C₁: 3/2, C₂: -1/2}" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\operatorname{y_{1}}{\\left(t \\right)} = \\frac{e^{2 t}}{2} + \\frac{3}{2}$" ], "text/plain": [ " 2⋅t \n", " ℯ 3\n", "y₁(t) = ──── + ─\n", " 2 2" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\operatorname{y_{2}}{\\left(t \\right)} = \\frac{3}{2} - \\frac{e^{2 t}}{2}$" ], "text/plain": [ " 2⋅t\n", " 3 ℯ \n", "y₂(t) = ─ - ────\n", " 2 2 " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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/906OAlFZWLtPV64/cUf22mxNfn77i3z/hmdZvKQ+77AkSUXGJIhWytlnn02/fv0+Vgy1sd///vdcffXV/Pe//6VPnz7tG5wklZEnJ83g/lemcNyn1qNbJ2/2pvLQrVMVYw7ZllN2s2CqJGnV2GvSCs2fP5+nn36aBx54gHPOOYfrrruO3r17L9Vu8uTJnHbaaay33nrstttuAFRVVTF+/Pj2DlmSSt4f7nqVvt2qOXTksLxDkdpVRUXwnb03ZsNBPfju9c+w33ljueiIGjYc1DPv0CRJRcAkiFborrvuYt9992Xw4MGcc8457L///s22W2eddbw+V5Lawbg3pnH/K1M483Ob0r2zH+UqT/tuPZih/bpx7OWPs/+Yhzj3oG3YbZM18g5LktTBeTmMVmj06NGklJg8eTInn3xy3uFIUllLKfHbO19mUK/OHLajo0BU3rYZ2pdbT7FgqiSp5UyCSJJURO59eQrjJ87g65/e0DvCdFARsVFEnBMRz0TE3Ih4NyJujYitmml7b0SkZqZv5hB6UbJgqiRpZRRNEiQi1omIcyPi4YiYX+ggDG/SZvgyOhIpIvo0adslIn5T6JgsKOz3U+15TJIkrYz6+sRv7nyZof268eWaIXmHo2XbC9gNuAzYBzgJGAg8EhEjmmn/DLBjk+ma9gm1NFgwVZLUUsV0IfEGwJeBx4EHyDoYy/Ir4NYmy+Y0+fki4PPAd4E3gJOBOyNix5TSU60RsCRJremO597lhXdn84evbEV1ZdF8j1GOrgHOS42uy4iI/wFvAt8ADm/Sfk5KaVz7hVeaLJgqSWqJYupB3Z9SGpRS+hxw3QravpFSGtdkqmtYWRiOejDwrZTS31JKd5MlWCYBZ7dWwF6T2jI+T5K0Ykvq6vn9f15ho0E9GL3V4LzD0XKklKamJh9uKaVZwCuAL14b23frwVx73EjmL67jgDEPcc/LH+QdkiSpAymaJEhKqTUv7hwN1ALXNtr/ErJvbvaOiM6r+wuqq6tZsGDB6u6mLCxYsIDOnVf7KZekknbjE2/zxtR5nLbXxlRWRN7haCVFRD/gE8CLzazeJiJmRURtoY7I0e0cXslpKJg6pF83jr7UgqmSpI8UTRJkJf0qIpYUOhS3RsQWTdZvDkxIKc1vsvx5oBPZpTerZY011uDtt99m/vz5fug2I6VEbW0t06dPZ/LkyfTv3z/vkCSpw1qwuI4/3PUKW63Tm702G5R3OFo15wIB/LHJ8vuBb5J9QXMg8CpwYUSctawdRcRxETE+IsZPmTKlbaItAQ0FU/fcbBA/v/1FzrjRgqmSpOKqCdISi4Dzgf8AU4BNgB8AD0XE9imlhm9f+gEzmtl+eqP1S4mI44DjAIYOHbrcQHr16gXAO++8Q21t7UodRLmoqqqiS5cuDB06lC5duuQdjiR1WBePncC7sxbyx69sTYSjQNpbROwB/LcFTe9LKe3azPZnkF2Ge3RK6bXG61JKP2rS/JaIuAk4MyL+mFKa23R/KaULgAsAampq/KZlObp1quIvh4zg9/99hT/f8xpvTJ3HXw8dQb/unfIOTZKUk5JKgqSU3gVOaLTogYj4N9kIjzOBQwvLA2iu07DcnuXKdjp69er1YTJEkqRVMWXOIsbc8xp7bTaIHdZz1FxOHgI2bUG7piNMiYgTgF8CZ6WULm7h77sa2A/YAni4hdtoGZoWTN33vAe56Ijt2MiCqZJUlkoqCdKclNJbEfEgsF2jxdOB5oZy9G20XpKk3P3xrldYtKSe7392k7xDKVuFy2dfWtntIuIwYAzwu5TSL1Zm04ZfvbK/U8u279aDGdqvG8dd8TgHjHmIcw/eht02XiPvsCRJ7axUa4I01XTkx/PAuhHRrUm7zYDFwGtIkpSzV9+fwzWPvcWhI4ex3sAeeYejlRAR+wOXABemlL6zkpsfDCwAnm31wMrcNkP7csvJoxhqwVRJKlslnwSJiKHAKOCRRotvBaqBLzVqVwV8BfhPSmlRuwYpSVIz/u9fL9GtupKvf3rDvEPRSoiIT5Fd0vIMcGlEjGw0bdOo3Scj4vaIODoiPh0RB0TELWRFUn+aUpqX0yGUtIaCqXtttiY/v/1Fvn+DBVMlqZwU1eUwEXFg4eGIwvyzETEFmJJSui8ifkeW2HmYrDDqxsAZQD3Z9bgApJSeiohrgT9GRDUwATgRWBc4pF0ORpKk5Xjotanc/dIHfP+zm1jEsfjsDnQGtgHGNlk3ERheePwuWb/lbGAAUEuWODk4pXR1u0Raprp1qmLMIdt+WDB1wjQLpkpSuYhiGgIYEcsK9r6U0q4RcRRZMmMDoCcwFfgf2bcpLzfZV1fgF2RDTvsATwPfSynd25JYampq0vjx41flMCRJWq66+sQ+5z7IrAW13H3aLnSprsw7pBaLiMdTSjV5x1Eu7I+svlueepvvXv8Ma/bqwkVH1LChBVMlqegtrz9SVJfDpJRiGdOuhfUXp5S2Syn1TSlVpZTWTCkd3DQBUmi7IKX07UKbLimlHVqaAJEkqS1d/egkXnh3Nt//7CZFlQCRitG+Ww/m2uNGMn9xHfuPeYh7Xv4g75AkSW2oqJIgkiSVuhnzFvPb/7zMyPX68YUt18o7HKksbDO0L7eeYsFUSSoHJkEkSepAfvffl5mzcAk/Gb05EbHiDSS1ioaCqXtuNoif3/4iZ9xowVRJKkUmQSRJ6iCee3sWVz0yicNGDmOTNXvlHY5Udrp1quIvh4zglN024JrH3uKwix5h+rzFeYclSWpFJkEkSeoAUkr85Nbn6dutE9/ac6O8w5HKVkVF8J29N+aPX9maJ9+ayX7njeXV9+fkHZYkqZWYBJEkqQO4+am3GT9xBqd/ZmN6d63OOxyp7O23zWCuKRRMPcCCqZJUMkyCSJKUs9kLa/nVHS+x1Tq9+dKIIXmHI6lg20LB1CEWTJWkkmESRJKknP32zpeZMncRZ+/7CSoqLIYqdSQWTJWk0mISRJKkHD05aQZXjJvIETsOZ6shffIOR1IzGgqmnrzb+hZMlaQiZxJEkqSc1NbVc8aNzzKoZxdO28tiqFJHVlERfHfvTSyYKklFziSIJEk5ufjBCbz03hx+MnpzenaxGKpUDCyYKknFzSSIJEk5eGv6fP5w1yvsudkgPvOJNfMOR9JK2HZoX25pVDD1ogcnWDBVkoqESRBJktpZSomzbn6Oygh+OnrzvMORtAoG9+nKdSdkBVN/9s8X+MFNFkyVpGJgEkSSpHZ2y1PvcN8rU/j2Xhuzdp+ueYcjaRV175wVTD1ltw24+tGsYOoMC6ZKUodmEkSSpHb0weyF/PjW59lmaB++ttPwvMORtJoqKoLv7L3xhwVT97VgqiR1aCZBJElqJyklfnDTcyyoreM3B25FZUXkHZKkVtK0YOq9FkyVpA7JJIgkSe3klqfe4a4X3+c7e23EBmv0yDscSa2sccHUoyyYKkkdkkkQSZLawQdzProM5uid18s7HEltZHCfrlx/4kcFU8+40YKpktSRmASRJKmNpZQ408tgpLLRrdNHBVOveSwrmDrdgqmS1CGYBJEkqY3d9OTb/PcFL4ORyknTgqn7WTBVkjoEkyCSJLWht6bP50e3PE/NsL5eBiOVoaYFU++xYKok5cokiCRJbaSuPvHtfzxFAH/4ytZeBiOVqYaCqev068bRFkyVpFyZBJEkqY385d7XeOzNGZy93+YM6dct73Ak5Whwn65cf8KO7LFpVjD1BzdZMFWS8mASRJKkNvD0WzP5412vss9Wa7Pf1oPzDkdSB9C9cxV/PXQEJ++2Plc/mhVMnWHBVElqVyZBJElqZfMWLeGb1z7FGj078/P9PkGEl8FIylRUBN/dexP+8JWtsoKpY8by2gcWTJWk9mISRJKkVvaTW5/nzWnz+P1XtqZ31+q8w5HUAe2/zTpcc9xI5i2qY//zHuJeC6ZKUrswCSJJUiu6/vHJXPf4ZE7edQNGrtc/73AkdWCNC6YeZcFUSWoXJkEkSWolr74/hx/e/Bw7rNuPb+6xYd7hSCoCFkyVpPZlEkSSpFYwf/ESTvr7E3TvXMm5B21DVaUfsZJaxoKpktR+7KFJktQKfnzL87w2ZS5/+MrWrNGrS97hSCoyFkyVpPZhEkSSpNXUUAfk1N024JMbDsw7HHUAEfFmRKRmpv2aaXtsRLwUEYsi4uWIOCGHkNVBWDBVktpW0SRBImKdiDg3Ih6OiPmFjsTwZtr1jYgLI2JqRMyLiLsiYotm2nWJiN9ExLsRsaCw30+1y8FIkkrGc2/P4sybnmXkev34xh