215_Neacsu-Miclea_Liviu-Stefan_Lab2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[y\\left(x\\right) = \\tan\\left(x^{2} + 2 \\, C\\right)\\right]</script></html>"
      ],
      "text/latex": [
       "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[y\\left(x\\right) = \\tan\\left(x^{2} + 2 \\, C\\right)\\right]$$"
      ],
      "text/plain": [
       "[y(x) == tan(x^2 + 2*_C)]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 1 a\n",
    "reset()\n",
    "x=var('x')6\n",
    "y=function('y')(x)\n",
    "eqd = diff(y,x)==2*x*(1+y^2)\n",
    "sol = desolve(eqd,y)\n",
    "show(solve(sol,y(x)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[y\\left(x\\right) = \\frac{1}{2 \\, C + \\log\\left(x + 1\\right) + \\log\\left(x - 1\\right)}\\right]</script></html>"
      ],
      "text/latex": [
       "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[y\\left(x\\right) = \\frac{1}{2 \\, C + \\log\\left(x + 1\\right) + \\log\\left(x - 1\\right)}\\right]$$"
      ],
      "text/plain": [
       "[y(x) == (1/(2*_C + log(x + 1) + log(x - 1)))]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 1 b\n",
    "reset()\n",
    "x=var('x')\n",
    "y=function('y')(x)\n",
    "eqd = (x^2-1)*diff(y,x) + 2*x*y^2==0\n",
    "sol = desolve(eqd,y)\n",
    "show(solve(sol,y(x)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[y\\left(x\\right) = \\frac{x \\log\\left(-\\frac{1}{\\sqrt{C x}}\\right) + x}{\\log\\left(-\\frac{1}{\\sqrt{C x}}\\right)}, y\\left(x\\right) = \\frac{x \\log\\left(C x\\right) - 2 \\, x}{\\log\\left(C x\\right)}\\right]</script></html>"
      ],
      "text/latex": [
       "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[y\\left(x\\right) = \\frac{x \\log\\left(-\\frac{1}{\\sqrt{C x}}\\right) + x}{\\log\\left(-\\frac{1}{\\sqrt{C x}}\\right)}, y\\left(x\\right) = \\frac{x \\log\\left(C x\\right) - 2 \\, x}{\\log\\left(C x\\right)}\\right]$$"
      ],
      "text/plain": [
       "[y(x) == (x*log(-1/sqrt(_C*x)) + x)/log(-1/sqrt(_C*x)), y(x) == (x*log(_C*x) - 2*x)/log(_C*x)]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 1 c\n",
    "reset()\n",
    "x=var('x')\n",
    "y=function('y')(x)\n",
    "eqd = 2*x^2*diff(y,x) == x^2+y^2\n",
    "sol = desolve(eqd,y)\n",
    "show(solve(sol,y(x)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}C x = e^{\\left(-\\frac{1}{6} \\, \\sqrt{3} {\\left(\\sqrt{3} \\log\\left(\\frac{x^{2} + x y\\left(x\\right) + y\\left(x\\right)^{2}}{x^{2}}\\right) - 2 \\, \\arctan\\left(\\frac{\\sqrt{3} {\\left(x + 2 \\, y\\left(x\\right)\\right)}}{3 \\, x}\\right)\\right)}\\right)}</script></html>"
      ],
      "text/latex": [
       "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}C x = e^{\\left(-\\frac{1}{6} \\, \\sqrt{3} {\\left(\\sqrt{3} \\log\\left(\\frac{x^{2} + x y\\left(x\\right) + y\\left(x\\right)^{2}}{x^{2}}\\right) - 2 \\, \\arctan\\left(\\frac{\\sqrt{3} {\\left(x + 2 \\, y\\left(x\\right)\\right)}}{3 \\, x}\\right)\\right)}\\right)}$$"
      ],
      "text/plain": [
       "_C*x == e^(-1/6*sqrt(3)*(sqrt(3)*log((x^2 + x*y(x) + y(x)^2)/x^2) - 2*arctan(1/3*sqrt(3)*(x + 2*y(x))/x)))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 1 d\n",
    "reset()\n",
    "x=var('x')\n",
    "y=function('y')(x)\n",
    "eqd = diff(y,x) == -(x+y)/y\n",
    "sol = desolve(eqd,y)\n",
    "show(sol)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}K_{2} \\cos\\left(x\\right) - \\frac{1}{2} \\, {\\left(x - 1\\right)} \\cos\\left(x\\right) + K_{1} \\sin\\left(x\\right) + \\frac{1}{2} \\, x \\sin\\left(x\\right)</script></html>"
      ],
      "text/latex": [
       "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}K_{2} \\cos\\left(x\\right) - \\frac{1}{2} \\, {\\left(x - 1\\right)} \\cos\\left(x\\right) + K_{1} \\sin\\left(x\\right) + \\frac{1}{2} \\, x \\sin\\left(x\\right)$$"
      ],
      "text/plain": [
       "_K2*cos(x) - 1/2*(x - 1)*cos(x) + _K1*sin(x) + 1/2*x*sin(x)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 1 e\n",
    "reset()\n",
    "x=var('x')\n",
    "y=function('y')(x)\n",
    "eqd = diff(diff(y,x),x)+y == sin(x)+cos(x)\n",
    "sol = desolve(eqd,y)\n",
    "show(sol)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}K_{2} e^{\\left(-x\\right)} + K_{1} e^{x} + \\frac{1}{3} \\, e^{\\left(2 \\, x\\right)}</script></html>"
      ],
      "text/latex": [
       "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}K_{2} e^{\\left(-x\\right)} + K_{1} e^{x} + \\frac{1}{3} \\, e^{\\left(2 \\, x\\right)}$$"
      ],
      "text/plain": [
       "_K2*e^(-x) + _K1*e^x + 1/3*e^(2*x)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 1 f\n",
    "reset()\n",
    "x=var('x')\n",
    "y=function('y')(x)\n",
    "eqd = diff(diff(y,x),x)-y == e^(2*x)\n",
    "sol = desolve(eqd,y)\n",
    "show(sol)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}K_{1} e^{x} + e^{x} \\log\\left({\\left(e^{x} + 1\\right)} e^{\\left(-x\\right)}\\right) + K_{2} - x + \\log\\left(e^{x} + 1\\right)</script></html>"
      ],
      "text/latex": [
       "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}K_{1} e^{x} + e^{x} \\log\\left({\\left(e^{x} + 1\\right)} e^{\\left(-x\\right)}\\right) + K_{2} - x + \\log\\left(e^{x} + 1\\right)$$"
      ],
      "text/plain": [
       "_K1*e^x + e^x*log((e^x + 1)*e^(-x)) + _K2 - x + log(e^x + 1)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 1 g\n",
    "reset()\n",
    "x=var('x')\n",
    "y=function('y')(x)\n",
    "eqd = diff(diff(y,x),x)-diff(y,x) == 1/(1+e^x)\n",
    "sol = desolve(eqd,y)\n",
    "show(sol)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\arctan\\left(y\\left(x\\right)\\right) = \\frac{1}{4} \\, \\pi + x</script></html>"
      ],
      "text/latex": [
       "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\arctan\\left(y\\left(x\\right)\\right) = \\frac{1}{4} \\, \\pi + x$$"
      ],
      "text/plain": [
       "arctan(y(x)) == 1/4*pi + x"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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XX9hbj/ziF9LAga4rA0LH0BsAIKKqqqS//EU69VR7A9uxY6VNm6Q//pGQhMRDUAIARMSRI9Kzz0onnSRNmyadcIK93P+//5t5SEhcBCUAQFhq5iCdeKIdXhsxwq6qvXixxHJYSHTMUQIAtMnu3TYg/f73UlmZNHWqvcyfFbWRTAhKAIBW2bBBeuopOw+pQwc7D+n226UhQ1xXBkQeQQkAcEzl5dL8+dIf/iCtXCllZkq/+pX0059KPXu6rg6IHoISACCoTz+1V6v9139J+/dL559vJ2dfeaXtTQKSHW9zAEADhw7ZVbPnzbO9R+np0k9+YnuPhg51XR0QWwQlAICOHpWWLJFefFFauNAOtZ13nvTKK9L3vielprquEHCDoAQA7ZQx9jL+F1+0gWjPHunkk+1K2tOm2XlIQHtHUAKAdqS6Wlq92k7MXrBA2r5dysiQfvhDafp0aeRIyeNxXSUQPwhKAOJKfn6+8vPzVVVV5bqUpHH0qJ1rNH++9Prr0pdfSv36SVddJV19tTRxopSS4rpKID55jDHhthF2AwDQWCAQkM/nk9/vl9frdV1OwvH7paVLpUWL7LZ3rx1KqwlHEyYQjtDuhdR3So8SACQBY6TNm+uC0fvv256knBy7IOTVV9vbiTCsBrQOQQkAEpTfL61YYa9We/NNads2qXNnu9bRb38rTZkiZWe7rhJIbAQlAEgQ5eVSQYH0zjvSsmXSunV2cnZ2tg1Fl1xi5xt17eq6UiB5EJQAIE5VVNgwtHKltHy5fSwvtwtAnn++XQTygguk73zHdaVA8iIoAUCcCASkVatsIFq5Ulq71oalbt2ks8+291b77nelU06RjjvOdbVA+0BQAgAHjLFrGK1ZY4fTVq6UPvrIDqX16WOD0SOP2MeRI7mvGuAK//QAIAYOHrTDaGvW1G1799rPDRpkA9Ett9jHoUO5Og2IFwQlAIiww4eljz+WCgvrQtGWLfZzPXpIY8ZIN90kjR1rP+7b12m5AFpAUAKAMOzfbwNRYaH04Yf2sbjYDqF16GCHzS64QPr5z20wGjKE+UVAIiEoAUAIqqvtnKKNG6UNG+pC0c6d9vNpaXWh6J57pFGj7A1mU1NdVg0gXAQlAKjHGOmrr2wgqr9t2iR98409pndvG4R+8AP7OGqU7SniliBA8iEoAWiXjJFKS+1tP4qKGoaigwftMV262F6hESNsKBoxwj4//ngmWwPtBUEJQFIrL5e2brWTqbdsscGo5uNAwB7TsaM0fLgNQpMn1wWiQYOYTwS0dwQlAAnv6FGppET65z+lzz5rGIq2b7e9R5LUq1ddILr6avvxsGHS4ME2LAFAYwQlAAmhvFz6/HMbhmoCUc3H27dLR47Y41JSbPAZPly65hobhGoCUXq6028BQAIiKAGIC9XV0u7d0o4dNvh8+qndP2WK3bdrV92xXbrYMDR4sHTZZdKJJ9Y9P+EEeocARA5BCUBMVFfbq8m2b68LQ/U/3rHD3teshsfjlyRlZEgTJzYMQ/37M5kaQGx4TM3gfduF3QCAxHfokO31KSmpeywpqQtEJSVSZWXd8b17S9nZUlaWfaz/cVaW5PEE5PP55Pf75fV6XXxLAJJbSP/dokcJwDEFAjb8NA5C9ffVXEFWIyNDGjjQXjk2alTDMJSVJXXvfuxzAoBrBCWgHTt61M4L+vJLOyxW8/jFFw3DULAQlJkpnX++fRw4sG7fgAFSp05uvicAiCSCEpCEjhxpPgA1ftyzp+7SecleMdavnw06mZn2dhw1IajmkRAEoD0hKAEJwhjpwAEbgBpvpaUNA9DevU0DUEaGDTn9+0vjxtnHmuc1j336cBsOAKiPoAQ4VFUllZXZnp3mAlD9bc8eO1RWX2qq7QGq6QWaMKH5AJSeTgACgLYgKAERZIydz1NWZnt19u6t+7i58FNWZi+bry8trS789OsnjRnT8HnfvnUfe71cJg8A0URQAlpw9Ki0b1/DwHOsj2tWiK6vR4+GIWfYsIbhp34ISkuL+bcJAAiCoIR2wxi71s++fU3DT7Dgc+BA03Y6dLBDWX361D0OH173cf39ffrY9YJYKRoAEhNBCQmpvFzav78u9OzbF9rzxnN8JNuDUz/cDB4sjR1bF3QaBx+fj+EuAGgvCEpwqqrK9tq0Juzs2yd9803TtjweO8TVu3fdlp0tjR5d97xXr7qPawJQly6x/q4BAImCoISIqKy0gadm27+/4fNg4efgwebbS0trGG7S0+28nsZhp/7zHj24sgsAEFkEJdQ6cqRhuGkp+DTe11wPj2QXJuzZs2GwOeWU4GGn5uPU1Nh+7wAANIeglGSOHrW9NC0FnGD7v/66+TY7drRhp2br1cuu0nzqqU3313/es6cd1mI+DwAgURGU4lBVVcOw05rQc+hQ82126NA0xAwYIJ18cvMBp37w6dqVsAMAaJ8ISlFSXS35/aEPXdXf/P7m20xJsfNw6oeYfv3spekt9er07Cl160bYAQCgtcIKSh6Px+MP9lc9CVRX21WWDx6s6+Gp+TjYVnNMsB9LzZVZjbfs7Ob39+xZ93H37m0LOzXrBwHxrKKiQhUVFbXPD/3/mzYQCLgqCUAS8/l8XkmHjKl/Z8ymPMf4fIs8Ho9XUvImJQAAkMx8xpgW/zcWblDy+P3+6mMfaf9XmJmZqZKSEnm93ladp3HPTig9Ohs3lqhbt0z5/Q3vol6fz9d8z82xNp9POu64unZyc3O1bt26Vn1PbZVs5wrnfdEWyfbzS6ZzNe5R+uqrrzRmzBgVFRXp+OOPj/j5GkuGn2F7OVey/t5Ixtcqludq7fvC5/P5FEKPUlhDb8dqvD5740+vDhzwae/e7kHn5zS3HTzY9Mahkh2G8vkazsXp00caOlQqKVmlf/3XG5udr9OzZ9OwE46UlJSY/GNN5nN5vd6YnCtZf37Jei5J6t69O+8NztWsZPu9kayvVby+L47Vk1QjZpO5zzwzTZJfp57acH9zYadXL2nQoOYDTqhh59RTKzVjRtS/LUnSjFidKInPFSvJ+vNL1nPFUrL+DJP1XLEUq+8rWV+rRH9fhDX09v9CauAvf/lG06blaeHC5zRwYFpUenaQeAKBgHw+n/x+f0z/x4H4t2vXrtpu9IEDB7ouB3GE3xtoThveFyFdHhWzHqWrrkrRAw+crIsv7sCqy6iVmpqqBx54QKm8KdBIzXuC9wYa4/cGmhOt90XMepQAoDXoNQAQZSH1KDHoBQAAEARBCQAAIAiCEgAAQBAEJQAAgCCiGpTmzJmjCRMmqGvXrurRo0dIX2OM0axZszRgwAB16dJFEydO1KZNm6JZJmLswIEDmj59unw+n3w+n6ZPn66DBw+2+DU33HCDPB5Pg23cuHGxKRhATP3ud7/ToEGD1LlzZ40ePVorV64Meuy7777b5HeDx+PR5s2bY1gxYuG9997TZZddpgEDBsjj8WjhwoXH/JoVK1Zo9OjR6ty5s77zne/omWeeafV5oxqUKisrde211+pf/uVfQv6axx57TE8++aTmzp2rdevWKSMjQxdeeGHtDTKR+KZNm6YNGzborbfe0ltvvaUNGzZo+vTpx/y6iy++WF999VXt9uabb8agWgCx9Oqrr+qOO+7Q/fffr8LCQp199tmaPHmydu7c2eLXbdmypcHvhyFDhsSoYsTK4cOHNXLkSM2dOzek47dt26YpU6bo7LPPVmFhoX7+85/rtttu0/z581t3YmNMuNsxPfvss8bn8x3zuOrqapORkWEeeeSR2n3l5eXG5/OZZ555JpRTIc4VFRUZSWb16tW1+woKCowks3nz5qBfl5eXZ6644ooYVIh44ff7jSTj9/tdl4IYGjNmjLn55psb7Bs+fLi57777mj1++fLlRpI5cOBADKpDvJBkXn/99RaPuffee83w4cMb7LvpppvMuHHjapsJZYurOUrbtm1TaWmpJk2aVLsvNTVV5557rlatWuWwMkRKQUGBfD6fxo4dW7tv3Lhx8vl8x3yN3333XfXt21dDhw7VjTfeqD179kS7XAAxVFlZqQ8++KDB3wBJmjRp0jF/P4waNUr9+/fXBRdcoOXLl0ezTCSIgoKCJu+liy66SOvXr9eRI0dCbieuglJpaakkqV+/fg329+vXr/ZzSGylpaXq27dvk/19+/Zt8TWePHmyXnrpJf3jH//QE088oXXr1un8889vcLd5AImtrKxMVVVVrfob0L9/f/3xj3/U/PnztWDBAg0bNkwXXHCB3nvvvViUjDhWWlra7Hvp6NGjKisrC7mdVt/CxOPxzJL0QEvHrFu3TmeccUZrm65/jgbPjTFN9iG+zJo1S7Nnz27xmHXr1klq+vpKx36Nf/CDH9R+PGLECJ1xxhnKysrSokWLdNVVV7WxagDxqDV/A4YNG6Zhw4bVPh8/frxKSkr0+OOP65xzzolqnYh/zb2Xmtvfkrbc622upFdqnnz66aefNj4gOzu7Dc1KGRkZkmwK7N+/f+3+PXv2NEmFiC+33nqrpk6d2uIx2dnZ+vjjj7V79+4mn9u7d2+rXuP+/fsrKytLW7dubXWtiG/5+fnKz89XVVWV61IQY+np6UpJSWnSe9TavwHjxo3Tiy++GOnykGAyMjKafS916NBBvXv3DrmdVgclY0yZpND7rFph0KBBysjI0NKlSzVq1ChJdsx6xYoVevTRR6NxSkRIenq60tPTj3nc+PHj5ff7tXbtWo0ZM0aStGbNGvn9fk2YMCHk8+3bt08lJSUNAjWSw4wZMzRjxozae72h/ejUqZNGjx6tpUuX6sorr6zdv3TpUl1xxRUht1NYWMjvBmj8+PH6n//5nwb7lixZojPOOEMdO3YMvaFQZ323sAW1Y8cOU1hYaGbPnm26detmCgsLTWFhoTl06FDtMcOGDTMLFiyoff7II48Yn89nFixYYD755BNz3XXXmf79+5tAINDi7HYkjosvvticeuqppqCgwBQUFJhTTjnFXHrppQ2Oqf++OHTokLn77rvNqlWrzLZt28zy5cvN+PHjzfHHH8/7Iolx1Vv79Morr5iOHTuaefPmmaKiInPHHXeYtLQ0s337dmOMMffdd5+ZPn167fG/+c1vzOuvv26Ki4vNxo0bzX333Wckmfnz57v6FhAlhw4dqs0RksyTTz5pCgsLzY4dO4wxTd8bn3/+uenatau58847TVFRkZk3b57p2LGjee2112oOCSnnRDUo5eXlGUlNtuXLl9ceI8k8++yztc+rq6vNAw88YDIyMkxqaqo555xzzCeffNLKHyfi2b59+8z1119vunfvbrp3726uv/76Jpf21n9ffPPNN2bSpEmmT58+pmPHjuaEE04weXl5ZufOnbEvHjFDUGq/8vPzTVZWlunUqZM5/fTTzYoVK2o/l5eXZ84999za548++qgZPHiw6dy5s+nZs6c566yzzKJFixxUjWirWQqi8ZaXl2eMafreMMaYd99914waNcp06tTJZGdnm9///vf1Px1SzvGY/5/YFIawGwCAxmqG3vx+v7xer+tyACSfkGZ0x9XyAAAAAPGEoAQAABAEQQkAACAIghIAAEAQBCUAAIAgCEoAAABBEJQAAACCICgBAAAEQVACAAAIgqAEAAAQBEEJAAAgCIISAABAEAQlAACAIAhKAOJKfn6+cnJylJub67oUAJDHGBNuG2E3AACNBQIB+Xw++f1+eb1e1+UASD6eUA6iRwkAACAIghIAAEAQBCUAAIAgCEoAAABBEJQAAACCICgBAAAEQVACAAAIgqAEAAAQBEEJAAAgCIISAABAEAQlAACAIAhKAAAAQRCUAAAAgiAoAQAABEFQAgAACIKgBAAAEARBCUBcyc/PV05OjnJzc12XAgDyGGPCbSPsBgCgsUAgIJ/PJ7/fL6/X67ocAMnHE8pB9CgBAAAEQVACAAAIgqAEAAAQBEEJAAAgCIISAABAEAQlAACAIAhKAAAAQRCUAAAAgiAoAQAABEFQAgAACIKgBAAAEARBCQAAIAiCEgAAQBAEJQAAgCAISgAAAEEQlADElfz8fOXk5Cg3N9d1KQAgjzEm3DbCbgAAGgsEAvL5fPL7/fJ6va7LAZB8PKEcRI8SAABAEAQlAACAIAhKAAAAQRCUAAAAgiAoAQAABEFQAgAACIKgBAAAEARBCQAAJDxjpOrqyLdLUAIAAAlv3jxp0iSpoiKy7RKUAABAQtu+XbrzTik7W0pNjWzbBCUAAJCwjJFuuknq2VN68snIt98h8k0CAADExosvSkuWSIsWSdG4LSQ9SgAAICHt3WuH3K67TpoyJTrnICgBiLjs7Gx5PJ4G23333ee6LABJ5s477dDbU09F7xwMvQGIigcffFA33nhj7fNu3bo5rAZAslm+XHrpJenZZ6W+faN3HoISgKjo3r27MjIyQj6+oqJCFfWu6w0EAtEoC0ASqKqS7rhDGj9eysuL7rkYegMQFY8++qh69+6t0047TXPmzFFlZWWLxz/88MPy+Xy1W2ZmZowqBZBo/vQn6eOPpd/+VvJ4onsujzEm3DbCbgBAcvnNb36j008/XT179tTatWs1c+ZMXXHFFfrTn/4U9Gua61HKzMyU3++XNxqXsgBISAcOSEOGSJddZofdwhBSxCIoAQjJrFmzNHv27BaPWbdunc4444wm++fPn69rrrlGZWVl6t27d0jnCwQC8vl8BCUADdx5p+1RKi6W+vcPqymCEoDIKSsrU1lZWYvHZGdnq3Pnzk32f/HFFxo4cKBWr16tsWPHhnQ+ghKAxj7/XBo2THrwQWnmzLCbCykoMZkbQEjS09OVnp7epq8tLCyUJPUP879/ANq32bOl9HTp9ttjd06CEoCIKigo0OrVq3XeeefJ5/Np3bp1uvPOO3X55ZfrhBNOcF0egAS1aZP0wgvS3LlS166xOy9DbwAi6sMPP9Qtt9yizZs3q6KiQllZWZo6daruvfdedW3FbzeG3gDUd/XV0ocfSlu2SJ06RaRJ5igBSFwEJQA1PvhAOuMM6bnnIrpuUkhBiXWUAABAXPvVr6ShQ6Uf/jD252aOEgAAiFtFRdLChdK8eVJKSuzPT48SAACIW48+Kg0c6KY3SSIoAQCAOLVjh/Tyy9Ldd0dsAnerEZQAAEBceuIJyeeTbrzRXQ0EJQAAEHcOHpT+/GdpxgwpLc1dHQQlAAAQd559VqqslG6+2W0dBCUAABBXqqrsCtzf/37YN74NG8sDAACAuLJ4sb0B7ssvu66EHiUAABBn/uM/pDFjpLFjXVdCUAIQZ/Lz85WTk6Pc3FzXpQBwYOtWaelS6Wc/c12Jxb3eAMQl7vUGtE8zZ0rPPCN99ZXUuXNUT8W93gAAQOI4elR6/nnp+uujHpJCRlACAABx4a23bE/ST37iupI6BCUAABAX5s2TRo2yW7wgKAEAAOd275b+/nfpxz92XUlDBCUAAODcSy9Jxx0nTZvmupKGCEoAAMC5v/xFuuQSqVcv15U0RFACAABOffaZtH69NHWq60qaIigBAACnXnlFSkuTLr3UdSVNEZQAAIBTr7wiXXGF1LWr60qaIigBAABnPvlE2rRJuu4615U0j6AEAACceeUVqWdPadIk15U0j6AEAACcee016Xvfkzp1cl1J8whKAADAic2bpeJiG5TiFUEJAAA48cYbdgL3hRe6riQ4ghIAAHDijTfs3KQuXVxXEhxBCUBcyc/PV05OjnJzc12XAiCKdu+WVq+2ywLEM48xJtw2wm4AABoLBALy+Xzy+/3yer2uywEQYX/6k3TTTTYwpac7KcETykH0KAEAgJh74w3pzDOdhaSQEZQAAEBMlZdL77wjXX6560qOjaAEAABiauVK6dtvpYsvdl3JsRGUAABATL39tjRggHTyya4rOTaCEgAAiKm337bLAnhCmk7tFkEJAADEzJdfShs3Shdd5LqS0BCUAABAzCxZYnuSvvtd15WEhqAEAABi5u23pdGj439ZgBoEJQAAEBPGSMuW2flJiYKgBAAAYqKoSCork847z3UloSMoAQCAmFixQurQQRo/3nUloSMoAQCAmFixQsrNldLSXFcSOoISAACIOmNsUDr3XNeVtA5BCQAARF1xsbR7tzRxoutKWoegBAAAom7FCiklRZowwXUlrUNQAgAAUbdihV0/qXt315W0DkEJQFzJz89XTk6OcnNzXZcCIEISdX6SJHmMMeG2EXYDANBYIBCQz+eT3++X1+t1XQ6AMOzcKWVlSW+8IV1+uetqaoV0S156lAAAQFStXm0fx41zW0dbEJQAAEBUrV4tDRok9e3rupLWIygBAICoWr06MXuTJIISAACIospK6cMPCUoAAABNfPSRVFEhjR3rupK2ISgBAICoWb1a6tRJOu0015W0DUEJAABEzerV0umnS6mpritpG4ISAACImkSeyC0RlAAAQJTs3y99/rmUyAvtE5QAAEBUFBbax9NPd1tHOAhKAAAgKgoLpbQ0acgQ15W0HUEJAABExYcfSiNHSikpritpO4ISAACIisJCadQo11WEh6AEAAAi7vBhacuWxJ6fJBGUAABAFHz0kWQMPUoAAABNFBZKHTtKJ5/supLwEJQAxJX8/Hzl5OQoN5EXXgGgDz+URoywty9JZB5jTLhthN0AADQWCATk8/nk9/vl9XpdlwOglUaPtvd3mzfPdSVBeUI5iB4lAAAQUVVVUlGRdMoprisJH0EJAABE1OefS+Xldugt0RGUAABARG3caB8TfSK3RFACAAARtmmT1KuXlJHhupLwEZQAAEBEbdxoh908IU2Xjm8EJQAAEFGbNiXHsJtEUAIAABFUWSlt3pwcE7klghIAAIigrVulo0cJSgAAAE1s2mQfGXoDAABoZONGe7Vb796uK4kMghIAAIiYoiIpJ8d1FZFDUAIAABFTXCwNH+66isghKAFolTlz5mjChAnq2rWrevTo0ewxO3fu1GWXXaa0tDSlp6frtttuU2VlZWwLBRBz1dV2MvfQoa4riZwOrgsAkFgqKyt17bXXavz48ZrXzG3Bq6qqdMkll6hPnz56//33tW/fPuXl5ckYo6efftpBxQBipaTE3uONoASg3Zo9e7Yk6bnnnmv280uWLFFRUZFKSko0YMAASdITTzyhG264QXPmzJHX641VqQBirLjYPg4b5raOSGLoDUBEFRQUaMSIEbUhSZIuuugiVVRU6IMPPgj6dRUVFQoEAg02AImluFjq2FHKynJdSeQQlABEVGlpqfr169dgX8+ePdWpUyeVlpYG/bqHH35YPp+vdsvMzIx2qQAibMsW6cQTpZQU15VEDkEJgGbNmiWPx9Pitn79+pDb8zRzJ0xjTLP7a8ycOVN+v792KykpadP3AsCd4uLkmp8kMUcJgKRbb71VU6dObfGY7OzskNrKyMjQmjVrGuw7cOCAjhw50qSnqb7U1FSlpqaGdA4A8am4WLr2WtdVRBZBCYDS09OVnp4ekbbGjx+vOXPm6KuvvlL//v0l2QneqampGj16dETOASD+lJdL27fTowSgndu5c6f279+vnTt3qqqqShs2bJAknXjiierWrZsmTZqknJwcTZ8+Xb/+9a+1f/9+3XPPPbrxxhu54g1IYv/8p2QMQQlAO/eLX/xCzz//fO3zUaNGSZKWL1+uiRMnKiUlRYsWLdItt9yiM888U126dNG0adP0+OOPuyoZQAwk49IAkuQxxoTbRtgNAEBjgUBAPp9Pfr+fniggATz2mDRnjnTwoNTCdRvxJKQqIxGUACDiPB6PV5Jfks8Yw6JKAJwgKAGISx67lkB3SYcMv6gAOEJQAgAACIIFJwEAAIIgKAEAAARBUAIAAAiCoAQAABAEQQkAACAIghIAAEAQBCUAAIAgCEoAAABB/B9HnFpB16VlJwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "Graphics object consisting of 2 graphics primitives"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 2 a\n",
    "reset()\n",
    "x=var('x')\n",
    "y=function('y')(x)\n",
    "eqd = diff(y,x) == 1+y^2\n",
    "sol = desolve(eqd,y,[0,1])\n",
    "show(sol)\n",
    "f(x)=solve(sol,y(x))[0].rhs()\n",
    "#yy=var('yy')\n",
    "plot(f(x),x,-1,1,detect_poles='True',ymin=-10,ymax=10)\n",
    "#implicit_plot(,(x,-1,1),(y,-1,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{\\sqrt{x^{2} - 1} \\sqrt{x + 1} x - \\sqrt{x + 1} {\\left(2 \\, \\sqrt{3} - \\log\\left(2 \\, \\sqrt{3} + 4\\right)\\right)} - \\sqrt{x + 1} \\log\\left(2 \\, x + 2 \\, \\sqrt{x^{2} - 1}\\right)}{2 \\, \\sqrt{x - 1}}</script></html>"
      ],
      "text/latex": [
       "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{\\sqrt{x^{2} - 1} \\sqrt{x + 1} x - \\sqrt{x + 1} {\\left(2 \\, \\sqrt{3} - \\log\\left(2 \\, \\sqrt{3} + 4\\right)\\right)} - \\sqrt{x + 1} \\log\\left(2 \\, x + 2 \\, \\sqrt{x^{2} - 1}\\right)}{2 \\, \\sqrt{x - 1}}$$"
      ],
      "text/plain": [
       "1/2*(sqrt(x^2 - 1)*sqrt(x + 1)*x - sqrt(x + 1)*(2*sqrt(3) - log(2*sqrt(3) + 4)) - sqrt(x + 1)*log(2*x + 2*sqrt(x^2 - 1)))/sqrt(x - 1)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "verbose 0 (3839: plot.py, generate_plot_points) WARNING: When plotting, failed to evaluate function at 100 points.\n",
      "verbose 0 (3839: plot.py, generate_plot_points) Last error message: 'math domain error'\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 1 graphics primitive"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 2 b\n",