4b5R2OOpY7gR2bTPc1bhARxwLnAzcAnwGuA8ZExIntG6o6kqYFUy+2YKoktZqiSYIAGwBfBmYADzTXICICuJWsE3Eq8EWgGrgnItZp0vwi4FjgR8AXgHeBOyNi67YIXpJUeqbPW8zxVzxO/+6d+PPB21JZEXmHpI5lakppXJNpRsPKiKgCfgFckVI6M6V0T0rpLOBS4GcR4f2Vy1jjgqln//MFfnDTc9TWWTBVklZXMSVB7k8pDUopfY7sW5LmjAZ2Bg5LKV2dUvp3YVkFcHpDo4jYCjgY+FZK6W8ppbvJEiyTgLPb8iAkSaVhSV09p1z1BFPmLuKvh41gQI/OeYek4rMjMBC4ssnyK4D+ZH0albGPF0ydZMFUSWoFRZMESSm1JPU9GngnpXRPo+1mAbcB+zZpVwtc26jdEuAaYO+IsCcrSVqu//fvl3jo9Wn8Yr9PsOU6ffIORx3TPoVLeBdFxLhm6oFsXpg/12T584X5Zm0anYpC44KpT0yyYKokra6iSYK00OYs3ZGArDMxNCJ6NGo3IaU0v5l2ncguvZEkqVm3PPU2f3tgAkfsOIwv1QzJOxx1TLeRXZq7N3AIsBC4KSIObdSmX2E+o8m205us/5iIOC4ixkfE+ClTprRiyOrI9t9mHa4+diTzFi1h//Me4r5XfO0laVWUWhKkH0t3JOCjzkTfFraz0yFJatZTb83k9OufYfvh/TjrC35RXw4iYo9l3Oml6XRvwzYppVNTSpenlB5IKV0PfBoYD/yq8a4bmq9MPCmlC1JKNSmlmoEDvRtRORkxrC+3nLIz6/TrxpGXPMolYy2YKkkrq9SSIEHzHYmmlepa2u5j7HRIUnl7e+YCjrlsPGv06sxfDt2W6spS+xjVMjwEbNqC6fBl7SClVEdW02ydiFirsHhZX770a7Je+lDjgqk/vc2CqZK0sqryDqCVTaf5URwNI0BmNGo3dDnt7HRIkj5m7qIlHH3pYyyqrePqY3egv4VQy0bh8tmXWmFXTUd+NNT+2JzsLnUNGoYYvdAKv1MlqKFg6m//8zJj7n2dCVPn8pdDRtC3e6e8Q5OkDq/UvsJ6no+KjDW2GTAppTS3Ubt1I6JbM+0WA6+1XYiSpGJTV5/4+tVP8uoHcxlz6LZsOKhn3iGpyBRuh/slsv7Ie4XFDwNTyWqGNHYo2RcyY9svQhWbiorg9M9swu+/vBVPTLRgqiS1VKklQW4FBkfELg0LIqIXsE9hXeN21WSdkYZ2VcBXgP+klBa1T7iSpGLw89tf4H8vfcBPR2/OJzf0ckgtX0QcFBHXRMThEbFbRHwVuAcYAXyvoV1KqRb4IXBERPw8InaNiLOBo4AfpZS8F6pW6IBt1+Hq4yyYKkktVVSXw0TEgYWHIwrzz0bEFGBKSuk+suTGw8CVEfFdsstfziAbfvrrhv2klJ6KiGuBP0ZENTABOBFYl6W/jZEklbG/3f8Gl4x9k6NGrcuhI4flHY6KwwRgDeA3ZJfpzgceAz6TUrqzccOU0l8jIgGnAd8FJgGnpJTGtG/IKmYjhvXl5pNHcezlj3PkJY9y1uc348hRw4lYbrk7SSpLUUwVpQudhObcl1LatdCmH/BbYD+gC1lS5Nsppaeb7Ksr8AvgYKAP8DTwvZTSvS2JpaamJo0fP36lj0GSVDxufvJtvnntU3x+i7X400HbUFnhPxQrEhGPp5Rq8o6jXNgfUWPzFi3hW9c+xX9eeJ+Dth/K2ftubgFnSWVpef2RohoJklJaYe8zpTSdbBjpUStotwD4dmGSJOlj7n9lCt+57mlGrteP3315KxMgkjo8C6ZK0oqZGpYkqYlnJ8/ixCsfZ4M1enDB4TV0qa7MOyRJapGGgql/+MpWPDHJgqmS1JRJEEmSGnljylyOvPRR+nTrxGVHbU+vLtV5hyRJK23/bdbhmkYFU+99+YO8Q5KkDsEkiCRJBW9Nn88hFz5CSnDZUdszqFeXvEOSpFW27dC+3HLKzqzTrxtHXfoYFz84gWKqByhJbcEkiCRJwPuzF3LoRY8wb9ESLj96ezZYo0feIUnSahvcpyvXn7Aje2w6iLP/+QI/uOk5auvq8w5LknJjEkSSVPamzV3EIRc+wtQ5i7j0qO3ZfO3eeYckSa2moWDqSbuuz9WPTuKwix5hxrzFeYclSbkwCSJJKmuz5tdy2EWP8tb0+Vx4xHZsO7Rv3iFJUqtrKJj6+y9vxRMTLZgqqXyZBJEkla2Z8xdzyEXjeO2Dufz1sBHsuH7/vEOSpDZ1wLbrcHWjgqn3vTIl75AkqV2ZBJEklaUZ8xZz8N8e4ZX353L+YSPYbeM18g5JktrFiGEfFUw98pJHLZgqqayYBJEklZ1pcxdx0N/G8dqUufzt8Bp228QEiKTyYsFUSeXKJIgkqaxMmbOIg//2CBOmzuPiI7Zjl40G5h2SJOXCgqmSypFJEElS2Zg8Yz5fPv9hJk6fxyVf246dNxyQd0iSlCsLpkoqNyZBJEll4bUP5vClvz7MtLmLuPLoHdhpAxMgktTAgqmSyoVJEElSyXtm8ky+9NeHqa1LXHv8jtQM75d3SJLU4YwY1pebTx7F4L5dOfKSR7lkrAVTJZUekyCSpJL20GtTOeiCcXTvXMX1J+zIpmv1yjskSeqw1unbjRtO3IlPbzqIn95mwVRJpcckiCSpZN305GSOuORRBvftyvUn7MTwAd3zDkmSOrzunas4/9ARnFgomHr4RY9aMFVSyTAJIkkqOSkl/vy/V/nWtU9TM6wf152wE2v27pJ3WJJUNCoqgu8VCqY+PnGGBVMllQyTIJKkklJbV88ZNz7Lb//zCvtvM5jLjtqe3l2r8w5LkoqSBVMllRqTIJKkkjFrQS1HXfoY1zz2FqfstgG///JWdKryo06SVocFUyWVEnuGkqSS8MaUuex/3ljGvTGN/ztgC76z98ZERN5hSVJJsGCqpFJhEkSSVPTuf2UK+543lpkLarny6B346vZD8w5JkkpO04Kph130iAVTJRUdkyCSpKKVUuKiByfwtUseZXCfrtxy8ih2WK9/3mFJUslqXDD1iYkzCwVT5+YdliS1mEkQSVJRmrdoCV+/5il+9s8X2GPTQdxw4k4M6dct77AkqSx8rGDqmLHcb8FUSUXCJIgkqei89sFc9jtvLLc/8w6nf2Zj/nroCLp3rso7LEkqKx8WTO3Tla9d8iiXWjBVUhEwCSJJKiq3P/Mu+/75QabPW8wVR+/ASbtuQEWFBVAlKQ+NC6b+5LYXOPNmC6ZK6tj82kySVBQW1tbx89tf4Mpxk9hmaB/GHLIta/XumndYklT2Ggqm/uY/L/OXe19nwpR5jDlkW/p275R3aJK0FEeCSJI6vFffn8N+543lynGTOO5T63HtcTuaAJGkDqRxwdTHJ86wYKqkDsskiCSpw0opcc2jk9jnzw8yZc4iLj1yO37wuU3pVOXHlyR1RFnB1B0smCqpw7IXKUnqkKbOXcRxVzzO9298lpph/fjXNz7JrhuvkXdYkqQVGDGsnwVTJXVYJkEkSR3Onc+/x95/uJ/7XpnCWZ/flMuP2p41enXJOyxJUgs1FEzdfRMLpkrqWEyCSJI6jFkLajntH09z/BWPs2bvLvzz1J055pPrefcXFZWI+FpEpOVMazZqe+8y2nwzx0OQWkX3zlVccNgITthlfa56ZBJHXPwoM+cvzjssSWWu5O4OExG7Avc0s2pWSqlPo3Z9gd8A+wFdgYeBb6WUnm3zICVJS/nP8+9x1s3PMW3eYr6++wacsvuG1v5Qsbod2LHJsgBuA95IKb3XZN0zwPFNlr3ZNqFJ7auiIvj+ZzdhwzV6cMaNz7LfeWO58Ijt2GCNHnmHJqlMlVwSpJGvA481+nlJw4OICOBWYF3gVGAGcAZwT0RsnVKa3J6BSlI5mzJnET+57Xluf+ZdNlmzJxceUcOW6/TJOyxplaWUpgAfqwYZEZ8E+gM/bmaTOSmlce0Rm5SXL45Yh+EDunH8FY+z/5ixnHfwtnxqo4F5hyWpDJXyV2wvppTGNZrGN1o3GtgZOCyldHVK6d+FZRXA6XkEK0nlpr4+8Y/xb7HnH+7jv8+/z3f22ojbTt3ZBIhK1RHAYuCavAOR8mLBVEkdQSknQZZnNPBOSunDy2ZSSrPIhqnum1tUklQmXnpvNl8+/2FOv/4ZNhjYgzu+sTOn7L4h1ZXl+rGkUhYRXYEvAf9MKU1rpsk2ETErImoj4pmIOLqdQ5TajQVTJeWtlHubf4+IuoiYFhFXRcTQRus2B55rZpvngaER4UWKktQG5i5awi9uf4HP/+lBXp8yl18fuCX/OH5HNlijZ96hSW1pP6AXcFkz6+4Hvkn2Bc2BwKvAhRFx1rJ2FhHHRcT4iBg/ZcqUZTWTOqymBVMPv8iCqZLaT5TaELSI2AY4BLgPmA1sA/wAqAW2SSl9EBGvAE+klL7aZNtjgL8BQ1NKbzWz7+OA4wCGDh06YuLEiW16LJJUKurrEzc++Ta//vdLfDBnEQdtP4TT996Evt075R2aWllEPJ5Sqsk7jtYUEXsA/21B0/tSSrs2s/2/gW2BtVNKS5baaun2NwGfAQamlOYur21NTU0aP3788ppIHdoNj0/mjBufZe0+XSyYKqnVLK8/UnKFUVNKTwJPNlp0X0TcDzxKViz1LLIK7c1lf5Z7D8aU0gXABZB1OlolYEkqcY9PnMHZtz3P05NnsdWQPvz1sBFsO7Rv3mFJK+MhYNMWtJvfdEFErAXsAZzbkgRIwdVko0e2ILt7nVSyLJgqqb2VXBKkOSmlJwqjP7YrLJoO9GumaUOvfEa7BCZJJWzStPn89j8vc+vT7zCoV2d+/+Wt2G/rwVRULDffLHU4KaX5wEuruPmhQCXNXwqzLA1vEr9wUVloKJh6zGXj+dolj/KjL2zGETsNJ7uhoyS1rrJIghQ0Hv3xPLBXM202AyataOipJGnZps1dxLn/e42/PzKRyorglN024MRd16d753L6yJE+dDjwTErpqZXY5mBgAfBsm0QkdUANBVO/cc1T/OS2F3jlg7n8dPTmFsyW1OrKokcaETXARsA/CotuBY6MiF1SSvcV2vQC9gGuyidKSSpucxct4ZIHJ3D+/W8wf/ESvrLdEL65x0YM6tUl79CkXETEtsAngNOWsf6TwPeBG4E3gd5kt9IdDXw/pTSvfSKVOoaGgqm/vvNl/nrf67w5dR5jDtmWPt2sHyWp9ZRcEiQi/g5MAJ4AZpIVRj0DeBs4t9DsVrJrbK+MiO+SXf5yBtlokV+3c8iSVNTmL17C5Q9P5Pz7XmfG/Fr23GwQ3/vMxt7xRcoSGkuAvy9j/btkd+o7GxhAVsT9GeDglNLV7RKh1MFUVATf/+wmbLhGD8648Vn2O2+sBVMltaqSS4KQ3fr2IOBUoBvwHtk3LD9OKU0FSCnVR8QXgN8CY4AuZEmR3Zq7K4wkaWnzFy/hqkcm8df7Xmfq3MXsstFAvr3nRmw1pE/eoUkdQkrpG8A3lrP+NeCz7ReRVDwsmCqprZTcLXLbi7ekk1SuZi+s5fKH3uTisW8yfd5idlq/P6fttREjhjVXb1rlphRvkduR2R9RqZs8Yz7HXDaeV96fY8FUSS1WVrfIlSS1jSlzFnHZQ29y2cNvMmfhEnbdeCCn7LYBNcNNfkiS2oYFUyW1NpMgkqTleu2DuVz04Bvc8MTb1NbV85nN1+Tk3TbgE4N75x2aJKkMWDBVUmsyCSJJWkpKiYden8bFD07g7pc+oHNVBV8asQ5H77wu6w20OJ0kqX1ZMFVSazEJIkn60LxFS7jxybe5/KE3efWDufTr3olv7rEhh40cRv8enfMOT5JU5hoKph53uQVTJa0akyCSJF55fw5XPTKJG56YzJyFS9hicG9++6Wt+MKWa9GlujLv8CRJ+tCIYf245ZRRHHPZeI689DF+9IXNOHzHYRZMldQiJkEkqUwtrK3j9mfe5epHJzF+4gw6VVbwmU+syRE7DWfboX3sTEqSOqzGBVN/fOvzvPL+HH5iwVRJLWASRJLKSEqJJ9+ayXXjJ/PPp99hzqIlrDegO2d+blO+OGId+nW3yJwkqTg0LZg6wYKpklrAJIgklYG3Zy7g1qfe4frH3+L1KfPoUl3B5z6xFgfWrMOO6/V31IckqShZMFXSyjIJIkklaub8xdzx7Hvc/NTbPDphOgAjhvXl/w5Yj89vuRY9u1TnHKEkSa3DgqmSWsokiCSVkFkLavnvC+9z+zPv8OBrU6mtS6w/sDun7bkR+249mKH9u+UdoiRJbcKCqZJawiSIJBW5aXMXcfeLH/Dv59/jgVenUFuXGNynK0eOWpd9tlybTwzuZQdQklQW1unbjetP3IlvWjBV0jKYBJGkIjRx2jzuevED7nz+Pca/OZ36BIP7dOVrOw3n81uuzVbr9DbxIUkqSz06V3H+YSP49Z0vcf59b1gwVdLHmASRpCJQW1fPExNncPdLH3D3i+/z+pR5AGw8qCen7LYBe22+Jpuv7YgPSZIAKiuCMz67KRuu0ZMfFAqmXvS17Vh/oAVTpXJnEkSSOqjJM+Zz/ytTuf+VKYx9bSpzFi2hujIYuV5/DtlhGJ/edA2G9e+ed5iSJHVYB45Yh3ULBVP3O8+CqZJMgkhShzFrfi0PvzGVsa9NY+zrU3mjMNpj7d5d+MJWa7HLRgPZecOB9Ojsn25JklrKgqmSGrMnLUk5mbWglscmTGfcG9N4ZMJ0nntnFilBt06V7LBuPw7efii7bjyQ9Qf2sKMmSdJqsGCqpAYmQSSpnbw3ayGPvTmd8W9O57E3Z/Die7NJCTpVVbDNkD58ffcN2XnDAWy1Th86VdkpkySpNVkwVRKYBJGkNrF4ST0vvDubJyfN4IlJM3li4gzenrkAgK7VlWwzNEt67Lh+f7Ye0ocu1ZU5RyxJUumzYKokkyCStJrq6hNvTJnL05Nn8czkmTwzeRYvvDubxUvqAVirdxe2GdqHo3Zel+2G92XTtXo5/FaSpBwdOGIdhvfvxvFXZAVTxxyyLZ/c0IKpUjkwCSJJK2HRkjpefX8uL7w7m+ffnsVz78zmhXdms6C2DsjqeWwxuDdf22k4Ww/pwzZD+7BW7645Ry1JkpqqGd6Pm08exbGXj+drlzzGj/fZjMN3HJ53WJLamEkQSWpGSol3Zy3k5ffn8PJ7c3jp3dm8+O4cXp8ylyX1CcgSHpuv3YuvbDeEzdfuxVZD+rD+wB5UVljEVJKkYjCkX0PB1Cf50S1ZwdQf72PBVKmUmQSRVNbq6xPvzFrAax/M/XB69YO5vPL+HOYsXPJhuzV7dWHTtXry6U3XYNO1erHpWr1Yd0B3Ex6SJBW5rGBqzccKpp53sAVTpVJlEkRSWZg5fzETps7jzWnzmDBlHq9PnccbU+YxYepcFtbWf9iuf/dOrL9GD/bdem02XrMXGw/qycaDetK7W3WO0UuSpLZkwVSpfJgEkVQSltTV8+6shbw1Yz6Tpy9g0vT5TJw+n0nT5jFx+nxmzq/9sG1FwDp9u7H+wO7stH5/1hvYnQ3X6MkGa/SgX3e/9ZEkqVxZMFUqfSZBJBWFBYvreGfWAt6duZB3Zi5g8swFvD1jAW/PnM/bM7PlDbU6IPtGZ3Cfrgzr343PbbEW6/bvzvAB3Vl3QDeG9OtG5ypvSStJkpZmwVSptJkEkZSrlBIz5tfy/uyFvD97IR/MXsR7sxdm06xsenfWAmY0GskBEAGDenZhcN+ubDOkL6O36sqQvt1Yp283hvTrytp9ulrUTJIkrRILpkqlyySIpFZXX5+YvbCWqXMXM23uIqbNW8zUuYuYOmcRU+YuZsqcRUyZszCbz11EbV1aah/9u3diUK8urNm7C1sP7cPgPl1Zq3cX1urdlcF9urJm7y50qrIjIkmS2oYFU6XSZBJE0nLV1yfmLFzCzAWLmTm/lhnzP5rPmF/LjHmLmT5/MdPnLmbG/MVMm7eY6fMWU1e/dGKjIqBf904M7NmFgT07s8EaPRnYszODenVmUK8uDOrVmTV6dmGNXp29XEWSJOWuoWDqBgN7cOZNz7H/mIe48IgaC6ZKRcwkiFTi6uoTcxctYe6iJcxZWMuchR/NZy9cwuwFtcxeWMvsBR89nrXgo2n2glqayWcA2SUpvbpU0797J/p178SQft3Yekgf+vfoRL/unRnQoxP9u3dmQM9s3q97J28pK2m1RcS6wIXAusDNwA9SSgsL6x5NKW2fY3iSStCXaoaw7oDuHH/F4+x/3ljOs2CqVLRMgkgdyJK6ehbU1mXT4jrmL65j/uIlhXn2eN6ibN28xUuYt2gJ8xbXZfNF2XzuoiUfzucuyrZdkU6VFfTqWk2vrlX07lpNv+6dWHdAd3p1qaZvt2p6d+tEn67V9O5aTd/u1fTp1om+3TrRu2u1SQ1JeRgD3AiMA04F7o6Iz6SU5gBtej/riPg2sBtQA6wJ/DSl9JNltD0WOI0sWfMm8IeU0l+babcf8GNgU+B94G/Ar1JKK/4DLqndWDBVKg0rTIJExFdTSte0RzDtLSKGAH8A9gQCuAv4ZkppUq6BKVcpJRbX1bN4SWEqPF60pOm87sOfFxV+XlibzRfV1rOwMG9YvrCQ3FhYu/TPCxZnyxbX1a9UrF2qK+jRuYpunaro3rmK7p0q6d+jE8P6d6NH52xZzy5V9OxSTc/OVfTo0ujnwuNeXarpUu2lJ5KKyqCU0nmFx1+LiDPIEiF7AssYu9ZqjgVmk41AOWFZjQoJkPOBX5H1Lz4NjImISCn9pVG7vYEbgIuAbwPbAL8EegLfa5tDkLSqLJgqFb+WjAS5PCKOA05JKb3Q1gG1l4joBvwPWAQcQdZp+jlwT0RsmVKal2d8HVVKifqUXWJRn7JpSX2ivj5RV5+oS4n6elhSX099PdSlRF19PXWFZXUN7eqz7T6aZ23q6utZUp9YUvfR8tq6xJK6wvLCNrV19SypS9TWZ/MldfXU1hfa1SVq6xO1S+pZUl/P4ob1ddnj2iXZ42zKEh61hURHw7LW0Kmqgi5VFXSurqRLdQVdqirpUl1J1+pKenapYmDPznTrlP3cpTB165RNDe26d66ka6eqD9s1JDq6dqqkW6cqR2FIKledG/+QUvpVRNQCd5MlD9rS5iml+oioYhlJkMK6XwBXpJTOLCy+JyLWBn4WERemlBpuefV/wIMppeMatesBnBURf0gpvdeGxyJpFVgwVSpuLUmCjCAbdvpkRJwL/CSlNLdtw2oXxwLrARunlF4DiIhngFeB44Hft1cgC2vr+P4Nz5CA+pQlGlLiwyRDw7LG8/qU/aNeX0g61DfZpu7Dth9fX/fhso+SGR8mNlL2uCFJ0dC+IeFRV9imo6gIqKqsoLoisnllUFVRQVVl0Kkym1dXVlBVWUGnwuNunT5q16mqgurKCjpVZes6VVZQXZXNOzWeN3rcueqjZZ2rKuncaFmX6kq6VFXSuTprX2GCQpLayisRsWdK6b8NC1JKv42IeuC3bfmLU0otGbK3IzAQuLLJ8iuAI4GdyZIdQ4CtgeOaafdT4LPAJasTr6S20bhg6g9uetaCqVIRWWESJKX0LPDJiDgC+H/AQRHxnZTS1W0eXdsaDYxrSIAApJQmRMRYYF/aMQlSv3gex71