    "reset()\n",
    "x=var('x')\n",
    "y=function('y')(x)\n",
    "eqd = diff(y,x) == 1/(1-x^2)*y+1+x\n",
    "sol = desolve(eqd,y,[2,0])\n",
    "show(sol)\n",
    "f(x)=sol\n",
    "plot(sol,x,0,2,detect_poles='True',ymin=-10,ymax=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{1}{2} \\, x^{2} + \\frac{1}{2} \\, x + \\frac{1}{4}</script></html>"
      ],
      "text/latex": [
       "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{1}{2} \\, x^{2} + \\frac{1}{2} \\, x + \\frac{1}{4}$$"
      ],
      "text/plain": [
       "1/2*x^2 + 1/2*x + 1/4"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "Graphics object consisting of 1 graphics primitive"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 2 c\n",
    "reset()\n",
    "x=var('x')\n",
    "y=function('y')(x)\n",
    "eqd = diff(y,x) - 2*y == -x^2\n",
    "sol = desolve(eqd,y,[0,1/4])\n",
    "show(sol)\n",
    "f(x)=sol\n",
    "plot(sol,x,0,2,detect_poles='True',ymin=-10,ymax=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}e^{\\left(4 \\, x\\right)} + 4 \\, e^{x}</script></html>"
      ],
      "text/latex": [
       "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}e^{\\left(4 \\, x\\right)} + 4 \\, e^{x}$$"
      ],
      "text/plain": [
       "e^(4*x) + 4*e^x"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 1 graphics primitive"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 2 d\n",
    "reset()\n",
    "x=var('x')\n",
    "y=function('y')(x)\n",
    "eqd = diff(y,x,2)-5*diff(y,x) + 4*y == 0\n",
    "sol = desolve(eqd,y,ics=[0,5,8])\n",
    "show(sol)\n",
    "f(x)=sol\n",
    "plot(sol,x,0,1,detect_poles='True',ymin=4,ymax=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\left(\\cos\\left(x\\right) - 2 \\, \\sin\\left(x\\right)\\right)} e^{\\left(2 \\, x\\right)} + {\\left(x^{2} + 2 \\, x + 1\\right)} e^{x}</script></html>"
      ],
      "text/latex": [
       "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\left(\\cos\\left(x\\right) - 2 \\, \\sin\\left(x\\right)\\right)} e^{\\left(2 \\, x\\right)} + {\\left(x^{2} + 2 \\, x + 1\\right)} e^{x}$$"
      ],
      "text/plain": [
       "(cos(x) - 2*sin(x))*e^(2*x) + (x^2 + 2*x + 1)*e^x"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 1 graphics primitive"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 2 e\n",
    "reset()\n",
    "x=var('x')\n",
    "y=function('y')(x)\n",
    "eqd = diff(y,x,2)-4*diff(y,x) + 5*y == 2*x^2*e^x\n",
    "sol = desolve(eqd,y,ics=[0,2,3])\n",
    "show(sol)\n",
    "f(x)=sol\n",
    "plot(sol,x,-5,3,detect_poles='True',ymin=-10,ymax=15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{1}{2} \\, {\\left(6 \\, \\pi - 1\\right)} \\cos\\left(2 \\, x\\right) - \\frac{1}{2} \\, {\\left(2 \\, x - 1\\right)} \\cos\\left(2 \\, x\\right) + x \\sin\\left(2 \\, x\\right) + \\frac{1}{2} \\, \\sin\\left(2 \\, x\\right)</script></html>"
      ],
      "text/latex": [
       "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{1}{2} \\, {\\left(6 \\, \\pi - 1\\right)} \\cos\\left(2 \\, x\\right) - \\frac{1}{2} \\, {\\left(2 \\, x - 1\\right)} \\cos\\left(2 \\, x\\right) + x \\sin\\left(2 \\, x\\right) + \\frac{1}{2} \\, \\sin\\left(2 \\, x\\right)$$"
      ],
      "text/plain": [
       "1/2*(6*pi - 1)*cos(2*x) - 1/2*(2*x - 1)*cos(2*x) + x*sin(2*x) + 1/2*sin(2*x)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 1 graphics primitive"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 2 f\n",
    "reset()\n",
    "x=var('x')\n",
    "y=function('y')(x)\n",
    "eqd = diff(y,x,2) + 4*y == 4*(sin(2*x)+cos(2*x))\n",
    "sol = desolve(eqd,y,ics=[pi,2*pi,2*pi])\n",
    "show(sol)\n",
    "f(x)=sol\n",
    "plot(sol,x,-5,5,detect_poles='True',ymin=-15,ymax=15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{\\frac{x^{4} x^{k}}{k + 4} + C}{x^{k}}</script></html>"
      ],
      "text/latex": [
       "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{\\frac{x^{4} x^{k}}{k + 4} + C}{x^{k}}$$"
      ],
      "text/plain": [
       "(x^4*x^k/(k + 4) + _C)/x^k"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 3 a\n",
    "reset()\n",
    "x=var('x')\n",
    "k = var('k')\n",
    "y=function('y')(x)\n",
    "eqd = diff(y,x) + k/x*y(x) == x^3\n",
    "sol = desolve(eqd,[y,x])\n",
    "show(sol)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 3 graphics primitives"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#3 b\n",