yLIkKEpCigkQA8eHjbKqACOo/XFYBDY8btomKwuOsLRR+jgpSNKyvhMpsfYoKiMoPt2t4TEVl1i4CKiohKonCcqISKgqPKyqJiqpsfUUlVFZRUVGVPa6oJCqz9RUVlURldTavqqKisoqKymoqKqqoqKqiorITlY2WV1ZVUVXdmYqqKqoqq6mq7kRlIdFRWRFUV5hkkKRy0uTy3K821yal9PuIuLYdw1qWzQvz55osf74w3wy4Z1ntCv2R+YV2kjowC6ZKxafFhVFTSpdFxM1k16le0egSmeeXv2WHtTlwSzPLnwe+1J6BdKuuYrN1hwIJUj2kRvOGZfV1hccN6+oh1WUX8Xzs5+bW12U/19U1Wtdkqq/7qF2LvuTKQVRCRRVUVhcSMNWFx9VQWVWYd1rO48bzaqjs3GhZJ6gqzBuWV3VutK5z4efOHz2u6tJkWZdsuzA5I0ltoEWX56aU3m7HmJalX2E+o8ny6U3WL6tdw7J+zSyn8DwcBzB06NBVj1JSq7BgqlRcVuruMCmlWcDJEXEhcDkfv0RmTlsE2Ib60XynYzrQt7kN2qzT0akbHHZj6+1vdTVOpDROjtTXfXxZfR3ULyk8rv9oWSosr69vtL6Z5fVLoL62yc/NTHVLPt6+rvHj2kKb2o9+/vDxElg8/6PHdYsbTbUfn9fXrvh5aYmo+Cg5UtUlm6q7Lnte3a3JvCt06l543D07N6q7FZYV5p16ZAkbSSovrX55bkTsAfx3hQ3hvpTSriuz68J8RReRLq/dMjPqKaULgAsAampqOtCFqlL5smCqVDxalASJiGqyauUjG03DC6tPBr4aESemlG5tiyDbkJ2O5kRkoy6ozEY2lIOUPkqQLFkMdYs+/nhJYapblC1bsrCwfmG2vHZBo3YLoXZhYd3Cj36uXQALZ8Kc92DJgixBs2RBtq5u0crFW1H9UUKkc49Gj3s2Wlb4uXMv6NKr8Ljxz72zebm8xpKKWhtdnvsQ2W1pV2T+Su638YiPdxst79dkfdORIY31abReUhGwYKpUHFpyi9yHyBIgnYB64GngNuBBYCwwl+ze9tdHxNdTSn9tu3Bb1bKGmfal+REiKmURH13m0nnFzVtdfR3Uzs8SJYvnZfPa+YXHhfmHj+dmCZTFcwvL58Kiudl8/jRYNDv7edGclo1wqe4OXXp/fOraB7r0ga59s8dd+3586tY/a1fhrXUlta/WvDw3pTQfeKmVQ4SPan9szseTIA01Pl5opt3DDY0iYjjQrVE7SUXCgqlSx9eSkSBzye5xP5askGhzt449LSLeB34AFEsS5Hk+KkjW2GbY6VB7q6j8aKRGa6pdWEiSzM6SIgtnZ48XzoaFs7JpUaPHC2fCnHdhyouwYBYsmrWcnUeWIOnWf+mp+0DoPqAwDYTua2SPHXUiqRUUweW5DwNTgUOAuxotP5RsdMdYgJTSpIh4utDuwibtaoF/tUu0klrdl2qGMNyCqVKH1JK7w+zVwn3dT3av+2JxK/DbiFgvpfQGfPjNyyjg+3kGJrWa6i7Z1H3Aqm1fX5clRxbMgAUzYcH07PH86dmokwWF+fxpMHMSvPMkzJu67BEoXftCj0HQY43CvDD1XLMwrZXNWzsZJKkkdITLcyOipvA7Gy703ywiDiw8viOlND+lVBsRPwTGRMTbZImQ3YGjgFNTSosb7fIHwD8j4nzg6sLxnQWck1J6r62OQ1Lb2254P245eRTHXGbBVKkjiZRap7RFRHQF9kgp3dYqO2xjEdGd7NKeBWSdjQT8DOgJbLmiYms1NTVp/PjxbR6nVHRSyhIn86bC/Kkw9wOYNyWb5n4Ac98vPH4f5ryf1UVpqlNP6LU29FoLeq6dPe69Tjb1GpzNu/Rq/2OTtEIR8XhKqaYN9tvc5bljWfry3FOBNrs8NyIuBY5Yxup1U0pvNmp7PHAaMAyYBPwhpTSmmX0eQBb7JsD7ZKNCfpFSqltRPPZHpI5v7qIlfPOaJ7nrxQ84dORQC6ZK7WB5/ZFWS4IUo4gYCvwB2JOsIOrdwDcbd2CWxU6H1ApSyi7Tmft+dhnOnPdg9jvZ44/N38vuLtRY597QZwj0HpLN+wyDvsM+mnfpnc8xSWWuDZMg/+GjhMeyLs8lIk4nqxFSFveOtT8iFYe6+vRhwdRRG/S3YKrUxpbXH1mpW+SWmpTSJOCLecchla2IbERHl14wYMNlt6tbkiVKZk2G2ZOz+cy3YNZb2WU4bz4Ii5uUAejaD/qtC33Xzeb91oN+60P/9bO6JbHMG0FJ6oBK+PJcSWXAgqlSx1HWSRBJRaKyCnoPziZ2WHp9SlmtkpkTYcbEbD59AsyYAJMfg+dv+vhIki69of8G0H/DLPkyYEMYsHGWKKnyWxmpyD0N7Jt3EJLUHAumSvkzCSKp+EVAt37ZtPY2S69fsjgbMTL9dZj2ejaf+iq8+QA8c81H7SqqstEiAzeCgZvCGpvCoM2zZZX+uZSKQUppAVAU9ckklScLpkr5slcvqfRVdYIBG2RTU4vmwrTXYOorMOVlmPISfPAivHQ7pPqsTWWnbKTImp+AQZ/I5mtumSVdJEmSVtKQft244aSd+MbVT/KjW57n1ffn8qN9NrNgqtQOTIJIKm+de8DaW2dTY7ULs8TIBy/CB8/D+8/D6/fA01d/1Kb3EFhrq4+mtbfJbv8rSZK0Aj06V3HB4TX8+t8vcf79b/DG1LmMOXgEvbtV5x2aVNJMgkhSc6q7wFpbZlNj86bCe8/Ce8/Au8/Au09no0Yo3Gmr1zoweBtYe1tYZ7ssMdLZomeSJGlplRXBGZ/blA3WyAqm7jdmrAVTpTZmEkSSVkb3AbD+btnUYNGcLDHy9hPwzhPZ/MVCSYKoyOqKrLMdDBkJQ0dCn6HenUaSJH3IgqlS+zEJIkmrq3NPGLZTNjWYPx3efhzeejS7Q82z18P4i7N1PdfKkiHDRmXTwE2gwmuAJUkqZxZMldqHSRBJagvd+sGGe2YTQH1dVl9k0sMwaVw2PX9Ttq5rPxg+CoZ/CtbbBQZs5EgRSZLKkAVTpbZnEkSS2kNFZeGuMp+A7Y/Nls2YCG8++NHUcAlNz7Vg3V1gvV1h/d2h56DcwpYkSe3LgqlS2zIJIkl56Tssm7Y5JPt5+gSYcB+8cS+89l945pps+Zpbwgafhg32gCE7QKWdIEmSSpkFU6W2EymlvGMoSjU1NWn8+PF5hyGpVNXXZ3egef1ueO1ueOsRqF8CXXpnyZCNPpPNu/XLO1LpYyLi8ZRSTd5xlAv7I1Lpe+zN6Rx/xeMsqau3YKrUQsvrj5gEWUV2OiS1q4WzsxEir9wJr94J86Zkd54ZNgo2+Xw29Rmad5SSSZB2Zn9EKg9vTZ/PMZeN57Upcy2YKrWASZA2YKdDUm7q6+GdJ+HlO+Cl22HKi9nytbaCzfaFzfaD/uvnGqLKl0mQ9mV/RCofcxct4RtXP8ndL33AYSOHWTBVWg6TIG3AToekDmPa6/DSP7PCqpMfy5attVWWDPnEF7O6I1I7MQnSvuyPSOWlrj59WDB11Ab9LZgqLcPy+iOmDiWp2PVfH0Z9A465C775HOz1C6iohrt/CudsCRftDY9dCPOn5x2pJElaDQ0FU39z4JY8OmE6+48ZyxtT5uYdllRUTIJIUinpMwR2OgWOvRu+8Qx8+kewcBbcfhr8dkO4+mB48Z9QV5t3pJIkaRV9qWYIVx07kpkLatnvvLE8+OrUvEOSioZJEEkqVX2HwSdPg5MehhMehJEnwtvj4dpD4HebwL/PgPefzztKSZK0CrYb3o9bTh7FWr27csQlj3LFw2/mHZJUFEyCSFKpi4A1t4C9fg7fegEO/gcM2wke/Rv8ZSe4cA948u+weH7ekUqSpJUwpF83bjhpJ3bdaCA/vOV5fnjzc9TW1ecdltShmQSRpHJSWQUb7Q1fuQJOexn2/iUsmAm3nJSNDrnjdJj6at5RSpKkFurRuYoLDq/h+E+txxXjJvK1Sx5l1nwve5WWxSSIJJWr7v1hx5PhlMfga3fARnvB+IvhzzVwxf7w8r+z2/FKkqQOzYKpUsuZBJGkchcBw0fBFy+Eb78Au50JH7wIV38Fzt0WHrkAFs/LO0pJkrQCFkyVVswkiCTpIz3WgF1Oh28+CwdeDN0HwL++C3/YHP73c5j7Qd4RSpKk5bBgqrR8JkEkSUurrIZPfBGOuQuO+g8MGwX3/zZLhtz2TZjxZt4RSpKkZRjSrxvXn7gjuxQKpv7oludYYsFUCTAJIklakaE7wFf/Dqc+DlsfDE/9Hf60Ldx4PEx5Oe/oJElSM3p2qeZvh9dw3KfW4/KHJ/K1Sx6zYKqESRBJUkv1Xx/2OQe+8TTscAK8eCuctwNc9zWTIZIkdUCVFcEPCgVTH5kwzYKpEiZBJEkrq9fa8JlfZnVDdv4WvPIfGDMSbjwOpr2ed3SSJKkJC6ZKHzEJIklaNd0HwB4/hm8+AzueAi/cCn/eDm49FWa/k3d0kiSpEQumShmTIJKk1dN9AOz1s+wyme2Pg6euzmqG3PVTWDAz7+gkSVKBBVMlkyCSpNbScxB89v/g1PGw6T7w4O/hT1vDw2OgzkJskiR1BBZMVbkzCSJJal19h8MX/wbH3w9rbQV3ngFjdoRX/5t3ZNJqi4hvR8RtEfFuRKSI+EkzbdaKiF9FxPiImBURUyLi7oj4VDNtLy3sp+n0x/Y4HknlqaFg6q8tmKoyVHJJkIh4cxmdif2aaXtsRLwUEYsi4uWIOCGHkCWpNK21FRx2Mxx0LaR6+PuBcOWBMOWVvCOTVsexwBrAzctpMwL4CnALcCDwNWAhcG9EfKGZ9lOAHZtMf2i1iCVpGb5cM4S/H/NRwdSxr1kwVaWv5JIgBXeydGfivsYNIuJY4HzgBuAzwHXAmIg4sX1DlaQSFgEbfwZOGgd7/QLeegT+shPc9RNYPC/v6KRVsXlKaQfg1OW0eRDYKKX0s5TSf1NKtwP7Aq8CpzfTfnFKaVyTaWIbxC5JS9l+3Y8Kph5+sQVTVfpKNQkytZnOxIyGlRFRBfwCuCKldGZK6Z6U0lnApcDPIqI6p7glqTRVdYKdToFTn4AtvwwP/gHOGwkv3ZF3ZNJKSSmtsIJgSmlmSmlJk2VLgKeAwW0UmiStMgumqpyUahJkRXYEBgJXNll+BdAf2LndI5KkctBjIOw3Bo78F3TqDtccBFd9FWZNzjsyqU1FRCey/seLzaxeIyKmRsSSiHglIr4XEZXtHKKkMmfBVJWLUk2C7BMR8wu1PsY1Uw9k88L8uSbLny/MN2vT6CSp3A3bCU54APY8Gybcl40KeewiqPdbJ5WsnwDrAP+vyfKngNOALwOjyS7f/RXZJbvNiojjCkVXx0+ZMqVNgpVUniyYqnJQikmQ28iu090bOISsENlNEXFoozb9CvMZTbad3mT9x9jpkKRWVFkNo74BJz4Eg7eF278Nl30Bpr2ed2QqExGxxzKKqTed7l3N33Mw8H3gZymlBxqvSyn9MaV0bkrpfymlO1JKxwLnAEdHxIbN7S+ldEFKqSalVDNw4MDVCU2SmmXBVJWyDp0EWZXOSUrp1JTS5SmlB1JK1wOfBsaTfavy4a4bmq9MPHY6JKkN9FsXDr8FRv8Z3nsuK5w67i+OClF7eAjYtAXT4av6CyJiH7KaYxellH7cws2uLsxrVvX3StLqaiiYumbvLlnB1HHWa1ZpqMo7gBVo6JysyPxlrUgp1UXEdcD/i4i1Ukrv8vERH+82at4wAmQ6kqT2EwHbHgYb7gm3fQP+/X146XbY7y/QZ0je0alEpZTmAy+11f4j4tNkd5+7CTh+ZTYtzFfqyxpJam1D+nXjhhN34hvXPMUPb36OV9+fw4++sBlVlR36u3RpuTr02ZtSmp9SeqkF06QV7KppZ6Kh9sfmTdo11AJ5oTXilyStpJ5rwkHXwOhz4Z0ns1EhT10Fyf8FVVwiYkfgFuBu4NCW3FWmkYPJ+iyPtUVskrQymhZMPfJSC6aquHXoJEhrKNwO90vApJTSe4XFDwNTyWqGNHYo2SiQse0XoSTpYyJg28PhhAdh0Cfg5hPhuq/Bgpl5RyYRETURcSBwQGHRZhFxYGHqVmizCXA7WV/jN8CIiBjZMDXa17CIuD8iToqIvSJin4i4mKy22fkpJQvkSOoQGhdMHfdGVjB1wtR5eYclrZKOfjnMSomIg4B9gTuAt4BBwMnACOCghnYppdqI+CEwJiLeBu4CdgeOAk5NKS1u79glSU30Wxe+9k8Yew787+fwzhPwxYthyHZ5R6bydgpwRKOfv1SYANYF3gRGAn0L0z3N7KNhhOocsi9fvkfWZ0lkt9D9OjCmleOWpNX25ZohDO/fnROufJz9zhvLXw7Zlp02GJB3WNJKiVRCQ4wL3678kuwyl35ktUIeA36TUrqzmfbHk92WbhgwCfhDSqlFnY6ampo0fvz41gpdkrQ8bz0GNxwFs96G3c+CUd+EipIfzFiUIuLxlJIFPduJ/RFJeXhr+nyOvuwxXp8yj5+M3pzDRg7LOyTpY5bXHympHmRKaVxKafeU0qCUUnVKqXdKaY/mEiCF9uenlDZKKXVOKW3Y0gSIJKmdDdkOjn8ANt0H7v4p/P1AmG8Na0mS8tBQMHWXjQbyw5uf40e3PMeSOu/qpuJQUkkQSVIJ69oHvnQpfP738OYDcP4u8PYTeUclSVJZsmCqipVJEElS8YiA7Y6Go/4NJLh4bxh/iXePkSQpBxZMVTEyCSJJKj6DR8Bx98HwneGf34RbT4Uli/KOSpKksvTlmiH8/ZiRzFxQy37njeWh16bmHZK0TCZBJEnFqXt/OOR6+OR34Mkr4LLRMHdK3lFJklSWtl+3H7ecPIpBvTpz2MWPcuW4iXmHJDXLJIgkqXhVVMKnfwgHXgzvPg1/2w3eezbvqCRJKkuNC6aedfNz/NiCqeqATIJIkorfJ74IR/0L6uvgor3gxdvyjkiSpLLUUDD12E+uy2UWTFUHZBJEklQa1t4GjrsH1tgMrj0MHvau55Ik5aGyIjjz85vx6y9aMFUdj0kQSVLp6LkmfO2fsOkX4M4z4F/fz0aHSJKkdvfl7YZw5dE7WDBVHYpJEElSaanuCl+6DEaeBI/8Bf5xOCyen3dUkiSVpR3W62/BVHUoJkEkSaWnohI+8yv4zP/BS7fD5aNh/vS8o5IkqSxZMFUdiUkQSVLpGnkifPny7M4xl34e5ryXd0SSJJWlZgumLrBgqtqfSRBJUmnbbDQcch3MmJjdOWb6G3lHJElSWbJgqjoCkyCSpNK33q5wxG2waDZc/Bl4//m8I5IkqWw1FEydMW+xBVPV7kyCSJLKwzoj4Mh/Q1TAJZ+Dt5/IOyJJkspWVjB1Z9boacFUtS+TIJKk8rHGJnDUndClF1y+H0x+PO+IJEkqW0P7d+PGk3biUxsOsGCq2o1JEElSeek7DL52B3TrC1fsB289mndEkiSVrZ5dqrnwiO04ZmcLpqp9mASRJJWfPkOyREj3AXDF/jBpXN4RSZJUtiorgrO+YMFUtQ+TIJKk8tR7MHztdui5JlxxAEx6JO+IJEkqaxZMVXswCSJJKl+91v4oEfL3A+Gdp/KOSJKksmbBVLU1kyCSpPLWc0044lbo0ie7NOaDF/OOSJKksmbBVLUlkyCSJPVeB464BSo7weX7wrTX845IkqSyZsFUtRWTIJIkAfRbDw6/BeqXwGWjYeZbeUckSVJZayiY+v++uIUFU9VqTIJIktRgjU3gsJtg0Ry48gCYPz3viCRJKntf2W6oBVPVakyCSJLU2FpbwUFXwYw34eqvQu2CvCOSJKnsNS6YevjFj/L3RyyYqlVjEkSSpKaG7wwH/A3eehSuPwrqluQdkSRJZa+hYOonNxzAmTc9x09ufd6CqVppJkEkSWrO5vvB534DL98Bd5wGKeUdkSRJZa9xwdRLH3rTgqlaaSZBJElalu2PhU9+Bx6/FO7/Td7RSJIkLJiq1WMSRJKk5dn9LNjqILjnF/Ds9XlHI0mSCiyYqlVhEkSSpOWJgH3OgaE7wc0nwVuP5R2RJEkqsGCqVlbRJEEi4tsRcVtEvBsRKSJ+spy2x0bESxGxKCJejogTltFuv4h4MiIWRsTEiDgrIirb7CAkScWpqjN85UrotTZccxDMsINVrlraH4mIewvrm07fbKat/RFJWg0NBVN3tmCqWqBokiDAscAawM3LaxQRxwLnAzcAnwGuA8ZExIlN2u1daPMY8FngHOAs4JetHbgkqQR07w8H/wPqFme3zl04O++IlI8W9UcKngF2bDJd07iB/RFJah09u1Rz0RHbcbQFU7UCkYqk2n1EVKSU6iOiCqgFfppS+kmTNlXAO8C/UkpHNFp+MTAaWCulVFtY9iQwO6W0S6N2PyLreAxNKb23vHhqamrS+PHjW+fgJEnF44174covwvq7w0HXQIVf2DcWEY+nlGryjqOttKQ/Umh3L1CVUtp5BfuzPyJJrezaxyZx5k3PMbR/Ny4+YjuGD+ied0hqZ8vrjxTNSJCUUkvGM+0IDASubLL8CqA/sDNARAwBtl5Gu2qyb2IkSVraervCZ/8fvPofuPdXeUejdtbC/kiL2B+RpLbxle2GcuUxWcHUfS2YqiaKJgnSQpsX5s81Wf58Yb7Z8tqllCYA8xu1kyRpaTVHwzaHZrfNffG2vKNRx7VNRMyKiNqIeCYijm6y3v6IJLWRkRZM1TKUWhKkX2E+o8ny6U3WL6tdw7J+zSyXJCkTAZ/7HQweATedAFNezjsidTz3A98kuxz3QOBV4MKIOKtRm1Xqj0TEcRExPiLGT5kypfUilqQSY8FUNSeXJEhE7LGMiulNp3tXdteF+YoKnSyvXTSzrCFuOx2SpEx1F/jyFVDdFa45GBbOyjsiraQ27I+QUvpRSulvKaX7Ukq3pJS+SFZM9cyI6NEQQkPz5sJbzr4vSCnVpJRqBg4cuLKhSVJZsWCqmqrK6fc+BGzagnbzV3K/jUd8vNtoeb8m65uODGmsT6P1H5NSugC4ALJCZCsZmySp1PQeDF+6DC4fnY0I+epV2SgRFYu26o8sy9XAfsAWwMOsYn9EkrRyKiuCH35hMzYa1IMzb3qO/ceMtWBqGcslCZJSmg+81Aa7bqj9sTkfT4I0XFP7QjPtHm5oFBHDgW6N2kmStHzDR8Fev4B/fw8e/jPsdGreEamF2rA/sixNR37YH5GkdvSV7YYyrH93TrzycfY9byx/OXRbdlp/QN5hqZ2VWk2Qh4GpwCFNlh9K9m3KWICU0iTg6WW0qwX+1bZhSpJKyg7Hw6b7wF0/gbcezTsadVwHAwuAZ8H+iCTl4WMFUy+yYGo5yutymJUWETXAcD5K3GwWEQcWHt+RUpqfUqqNiB8CYyLibeAuYHfgKODUlNLiRrv8AfDPiDifbHjqNsBZwDkppffa/ogkSSUjAkb/Gc7/FFx3JJzwAHSzxnYpakl/JCI+CXwfuBF4E+gNHEFWJPX7KaV5jXZpf0SS2llDwdRTr36SM296jlffn8tZn9+UqspSGyOg5kRKxVHaIiIuJetANGfdlNKbjdoeD5wGDAMmAX9IKY1pZp8HAD8GNgHeBy4EfpFSqltRPDU1NWn8+PEreRSSpJL29hNw0