    "C = var(\"_C\")\n",
    "sol1 = sol.substitute(C==1,k==1)\n",
    "sol2 = sol.substitute(C==2,k==1)\n",
    "sol3 = sol.substitute(C==3,k==1)\n",
    "plot([sol1, sol2, sol3], x, -1, 1,ymin=-10,ymax=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 1 graphics primitive"
      ]
     },
     "execution_count": 142,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#3 c\n",
    "sol = desolve(eqd,[y,x],ics=[1,0])\n",
    "plot(sol.substitute(k==1),x,-1, 1, ymin=-10, ymax=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img 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\"/>"
      ],
      "text/plain": [
       "Animation with 8 frames"
      ]
     },
     "execution_count": 160,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#3 d\n",
    "sols = [plot(sol.substitute(k==i),x,-1,1,ymin=-5,ymax=5) for i in [-3..-1]]\n",
    "sols += [plot(sol.substitute(k==i),x,-1,1,ymin=-5,ymax=5) for i in [1..5]]\n",
    "animate(sols)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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p5NSbStnjj8Ohh4awdPHFSVdTttzrTVLxMiipVL3zTtjH7Sc/gZEjYQ3ndpLiGiVJktJk/nzo1QvWXz9sUWJISj/7KEmSVABxDKecAu++C+PHwzrrJF2RsmFQkiSpAK67DoYMCVe4demSdDXKloN+kiTl2TPPhKaSF14IRx+ddDVqDBdzS0olF3OrVMyYERZvd+0Ko0fDms7lpIWLuSVJStKCBXDUUdC6dZh2MyQVH39lkiTlQRxDv37wxhswbhyst17SFWl1GJQkScqDG26Af/wD7r4bdtop6Wq0upx6k5QqbmGiUvDii3DuuXDOOXD88UlXo6ZwMbekVHIxt4rV++9Dt26hBcATT7jZbYq5mFuSpEKaNw+OOALatoUHHzQklQLXKEmSlAP19WGa7f334eWXXbxdKgxKkiTlwMUXh01uR46Ezp2Trka5YlCSJKmJ7r0XqqrgmmvgsMOSrka55BolSZKa4JVXoG9fOPFE+M1vkq5GuWZQkiRpNc2cCT17ws47w803Q5TVdVQqJgYlSZJWwzffhJDUvDkMGwYVFUlXpHxwjZIkSY0Ux3DSSfDmmzB2LLRvn3RFyheDkiRJjfSnP8H994deSW5PUtqcepMkqRH++U+49FK4/HLo3TvpapRvBiVJqeJeb0qzF1+EPn3g178OfZNU+tzrTVIqudeb0mbaNOjRA3bcEcaMgRYtkq5ITeReb5Ik5cLs2aGR5IYbhivcDEnlw8XckiStxMKFcOSRMHcujB8P7dolXZEKyaAkSVIG9fVhTdKkSfDcc7DVVklXpEIzKEmSlMEll4Q2AA88AN27J12NkmBQkiRpBW6/HQYNChvd2gagfLmYW1LO3Xjjjey44460bduWtm3b0qNHD0aPHp10WVLWnnoKTj893NzotrwZlCTl3KabbspVV13FxIkTmThxIvvuuy9HHnkkU6dOTbo0aZVeew2OOgr23x8GD3aj23JnHyVJBbHuuutyzTXX0Ldv36xebx8lJeG99+AnP4FNN4Vnn4XWrZOuSHmUVQR2jZKkvKqrq+OBBx5g/vz59OjRI+lypIxmz4aDDoJWreCxxwxJCgxKkvLi3//+Nz169GDhwoW0bt2ahx9+mE6dOmV8fW1tLbW1td99XVNTU4gyJQDmz4ef/zz0Sho3LjSWlMA1SpLyZNttt+W1115j/Pjx9OvXjxNPPJE33ngj4+urqqqorKz87taxY8cCVqtytmgRHH00TJkCo0bB1lsnXZHSxDVKkgpi//33Z+utt+bmm29e4fdXNKLUsWNH1ygpr+IY+vaFu+8O020HHph0RSog1yhJSo84jpcLQt9XUVFBRUVFASuSQkPJO+4IQcmQpBUxKEnKuYEDB3LIIYfQsWNH5s2bx5AhQ3juued4/PHHky5N+s4NN8CVV4aGkscfn3Q1SiuDkqSc++yzzzjhhBP45JNPqKysZMcdd+Txxx/ngAMOSLo0CQhbkpx5Jpx3ng0ltXKuUZKUSvZRUr48/jgccURYwH3XXbCGlzWVq6zWKHl6SJLKxtixoev2wQeHtUmGJK2Kp4gkqSxMngyHHQbdu8P990Pz5klXpGJgUJIklby33gpdt7fdFkaMgJYtk65IxcKgJEkqaR98AAccABtsAKNHQ5s2SVekYmJQkiSVrFmzQkhq1gyeeALWWy/pilRsDEqSUqW6uppOnTrRrVu3pEtRkfvqqzDdVlMDTz0Fm2ySdEUqRrYHkJRKtgdQU3zzTei0/cYb8MIL0KVL0hUphdzCRJJUfhYuhF694LXX4OmnDUlqGoOSJKlkfPst/OIXYRRp1KjQCkBqCoOSJKkkLFoExxwDTz4JI0fCPvskXZFKgUFJklT0Fi+G446Dxx6Dhx8O65OkXDAoSZKKWl0d9OkTAtIDD4Tu21KuGJQkSUWrvh5OPRX++U8YMgR69ky6IpUag5IkqSjFMZxxBtx5J9x9N/zyl0lXpFJkUJIkFZ04hrPPhptvhttvD+uTpHwwKEmSikp9PZx5Jtx4YwhKJ52UdEUqZQYlSVLRqK+Hfv3g1lvh73+Hvn2Trkilzr3eJKWKe70pk/p6OO20EJJuv92QpMJwrzdJqeReb1pWXR2ccgrcdVdYvH3CCUlXpBLgXm+SpOJXVxfWId17b7i67b/+K+mKVE4MSpKk1Fq8ODSTHDIkBKVf/SrpilRuDEqSpFRavDhMsT3wQGgoaZ8kJcGgJElKndpaOPbYsLnt0KHQu3fSFalcGZQkSanyzTfQqxc8/3zYv+3nP0+6IpUzg5IkKTVqakIwmjQJHnsM9tsv6YpU7gxKkqRUmDMHDj4Ypk+HJ5+EHj2SrkgyKEmSUuCTT+CAA2DWLHjuOejaNemKpMCgJElK1IwZsP/+YW3SCy/AdtslXZG0lFuYSJISM20a7LlnaCr54ouGJKWPQUlSqrjXW/mYOBF++lNo1SqEpK22Sroi6Yfc601SKrnXW2l76qnQAqBz53B123rrJV2RylBWe705oiRJKqj774dDD4U99oCnnzYkKd0MSpKkgqmuDvu1HX00jBgRpt2kNDMoSZLyLo7h0kvhzDPhnHPgrrugefOkq5JWzfYAkqS8qqsLAemmm6CqCgYMgCir1SFS8gxKkqS8WbgQTjgBhg2Dv/8d+vZNuiKpcQxKkqS8mDMHjjwS/vWvEJSOPDLpiqTGMyhJknLunXfClW1ffAHPPgu77550RdLqcTG3JCmnXnklbGgbxzB+vCFJxc2gJEnKmUcegX32gW22gXHjYOutk65IahqDkqRUcQuT4jV4cOi2feihofP2+usnXZHUdG5hIimV3MKkeNTXw4UXwv/8D/zmN3D11bCG/wxX+mXVpMLF3JKk1TZ/Pvz61/Dww/DXv8JZZyVdkZRbBiVJ0mqZOROOOAKmTYPhw8NjqdQYlCRJjTZhQghGLVqERds77ph0RVJ+OIssSWqU+++HvfaCLbaAV181JKm0GZQkSVmJY7jsMjjmGOjdOzSS3GijpKuS8supN0nSKi1YACedBEOHwhVXwMCBbmyr8uCIkqScq6qqolu3brRp04YNN9yQnj178tZbbyVdllbTJ5/Az34GI0bAAw/ARRcZklQ+DEqScu7555+nf//+jB8/nieffJLFixdz4IEHMn/+/KRLUyO98grsuit89BG8+CL84hdJVyQVlg0nJeXd559/zoYbbsjzzz/PXnvtldXP2HAyebffDv36wc47w0MPQYcOSVck5ZQNJyWlw9y5cwFYd911M76mtraW2tra776uqanJe11asUWL4LzzoLoaTj0V/vY3qKhIuiopGU69ScqrOI45//zz2WOPPejSpUvG11VVVVFZWfndrWPHjgWsUg0++wz22w9uuQVuuincG5JUzpx6k5RX/fv357HHHmPs2LFsuummGV+3ohGljh07OvVWQBMmwFFHweLF8OCD8NOfJl2RlFdOvUlK1llnncWIESN44YUXVhqSACoqKqhw6CIxd9wR1iN17RrWI22ySdIVSeng1JuknIvjmDPPPJNhw4bxzDPPsOWWWyZdkjJYuDCsQzr5ZDjhBHj+eUOStCxHlCTlXP/+/bnvvvt45JFHaNOmDZ9++ikAlZWVrLXWWglXpwbvvhsu93/zzXCF20knJV2RlD6uUZKUc1GGboR33HEHffr0yeo9bA+QX48+GkaQ1l03TLV17Zp0RVLBuUZJUjJy8A8w5UldHfzhDzBoEBxxBPzjH7DOOklXJaWXQUmSysSnn8Jxx8Fzz8FVV8FvfwtruFJVWimDkiSVgSefhOOPD8Hoqadgn32SrkgqDv5bQpJK2OLFMHAgHHRQWIf02muGJKkxHFGSpBL14Ydw7LEwfnxYk3ThhU61SY1lUJKkEjRiRLjcv1Wr0BvJLtvS6vHfFpJSpbq6mk6dOtGtW7ekSylKtbVw7rlw5JGwxx5hqs2QJK0++yhJSiX7KDXef/4TFmy//jpcey2cdRZkaGklKcs+So4oSVKRi2O46SbYeWeYNw9efhnOPtuQJOWCQUmSithnn8Hhh4cNbU88ESZNgl12SboqqXS4mFuSitSjj4bNbAFGjoSf/zzZeqRS5IiSJBWZ+fPDCNLhh0P37vDvfxuSpHxxREmSisjEiWEbkg8/DOuSTjvNtUhSPjmiJElFYPFiuPJK6NED2raFyZPh9NMNSVK+GZQkKeWmTIHdd4c//AEGDIBx42DbbZOuSioPBiVJSqnFi8PWI7vsAgsWhK1IrrgCmjdPujKpfLhGSZJSaMoU6NMnTLFdeCFceim0bJl0VVL5cURJUqqU+xYmDWuRdt556ShSVZUhSUqKW5hISqVy3MLk3/8OG9lOnhzWIl16KVRUJF2VVLLcwkSSisGiRWEUadm1SIMGGZKkNDAoSVKCXnklBKQ//AEuuCBsQVKms45SKhmUJCkBNTVw1lmhL1KLFqGRpKNIUvp41ZskFdjw4XDmmfDVV3DddeHxmn4aS6nkiJIkFchHH8FRR0GvXtC1K0ydCueea0iS0sygJEl5VlcH1dWw/fahq/bQoTByJGy+edKVSVoVg5Ik5dH48bDbbmF67Ve/gjffhKOPdo82qVgYlCQpDz7/HPr2DYu1AV5+GW65Bdq1S7YuSY3jzLgk5VBdHdx0E1x8cRg1uuEGOO00aNYs6cokrQ5HlCQpR8aNg113DdNsv/gFTJsG/foZkqRiZlCSlCrFuNfbrFlh65Gf/jSEovHj4dZbYf31k65MUlO515ukVCqGvd5qa+Fvf4MrrggBadAgOOUUR5CkIuFeb5KUD3EMw4ZB587wu9/B8cfDW2/B6acbkqRSY1CSpEaYNAn22Qd694b/9//g9ddh8GCn2aRSZVCSpCx8/DH06RMWa3/+OTz+OIwaBZ06JV2ZpHyyPYAkrcQ338C118Kf/wxrrx0u9z/lFLcdkcqFf9QlaQUWL4bbb4fLLoPZs+Gcc+Cii6CyMunKJBWSU2+StIw4hgcfDAu1Tz8d9t47bDty9dWGJKkcGZQkaYlnnoHu3eGXv4SttoLJk+Hee8NjSeXJoCSp7E2aBAcdBPvtF7YdefZZGD0aunZNujJJSTMoSSpbb7wBxxwDu+wCM2bAQw+Frtp77510ZZLSwqAkqey8+SYceyx06bJ0u5EpU+Coo8KIkiQ1MChJSpV87vU2bVroot25M7z0Etx4I0yf7uX+kjJzrzdJqZTLvd6mT4c//SkszN5443CZ/8knQ0VFjoqVVIyyGj/231CSStY774QNa+++GzbaCP73f8PoUcuWSVcmqVgYlCSVnClT4KqrYMgQ2GADuO46OO00A5KkxjMoSSoZ48dDVRWMGAEdO8Jf/hJGkNZaK+nKJBUrF3NLKmpxDE8+CfvuCz16hAXbd9wBb78NZ51lSJLUNAYlSUWprg6GDYPddoMDD4SamtAHaepU6NMHWrRIukJJpcCgJCkvXnjhBQ4//HA6dOhAFEUMHz48J+/79dcweDBsuy307g2tW8OYMTBhQuiDtIafapJyyI8USXkxf/58fvzjHzN48OCcvN/MmTBgQFh7dO65sOuuYU3Ss8+GESUbRUrKBxdzS8qLQw45hEMOOaTJ7zNpUuicff/9sPba4eq1s86CzTbLQZGStAoGJUmpUFtbS21tLRDWHz300DcA7LMPbLklXHttaBLZpk2SVUoqNwYlSalQVVXFZZf9FegDnAFsCIRmkcceC82aJVicpLLlGiVJiZs4Ed577xJatpxD8+b/wy9+sTkjR34NwBFHGJIkJccRJUmJWLAgrDu64QZ49VXYbLNm/OEP0LcvbLhhc2pqWiddoiQZlCQV1vTpYXH2bbfBF1/AQQfBI4/AYYc5ciQpfQxKkvLi66+/5u23317yVUsefLCCK6+cx8SJbVhnnbAw+7//G7bZJskqJWnlDEqS8mLixInss885wCnAx9x7bzvgWfbccxpjxpzu1iKSioJBSVJOffFFWHt02217A/9H+/ZhS5GTT4ZtttkH2CfZAiWpEQxKkprs229h1KhwKf+jj4Y+SAcfDMOHw6GHQvPmSVcoSavHoCRptcQxvPJKCEdDh8KcObDTTnDVVaHvUfv2SVcoSU1nUJLUKO+9B/fcEwLS9OmwySbhkv4TToAuXZKuTpJyy6AkaZU++QQefDCMHL30ErRqBb17w403wt57e1m/pNJlUJK0Qp99BsOGhXD0wgshDB14YBhJ6tUrhCVJKnUGJUnfmT17aTh67jmIIth/f/j736FnT1h33fzXUF1dTXV1NXV1dfk/mCStQhTHcVPfo8lvICk5M2aEztjDh4eRoziGffeFo48OI0frr59MXTU1NVRWVjJ37lzatm2bTBGSSlmUzYscUZLKTBzD66+HYDR8OLz2Wrh8f7/9oLo6hKMNN0y4SElKCYOSVAYWL4axY5eGoxkzoLIy9Dj6/e9DzyMHbSTphwxKUomaPRueeAJGjw7NIL/4IlzK37MnHHkk/Oxn0KJF0lVKUroZlKQSUV8PEyeGYDR6NLz6aphm69oV+vULAWmXXcICbUlSdgxKUhH79FN4+ukQjMaMCaNIlZXhMv7TTw9TahtvnHSVklS8DEpSEfnqK3j++RCOnn4a3ngjPN+1K5x6KhxyCPToAWv6J1uScsKPUynFFiwInbCffhqeeSZMrdXXwxZbhKvULr44XMq/0UZJVypJpcmgJKXI/Plho9mxY0PDx3HjoLY2XK6/775h1Gi//WDLLZOuVJLKg0FJStCsWWHEaOxYePFFmDQJ6uqgXTvYYw+46qoQjLp0cRG2JCXBoCQVSH09vPXW0hGjsWPD1wCbbx6C0cknw557wvbbwxprJFuvJMmgJOXNJ5+ES/RffTWEowkToKYmjAztsEMYKbr00hCQOnZMutr0cK83SWniXm9SDsyeHbYCmTRpaTj68MPwvfbtoXt32G23cL/rruESfq2ce71JyjP3epNyLY7hgw9g8uTlbzNnhu+3ahWaOv7qV0uD0aabur5IkoqVQUnKoKYm9Cl64w2YOjWMGE2eDF9+Gb6/wQaw005w3HHhvmtX+NGPoFmzJKuWJOWSQUll7/uBaOrU8Lhh6iyKYKut4Mc/hvPOC6Fop52gQwdHiiSp1BmUVBYWLYL33oO334bp05ferygQdeoURok6dw63bbeFtddOtn5JUjIKFpQuuADmzg27ly9723RTWHdd/2WupluwIKwfeuedpUGoIRS9/37oTwRQUQFbbw3bbBMCUadOIRBtt52BSJK0vIIFpZqasL7j0Ufhs8/CotgGFRU/DFDL3tq3D1s0tG5dqGqVNnEM8+aFIPT++zBjRrg1PH7//dC8sUFDGPrRj6BnzxCKfvSjcL/ppvYokiRlJ5H2AIsWhV3PP/po6W3mzOW//uijMEKwrLXXDoFpww3DfcNtRV+3a+coVbFYsCCE548+go8/Xnq/7OOPPgrbezRo3jz0Htpii9CscfPNlz7ecssQhlxUXdxsDyApz7JKCantoxTHYaf0jz4Kf4k23GbNWv7rhue+/Xb5n2/ePEzprbdeuF/2trLnWrc2YDXFokXh9/bll0tvs2fD55+H39OsWUsfN9x//fXy79Gy5dLRxA4dlt536ACbbRbCUPv2BqFSZ1CSlGfFHZQaVUAc1j99PzzNmQNffPHDW8Pz9fU/fK8ogjZtoG3bpbfvf73sc61ahb/Y11pr1bc0/sVeVxdC5jffhMAyf/7S+2Uff/9+7tzlw1BDOFp21GdZrVqFkb4NNlj+vuHxRhstDUeVlYZVGZQk5V35BKXVUV8f1rx8P0DV1ITna2qWv33/uYavVxS2MmnefGloat483NZcM/Ot4ftRtHRNVxyv+nFdXRjZ+fbbVd+yrX+ttcJoW6tW4VZZGaY327WDddZZ+eP113eRtLK37BYm06ZNMyhJyheDUr7FMdTWhjU2jb0tWgSLF6/6tmjR0uM1jLJE0cofR1FYzNyixYpvzZv/8Lm1114+CDU8bt06fM/Fzyo0R5Qk5ZlbmORbFIVpt5Ytw8iJJEkqLY4TSJIkZWBQkiRJysCgJEmSlIFBSZIkKYNcXPUmSTkXRVFbYC5QGcdxTdL1SCpPBiVJqRRFUQS0AebFflBJSohBSZIkKQPXKEmSJGVgUJIkScrAoCRJkpSBQUmSJCkDg5IkSVIGBiVJkqQMDEqSJEkZGJQkSZIyMChJkiRlYFCSJEnKYM2m/PAyezFJkiQVm1XuJdmkoEQISXOb+B6SJElJqARqVvaCJm2K28gRpTbATGBTYN5qHzR7rwK7FeA4HqtpPC88ViaeGx4rk1I9N0rxd1XIY63OeZHfEaUlb77SJNYgZKrvisrqZ5oiiqL6QhzHYzX5GA0PPS881veP0/DQc8Njff84DQ9L6twoxd9VIY+Vr/OilBdzV3usojpWoZTq/79SPVYhler/w1I9ViEV6r+rVH9XRX1eNGnqrVEHiqK2hPVMlYVKsUo/zwtl4rmhTDw3tCL5Oi8KOaJUC1y25F5q4HmhTDw3lInnhlYkL+dFwUaUJEmSik0pr1GSJElqEoOSJElSBgYlSZKkDAxKkiRJGeQ1KEVRdFEUReOiKPomiqKvsvyZKIqiP0ZR9HEURQuiKHouiqLO+axThRVFUbsoiu6OomjuktvdURSts4qfuTOKovh7t/EFKll5EkXRGVEUvRdF0cIoiv4VRdGeq3j9z5a8bmEURe9GUfTfhapVhdOY8yKKor1X8NkQR1G0XSFrVv5FUbRXFEUjl+SDOIqinln8TJM/M/I9otQCeAC4sRE/cyFwPnAm0A34FHgyiiI33y0d9wFdgYOX3LoCd2fxc48DGy9zOzQ/5akQoig6BrgeuBLYCXgRGB1F0WYZXr8lMGrJ63YCBgF/jaKod0EKVkE09rxYxrYs//kwPY9lKhmtgP8j5INVytVnRkHaA0RR1Ae4Po7jdVbxugj4eMlr/7zkuQrgM2BAHMc357lU5VkURdsDbwC7x3H8ypLndgdeBraL4/itDD93J7BOHMc9C1Sq8iyKoleASXEc91vmuTeB4XEc/34Fr/8zcEQcx9sv89xNwI/jOO5RiJqVf6txXuwNPAu0i+P4qwKVqYRFURQDveI4Hr6S1+TkMyNta5S2BNoDTzQ8EcdxLfA88JOkilJO9QDmNoQkgDiOxxO6qa7qd7x3FEWzoiiaFkXRrVEUbZjPQpU/URS1AHZhmT/rSzxB5vOgxwpePwbYNYqi5rmtUElYzfOiweQoij6JoujpKIr2yUuBKjY5+cxIW1Bqv+T+s+89/9ky31Nxaw/MWsHzs1j573g0cBywL/AbwrTsM0tGHFV81gea0bg/6+0zvH7NJe+n4rc658UnwGlAb+Ao4C3g6SiK9spXkSoaOfnMWLOxR42i6I/Apat4Wbc4jic29r2X8f35wGgFzylFsj0vltyv6He50t9xHMdDl/lyShRFE4EZwGHAsOwrVco09s/6il6/oudV3LI+L5ZM1y87Zf9yFEUdgQuAF/JTnopIkz8zGh2UgMHAkFW85v3VeF8IC7chpMBPlnl+Q36YCpUu2Z4XOwIbreB7G9CI33Ecx59EUTQD2Cbbn1GqzAbq+OEowcr+rH+a4fWLgTk5rU5JWZ3zYkXGA8fnqigVrZx8ZjQ6KMVxPJtwMufDe4T/sAOAyfDdnPXPgAF5OqZyINvzIoqil4HKKIp2i+P41SXPdQcqgXHZHi+KovWAjiwfqFUk4jj+NoqifxH+rD+8zLcOAB7J8GMvA4d/77kDgYlxHC/KfZUqtNU8L1ZkJ/xsUI4+M/LdR2mzKIq6ApsBzaIo6rrk1nqZ1/wniqJeAHG4BO96YGAURb2iKOoC3Al8Q7ikXEUujuM3CZf53xpF0e5Lrni7FXh02Svelj0voihqHUXRtVEU9YiiaIslV7mMJASzh39wEBWL64BToig6OYqi7aMo+gvhs+ImgCiKqqIoumuZ198EbB5F0XVLXn8y0Be4tuCVK58adV5EUXRuFEU9oyjaJoqizlEUVRHWKw1OpHrlzZK/C7ouyRUAWy75erMl38/LZ8bqTL01xuXAict8PXnJ/T7Ac0seb0sYTWhwNbAWcAPQDngFODCO43l5rVSFdBzwV5ZejTCCH/bFWPa8qAN2AH4NrEP4l+KzwDGeF8UrjuOhS0YG/0DoezMFODSO4xlLXrIx4S/Ihte/F0XRocBfgP6EViJnx3H8UGErVz419rwg9Ou7FtgEWABMBQ6L43hU4apWgexK+OxvcN2S+38AfcjTZ0ZB+ihJkiQVo7S1B5AkSUoNg5IkSVIGBiVJkqQMDEqSJEkZGJQkSZIyMChJkiRlYFCSJEnKwKAkSZKUgUFJkiQpA4OSJElSBgYlSZKkDAxKkiRJGfx/F8e/ct3PBFEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "Graphics object consisting of 1 graphics primitive"
      ]
     },
     "execution_count": 175,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 4\n",
    "reset()\n",
    "x=var('x')\n",
    "a,b = var('a,b')\n",
    "y=function('y')(x)\n",
    "eqd = diff(y,x) == y(x)+a*x+b\n",
    "sol = desolve(eqd,[y,x],[0,1])\n",
    "resab = solve([sol(a,b,1)==-5+4*e, sol(a,b,2)==-7+4*e^2],a,b)[0]\n",
    "f(x) = sol.substitute(a==resab[0].rhs(), b==resab[1].rhs())\n",
    "plot(f,x,-1,1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{1}{3} \\, {\\left(a + 2\\right)} e^{\\left(2 \\, x\\right)} + \\frac{2}{3} \\, {\\left(a - 1\\right)} e^{\\left(-x\\right)}</script></html>"
      ],
      "text/latex": [
       "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{1}{3} \\, {\\left(a + 2\\right)} e^{\\left(2 \\, x\\right)} + \\frac{2}{3} \\, {\\left(a - 1\\right)} e^{\\left(-x\\right)}$$"
      ],
      "text/plain": [
       "1/3*(a + 2)*e^(2*x) + 2/3*(a - 1)*e^(-x)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 1 graphics primitive"
      ]
     },
     "execution_count": 190,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 5\n",
    "reset()\n",
    "x,a=var('x,a')\n",
    "y=function('y')(x)\n",
    "eqd = diff(y,x,2) - diff(y,x) - 2*y == 0\n",
    "sol = desolve(eqd,[y,x],[0,a,2])\n",
    "show(sol)\n",
    "plot(sol.substitute(a==-2),x,-1,10, ymax=1, ymin=-5)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "SageMath 9.3",
   "language": "sage",
   "name": "sagemath"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}