V6wwafhoGvKsj5IRDyeUqrJO4620pL+SERsAJwLbAkMIBvV8Qxwbkrp6mb2aX9EknJQV5/45R0vctGDE/jkhgP488Hb0rtrdd5hqRUsrz9SNEmQjsZOhySpWY+cD/86Hfb6eVnWByn1JEhHY39EklbftY9N4sybnmNo/24WTC0Ry+uPON5HkqTWtP1xH9UHefuJvKORJEkr8JXthnLlMTswY95i9j1vLA+9PjXvkNSGTIJIktSaImD0udBjENx4LCyet+JtJElSriyYWj5MgkiS1Nq69oX9/wrTXoc7z8w7GkmS1AINBVN33nAAZ970HD+59XmW1NXnHZZamUkQSZLawrqfymqCPH4JvHR73tFIkqQW6NmlmouO2I6jd16XSx96kyMvfYxZC2rzDkutyCSIJEltZfezYM0t4NZTYc77eUcjSZJaoLIi+OEXNuP/fXELHn59GvuPGcubU728tVSYBJEkqa1UdYYvXpTVBbnlJPCObJIkFQ0LppYmkyCSJLWlgRtnt8t97S54/NK8o5EkSSvBgqmlxySIJEltbbtjshoh/zkLZk7KOxpJkrQShvbvxg0WTC0ZJkEkSWprETD6z9njW0/1shhJkopMLwumlgyTIJIktYe+w2DPs+GNe70sRpKkImTB1NJgEkSSpPYy4kgvi5EkqchZMLW4mQSRJKm9VFR4WYwkSSXAgqnFyySIJEntqfFlMU9ekXc0kiRpFVkwtTiZBJEkqb2NOBKG7gT/+SHMnZJ3NJIkaRU1LZh61GXjLZjawZkEkSSpvVVUwD5/hMXz4D9n5h2NJElaDY0Lpj702lQLpnZwJkEkScrDwI1h52/BM9fC6//LOxpJkrSaLJhaHEyCSJKUl0+eBv3Wh39+G2oX5B2NJElaTRZM7fhMgkiSlJfqLvCFP8CMCXD/b/KORpIktQILpnZsJkEkScrTervAVgfD2HPggxfzjkaSJLUCC6Z2XCZBJEnK214/h8494Y7vQkp5RyNJklpBQ8HU/zsgK5h6gAVTOwSTIJIk5a17f9j9h/DmA/D8TXlHI0mSWtFXt88Kpk63YGqHYBJEkqSOYMTXYM0t4T9nZbfOlSRJJcOCqR2HSRBJkjqCikr43G9g9tvwwO/yjkaSJLUyC6Z2DCZBJEnqKIaOhC2/Cg+dC9NezzsaSZLUyiyYmj+TIJIkdSR7/hQqO8OdP8g7EkmS1AYsmJovkyCSJHUkPdeEXU6HV/4Nr9yZdzSSJKmNfHX7oVxx9A5Mm7eY/cZYMLW9mASRJKmj2eEE6L8h3Hkm1DlEVpKkUrXj+v255eRRDOiRFUy96pFJeYdU8kyCSJLU0VR1gj3PhmmvwuOX5h2NJElqQ8P6d+fGQsHUH9z0LD+9zYKpbckkiCRJHdHGn4Xhn4R7fwULZ+UdjSRJakONC6ZeMjYrmDp7oaNB24JJEEmSOqII2OtnMH8aPPiHvKORJEltbOmCqQ8xcZoFU1tb0SRBIuLbEXFbRLwbESkifrKMdvcW1jedvtlM2/0i4smIWBgREyPirIiobOtjkSSpRdbeJrtl7sNjYKbXCHcELemPRMSuy+iLNEwjG7W9dBlt/tiexyVJ6jgaCqZOnbuIfc8by8OvT8s7pJJSNEkQ4FhgDeDmFrR9BtixyXRN4wYRsTdwA/AY8FngHOAs4JetFrEkSatr97OyUSF3/yzvSJRpSX/kCZbuh+wIvAC8R9b3aGxKM20d/iNJZaxxwdTDLnqEqx/1y5DWUpV3ACth85RSfURUASesoO2clNK4FbT5P+DBlNJxhZ/viYgewFkR8YeU0nurG7AkSautzxAYeRI8+HsYeSIM3jbviMrdCvsjKaXZwMf6IRExDNgU+F1Kqa7JJotb0G+RJJWZhoKpp171JGfc+CyvvD+HMz+3KVWVxTSWoeMpmmcvpdRq5XEjYgiwNXBlk1VXANVkI0MkSeoYdv4WdBsA//0RpJR3NGVtNfojhwEBXNaK4UiSSlxWMLWGo0ZZMLW1FE0SZCVtExGzIqI2Ip6JiKObrN+8MH+u8cKU0gRgPrBZewQpSVKLdOkFu5wObz4Ab9yTdzRaNYcDT6SUnmtm3RoRMTUilkTEKxHxPWuUSZIaVFVW8KN9NuNXFkxtFaWYBLkf+CYwGjgQeBW4MCLOatSmX2E+o5ntZzRa/zERcVxEjI+I8VOmTGm9iCVJWpERX4PeQ+Dusx0NUmQiYkdgQ5ofBfIUcBrwZbK+y33Ar4Dzl7M/+yOSVIYOsmBqq8glCRIRe6yganrDdO/K7jul9KOU0t9SSvellG5JKX2RrHjZmYWaH5ANRwVorhcZzSxr2PcFKaWalFLNwIEDVzY0SZJWXVVn2PX78M6T8NI/846mJLRlf6SJI4Ba4KqmK1JKf0wpnZtS+l9K6Y6U0rFkxdqPjogNm9uZ/RFJKl8WTF19eRVGfYisONiKzG+l33c1sB+wBfAwML2wvLkRH30arZckqePY8qsw9hz4389h489BhVdMrKY2749ERGeyUR63p5SmtnCzq8lGtdaQjWiVJOlDTQumvvr+XH7wuU0smNpCuSRBUkrzgZfa8Vc2HfnxfGG+OVlSJGsUMRzoRnYLO0mSOpbKKtjtTLjuCHj2Otjqq3lHVNTaqT8yGujLyhVEXd6IVUmSPiyY+ss7XuLisRN4fcpczj14G3p1qc47tA6vXFJFBwMLgGcBUkqTgKeBQ5q0O5RsuOq/2jU6SZJaatPRsNZWcM8vYcnivKPRih0BTANuX4ltDiZLgDzWJhFJkkpC44KpYy2Y2mJFkwSJiJqIOBA4oLBos4g4sDB1K7T5ZETcHhFHR8SnI+KAiLiF7FuYn6aUGp8RPwB2iYjzI2LXiPgWcBZwTkrpvfY8NkmSWqyiAnb/EcycCE9ennc0Zacl/ZFGbdcA9gauSiktdT/DiBgWEfdHxEkRsVdE7BMRFwOnAuenlF5v6+ORJBU/C6aunKJJggCnANcB1xZ+/lLh5+uANQrL3iU7prOBO4DLgYHAwSml/9d4ZymlO8juHjMSuBP4FvBL4PttehSSJK2uDT4NQ3eC+34DtQvzjqbctKQ/0uAQskuPl3UpzByyOmTfA24F/gFsDXwdOLk1g5YklbYd1+/PzSdZMLUlInmbvVVSU1OTxo8fn3cYkqRyNeF+uGwf+OxvYIfj8o7mQxHxeEqpJu84yoX9EUlSY7MX1nLqVU9y3ytTOGrUumVbMHV5/ZHyezYkSSoFwz+ZjQZ58A+wZFHe0UiSpA6goWDqUaPW5eKxEzj6svHMXrjUFZllzSSIJEnFKAJ2OR3mvANPXpl3NJIkqYOwYOrymQSRJKlYrbcrrLN9YTSId4qRJEkfsWBq80yCSJJUrCJg1+/BrLfg6avyjkaSJHUwDQVT+3fvZMHUApMgkiQVs/U/DYNHwAO/gzqv+ZUkSR83fEB3bjp5FKM2GMAZNz7L2be9wJK6+rzDyo1JEEmSilkE7PI9mDkJnr4m72gkSVIHZMHUj5gEkSSp2G24F6y1NTzwW6hbknc0kiSpA7JgasYkiCRJxS4CPvVdmPEmvHBz3tFIkqQOrNwLppoEkSSpFGz8ORiwEYz9I6SUdzSSJKkDK+eCqSZBJEkqBRUVsNPX4b1n4fX/5R2NJEnq4BoKpu5UZgVTTYJIklQqtvwy9FwrGw0iSZK0Ar26VHPxETUcOWp42RRMNQkiSVKpqOoMI0+CCffD20/kHY0kSSoCVZUV/HifzcumYKpJEEmSSsmIr0Hn3o4GkSRJK6VcCqaaBJEkqZR06QXbHQ0v3ArTXs87GkmSVETKoWCqSRBJkkrNDidAZSd46E95RyJJkopM04KpP73t+ZIqmGoSRJKkUtNzEGx9EDx1Ncx5P+9oJElSkWlcMPWSsW+WVMFUkyCSJJWinb4OdYth/MV5RyJJkopQQ8HUX+5fWgVTTYJIklSK+q8PG+0N4y+C2oV5RyNJkorUwTuUVsFUkyCSJJWqkSfCvCnw3PV5RyJJkopYKRVMNQkiSVKpWncXWGMzGPcXSCnvaCRJUhFrWjD17NteKMqCqSZBJEkqVRHZaJD3n4M3H8g7GkmSVOQaF0y9eOyEoiyYahJEkqRStsWXoFv/bDSIJEnSair2gqkmQSRJKmXVXaHmKHj5XzDt9byjkSRJJaJpwdRxbxRHwVSTIJIklbqao6GiCh69IO9IJElSCWlcMPXQCx/hmiIomGoSRJKkUtdrLfjEAfDklbBwVt7RSJKkEtK4YOr3i6BgqkkQSZLKwcgTYfFcePLveUciSZJKTDEVTDUJIklSOVh7GxhcA+Mv9na5kiSp1RVLwVSTIJIklYvtjoFpr8KE+/OORJIklaiDdxjK5Udv32ELppoEkSSpXGy+P3TtC+MvyjsSSZJUwnZaf0CHLZhqEkSSpHJR3QW2ORRe/CfMfjfvaCRJUglrrmBqXX3+l+QWRRIkIjaKiHMi4pmImBsR70bErRGx1TLaHxsRL0XEooh4OSJOWEa7/SLiyYhYGBETI+KsiKhs26ORJClHI46EVAdPXJ53JEXH/ogkSStn6YKpj+VeMLUokiDAXsBuwGXAPsBJwEDgkYgY0bhhRBwLnA/cAHwGuA4YExEnNmm3d6HNY8BngXOAs4BftumRSJKUp/7rw/qfhscvhboleUdTbOyPSJK0khoXTH3w1fwLpkYqggrxETEAmJYaBRsRvYE3gdtSSocXllUB7wD/Sikd0ajtxcBoYK2UUm1h2ZPA7JTSLo3a/Yis4zE0pfTe8mKqqalJ48ePb6UjlCSpHb10O1xzMHzlSth0n1bddUQ8nlKqadWddhD2RyRJWj0PvT6Vk/7+BAH85dARjFyvf5v8nuX1R4piJEhKaWpqkq1JKc0CXgEGN1q8I9k3Mlc22cUVQH9gZ4CIGAJsvYx21WTfxEiSVJo23Bt6DYbHLsw7kqJif0SSpNXTUDC1X44FU4siCdKciOgHfAJ4sdHizQvz55o0f74w32x57VJKE4D5jdpJklR6Kquy2iBv3AtTX8s7mqJmf0SSpJWTd8HUok2CAOcCAfyx0bJ+hfmMJm2nN1m/rHYNy/o1s5yIOC4ixkfE+ClTpqx0wJIkdRjbHg4VVfDEpXlHUuzsj0iStJKaFky9uh1HhOSSBImIPSIitWC6dxnbnwEcDJySUmr8FVYU5itKIy2vXTSzLGuc0gUppZqUUs3AgQNX8CskSerAeg6Cg66FT52edyS5sT8iSVJ+Ggqm/u3wGr663ZD2+73t9ps+7iFg0xa0m990QeH2cr8EzkopXdxkdeNvWN5ttLxfk/VNv4lprE+j9ZIkla4N98g7grzZH5EkKWd7bjaoXX9fLkmQlNJ84KWV3S4iDgPGAL9LKf2imSYN19puzsc7HQ3X1L7QTLuHG+1/ONCtUTtJklSi7I9IklR+iqYmSETsD1wCXJhS+s4ymj0MTAUOabL8ULJvU8YCpJQmAU8vo10t8K9WCluSJJUQ+yOSJBW3vC6HWSkR8SngauAZ4NKIGNlo9aKU0pMAKaXaiPghMCYi3gbuAnYHjgJOTSktbrTdD4B/RsT5hX1vA5wFnJNSeq/ND0qSJBUV+yOSJBW/okiCkHUcOpN1DMY2WTcRGN7wQ0rprxGRgNOA7wKTyAqWjWm8UUrpjog4EPgx8DXgfbJre5sb1ipJkmR/RJKkIhcptd/9eEtJTU1NGj9+fN5hSJLUoUTE4ymlmrzjKBf2RyRJWtry+iNFUxNEkiRJkiRpdZgEkSRJkiRJZcEkiCRJkiRJKgsmQSRJkiRJUlkwCSJJkiRJksqCSRBJkiRJklQWTIJIkiRJkqSyYBJEkiRJkiSVBZMgkiRJkiSpLJgEkSRJkiRJZSFSSnnHUJQiYgowsZV3OwCY2sr7LHY+J0vzOVmaz8nSfE6a5/OytNZ+ToallAa24v60HK3QHym194TH03GV0rFAaR1PKR0LlNbxlNKxQPsezzL7IyZBOpCIGJ9Sqsk7jo7E52RpPidL8zlZms9J83xeluZzUt5K7fX3eDquUjoWKK3jKaVjgdI6nlI6Fug4x+PlMJIkSZIkqSyYBJEkSZIkSWXBJEjHckHeAXRAPidL8zlZms/J0nxOmufzsjSfk/JWaq+/x9NxldKxQGkdTykdC5TW8ZTSsUAHOR5rgkiSJEmSpLLgSBBJkiRJklQWTIJIkiRJkqSyYBKkjUXEkIi4PiJmRcTsiLgxIoa2cNsuEfGbiHg3IhZExMMR8am2jrmtreZzkpYxbd3GYbepiFgnIs4tvMbzC8c0vIXblup5sjrPSameJwdGxA0RMbHwWr8cEb+KiJ4t2LZUz5PVeU5K9TzZOyL+FxHvRcSiiJgcEf+IiM1asG1Jnif6uNX5HM5TS97vETF8Oe/tPjmGv5SI2HUZcc5s0q5vRFwYEVMjYl5E3BURW+QUdrMi4t7lPO//LrTpkK9NS/sbLX0d8v472pLjiYhPR8SVEfF6IcbXI+IvEbFGM/vL7bOyhcfS4vOqSF6bS5dzPC81aZvna9Oi/ldHfd9UtdWOBRHRDfgfsAg4AkjAz4F7ImLLlNK8FeziIuDzwHeBN4CTgTsjYseU0lNtFngbaoXnBOBS4Pwmy15pzThzsAHwZeBx4AFgr5XYtuTOk4LVeU6gNM+T7wCTgB8Ak4FtgJ8Au0XETiml+uVsW6rnyeo8J1Ca50k/svfNGGAKMBT4PjAuIrZIKU1czralep6ooJU+h/OyMu/3XwG3Ntl+TnsEuQq+DjzW6OclDQ8iIsiOY13gVGAGcAbZ67V1Smlyewa6HCcBvZos2xH4PUu/Dh3ttVlhf2MlX4e8/462pP90AtCD7L3/BrAh8FNg78LfgblN2l9KPp+VK9MXbMl5VQyvzc+AvzZZNhy4mqWPD/J7bVb497hDv29SSk5tNAHfAOqADRotW5fsw+3bK9h2K7KOyZGNllUBLwO35n1seTwnhbYJ+Hnex9EGz0tFo8fHFI5zeAu2K8nzZHWekxI/TwY2s+zwwvHuXqbnySo9J6V8nizjWDcuHO9p5XieOH3sdV6tz+GcY1/h+53sn4UEHJN3vC04nl0Lse6xnDb7Ftrs1mhZb2A68Ke8j2EFx3cRWbKtX0d+bVrS32jp69AR/o628Hiaey99qtD2qCbLc/usbOGxtOi8KpbXZhnb/bDQdvMO9Nq05O9xh33feDlM2xoNjEspvdawIKU0ARhLdlKsaNta4NpG2y4BriHL0nZu/XDbxeo8JyUrrfjb6mUp1fNkdZ6TkpVSmtLM4oZvDwcvZ9NSPk9W9TkpN9MK89rltCnZ80QfU7Sfw2X6fh8NvJNSuqdhQUppFnAbHfj1ioiuwJeA21JK0/OOZ3la2N9o6euQ+9/RlhxPsbyXWrkvWBSvzTIcDjyeUnq+NeNZHS08hzrs+8YkSNvaHHiumeXPAyu6NntzYEJKaX4z23YiG05VjFbnOWlwYmTXuc+P7Lr3T7ZeeEWnVM+T1lAu58kuhfmLy2lTbudJS56TBiV7nkREZUR0iogNyYbKvkfWoViWcjtPylVrfA53JMt6v/8qIpZEVvfk1uauQe9A/h4RdRExLSKuio/XZ1ne6zU0Inq0T4gr7QCgJ3BZM+uK6bVp0NLXoZj/ji7vs7MYPitXdF4V5WsTEaPIYmvuvQQd67Vpeg512PeNSZC21Y/s2qempgN9V2PbhvXFaHWeE4Arya473QM4DugP/C8idm2l+IpNqZ4nq6sszpOIGAycDdyVUhq/nKZlc56sxHMCpX+ePEI2FP0VYEuy4akfLKd92ZwnZW51P4c7jGW83xeRJf2OB3Yju259C+ChiNg0l0CXbRbwO7Jh8buT1QLYA3g4PipQuaL3ZUd9zQ4HPgD+1WhZMb02TbX0dSjKv6OFYpZ/JPvn9eYmqzv6Z2VLz6uifG3I3ku1ZDVBmuowr80y/h532PeNhVHbXmpmWbRgu1iNbTu6VT6ulNJhjX58ICJuIcsw/hzYuRViKzalfJ6ssnI4TwrZ81vIruM/ckXNKYPzZCWfk3I4Tw4jK1S4Hlmn8L8RsXNK6c1ltC+L80RACbzOy3q/p5TeJSv62OCByO5O8jxwJnBoe8a5PCmlJ4EnGy26LyLuBx4lK5Z6FkX4voyItcn+KTunMKQdKK7XphktfR2K8fWqIvsHezAwqvFrBh3/s3IlzqtifG06kxVS/WdKaWrT9R3ltVlO/6vDvm8cCdK2ZtB85qovzWe7Gpu+nG0b1hej1XlOlpJSmgPcDmy3mnEVq1I9T1pVqZ0nEdGFrNr2esDeacV3Byj582QVnpOllNp5klJ6MaX0SErpauDTZHcC+P5yNin580RAK38O52Fl3+8ppbeABymC93ZK6Qmy0VsNsa7ofdkRX7NDyf7HWNbw/Q8V0WvT0tehqP6ORkTD67QHsF9K6ZkVbVMMn5XLOK+K6rUp2BfoQwveS5DPa7OCv8cd9n1jEqRtPU92jVNTmwEvtGDbdQu3smu67WLgtaU3KQqr85wsy7Kyh+WgVM+TtlAS50lEVAM3ANsDn0spPduCzUr6PFnF52SZu6MEzpOmUkozyV7n5V1XW9LniT7UFp/D7WY13u/F9N5uHOvyXq9JaelbmXYEhwNPp5SebmH7YnhtWvo6FNvf0b8CXwG+mlK6eyW2K4bXrGmMxfbaQHYb86nAHSuxTbu9Ni34e9xh3zcmQdrWrcDIiFivYUFEDAdG0fx9nptuW01WWbth2yqyP1T/SSktavVo28fqPCdLiYheZPeUfqS1AiwypXqetKpSOU8K39j8nexb/X1TSuNauGnJnier8Zw0t6+SOE+aExGDgE2A15fTrGTPE31Mq34Ot6dVfb8XCo2Oogje2xFRA2zER7HeCgyOiF0atekF7EMHfL0K8W9OC7+5LqLXpqWvQ9H8HY2Ihno0R6aUbl6J7Tr8Z+UyzquieW3gw8/tvYCrUkrLu7Nb423a7bVp4d/jDvu+sSZI2/obcApwS0ScRZaV+xnwFlkBHwAiYhhZx/TslNLZACmlpyLiWuCPhSzbBOBEYF3gkHY9ita1ys9JRHwH2Bi4B3gHGEZ2nfuaFPdzAkBEHFh4OKIw/2xETAGmpJTuK7PzBFi156TEz5PzyD4gfgHMi4iRjdZNTilNLsPzZJWek1I+TyLiJuAJ4BlgNtk/VN8iu1b3d4U25Xae6CMt+hzuoFryfv8d2Zd8DwNTyN7nZwD1wC/bOd7lioi/k73PngBmAtuQxfo2cG6h2a1kx3JlRHyXbPj4GWTf9v66nUNuicPJ/tZc1XRFR35tVtTfoIWvQ0f5O9qC/tP3gG8DFwOvNnkvTUkpvV7YT+6flS04lhadV8Xy2jRqegjZ/+rNJhQ7wGuzwr/HdOT3TUrJqQ0nYCjZMKHZwByyisvDm7QZTtYJ+UmT5V2B35Pd1nAhWVZv17yPKa/nhCxrOJZsWFgtMI3szbV93sfUSs9LWsZ0bzmeJ6v6nJTyeQK8uZzn5CfleJ6s6nNS4ufJ94DHyf6pmg+8TPbP7fBGbcrqPHFa6hxZ4edwR5xa+H4/CniMrLO9pHAuXwVsnHf8zRzPGWTJylmFv0NvARcAazVp14/sn9Xphff03cBWecffzPFUk/0Tetsy1nfY12Y559W9K/s6dIS/oys6HuDe5bS5tNF+cv+sbMGxtPi8KobXplG7p4Fnl7OfXF8bWvD3OHXg900UfqkkSZIkSVJJsyaIJEmSJEkqCyZBJEmSJElSWTAJIkmSJEmSyoJJEEmSJEmSVBZMgkiSJEmSpLJgEkSSJEmSJJUFkyCSJEmSJKksmASRVNQioldE/CQiNs07FkmSJEkdm0kQScWuBvgxUJ13IJIkqbRFxH8j4uFmlm8REbURcXAecUlqOZMgkordNsAi4IW8A5EkSSXvQWDbiOjcsCAiAhgDPJRSuiq3yCS1SFXeAUjSqoqIF4FNCj/WZn0QbkgpHZhfVJIkqYSNBTqRfQkzrrDscGAksG1eQUlqOUeCSCpmhwNvALcBOxam03KNSJIklbJxQB1Z0oOI6AP8GvhzSunZwrIfRMTLEVEfEfvlFaik5pkEkVTMngbWAf6XUhpXmCbmHZQkSSpNKaW5ZP2PkYVFvwDqyeqTNbgb+Bxwf/tGJ6klvBxGUjHbnGxI6hN5ByJJksrGWGB0RGwLnAAckVKa3bAypfQIQOEyXUkdjCNBJBWzbYEEPJVzHJIkqXw8CAwDLgfGppSuzDkeSSvBkSCSitk2wOuNv32RJElqY2ML802wGKpUdEyCSCpmm+GtcSVJUvuaCywG/pJSeibvYCStHJMgkorZTGDbiNgbmAW8mlKalm9IkiSpxP0ImM7Hi6FKKhKRUso7BklaJRHxCeAiYEugC/DJlNKD+UYlSZJKTUR0A7YCPgn8EvhSSummZbQ9i6xg6kBgDrAQqEkpvddO4UpaDpMgkiRJkrQcETEauAV4G/hVSum8nEOStIpMgkiSJEmSpLLgLXIlSZIkSVJZMAkiSZIkSZLKgkkQSZIkSZJUFkyCSJIkSZKksmASRJIkSZIklQWTIJIkSZIkqSyYBJEkSZIkSWXh/wMdGaLQSmlxCQAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "t0 = 0\n", "y1_0 = 2\n", "y2_0 = 1\n", "consts = sym.solve( [sym.Eq( y1_0, solgen[0].rhs.subs(t,t0)) , \n", " sym.Eq( y2_0, solgen[1].rhs.subs(t,t0)) ] , dict=True)[0]\n", "display(consts)\n", "\n", "solpar_1 = solgen[0].subs(consts)\n", "solpar_2 = solgen[1].subs(consts)\n", "display(solpar_1)\n", "display(solpar_2)\n", "\n", "func_1 = sym.lambdify(t,solpar_1.rhs,'numpy')\n", "func_2 = sym.lambdify(t,solpar_2.rhs,'numpy')\n", "\n", "from matplotlib.pylab import *\n", "# rcdefaults()\n", "rcParams.update({'font.size': 16})\n", "figure(figsize=(18,7))\n", "\n", "tt = linspace(0,3,101)\n", "yy_1 = func_1(tt)\n", "yy_2 = func_2(tt)\n", "\n", "subplot(1,2,1)\n", "plot(tt,yy_1,tt,yy_2)\n", "legend([r'$y_1$',r'$y_2$'])\n", "xlabel(r'$t$')\n", "ylabel(r'$y$')\n", "\n", "subplot(1,2,2)\n", "plot(yy_1,yy_2)\n", "xlabel(r'$y_1$')\n", "ylabel(r'$y_2$');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## ✍ Exercices" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 🐍 Exercice (sympy)\n", "
\n", " \n", "Calculer la solution **exacte** du problème de Cauchy \n", "$$\\begin{cases}\n", "y'(t)=\\dfrac{3}{2} y(t) \\left( 1-\\dfrac{y(t)}{6} \\right),& t>0\\\\\n", "y(0)=1.\n", "\\end{cases}$$\n", " \n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### ✨ Exercice (scipy)\n", "
\n", " \n", "Calculer la solution **approchée** du problème de Cauchy\n", "$$\\begin{cases}\n", "y'(t)=\\sin\\left(t y(t)\\right), & t>0\\\\\n", "y(0)=a\n", "\\end{cases}$$\n", "pour $a=-2,-1,-\\frac{1}{2},-\\frac{1}{10},0,\\frac{1}{10},\\frac{1}{2},1,2$ et afficher le champ de vecteurs.\n", " \n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 🐍 Exercice (sympy - système)\n", "
\n", " \n", "1. Calculer la solution générale **exacte** du système \n", "$$\n", "\\begin{pmatrix}\n", "x(t)\\\\\n", "y(t)\n", "\\end{pmatrix}'\n", "=\n", "\\begin{pmatrix}\n", "0&1\\\\\n", "-1&0\n", "\\end{pmatrix}\n", "\\begin{pmatrix}\n", "x(t)\\\\\n", "y(t)\n", "\\end{pmatrix}\n", "$$\n", "1. Pour $x(0)=-1$ et $y(0)=1$, afficher $t\\mapsto x$ et $t\\mapsto y$ dans un même graphe.\n", "2. Afficher ensuite $x\\mapsto y$.\n", "1. Calculer analytiquement $E'(t)$ avec\n", "$$\n", "E(t)=\\frac{x^2(t)}{2}+\\frac{y^2(t)}{2}.\n", "$$\n", " \n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### ✨ Exercice (scipy - système)\n", "\n", "
\n", "\n", "1. Calculer la solution particulière **approchée** du système \n", "$$\n", "\\begin{cases}\n", "x'(t)= -y(t)+y^2(t)x(t)\\\\\n", "y'(t)= x(t)-x^2(t)y(t)\n", "\\end{cases}\n", "$$\n", "avec $x(0)=0$ et $y(0)=1$.\n", "1. Afficher $t\\mapsto x$ et $t\\mapsto y$ dans un même graphe pour $t\\in[0,14]$. \n", "Afficher ensuite $x\\mapsto y$.\n", "1. On définit la fonction\n", "$$\n", "t\\mapsto E(t)=\\frac{x^2(t)}{2}+\\frac{y^2(t)}{2}.\n", "$$\n", "Calculer analytiquement $E'(t)$. Afficher ensuite $E(t)$ calculé à partir des solutions approchées.\n", " \n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### ✨ Exercice (scipy - système - stabilité)\n", "\n", "
\n", " \n", "Considérons le système \n", "$$\n", "\\begin{cases}\n", "x'(t)= x^2(t)+y^2(t)-25\\\\\n", "y'(t)= x(t)y(t)-12\n", "\\end{cases}\n", "$$\n", "1. Afficher le champ des vecteurs et les solutions stationnaires.\n", "1. Calculer les solutions particulières **approchées** pour des données initiales proches des points stationnaires.\n", " \n", "
" ] } ], "metadata": { "hide_input": false, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.6" }, "toc": { "base_numbering": 1, "nav_menu": { "height": "171px", "width": "166px" }, "number_sections": true, "sideBar": true, "skip_h1_title": true, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": true, "toc_position": { "height": "calc(100% - 180px)", "left": "10px", "top": "150px", "width": "308px" }, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }