6.173 Problems 17201 to 17300

Table 6.345: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

17201

\[ {} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-4 y \left (t \right )+1, y^{\prime }\left (t \right ) = -x \left (t \right )+5 y \left (t \right )] \]

17202

\[ {} [x^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right )+{\mathrm e}^{t}, y^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )-{\mathrm e}^{t}] \]

17203

\[ {} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+4 y \left (t \right )+\cos \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right )+\sin \left (t \right )] \]

17204

\[ {} x^{\prime }+3 x = {\mathrm e}^{-2 t} \]

17205

\[ {} x^{\prime }-3 x = 3 t^{3}+3 t^{2}+2 t +1 \]

17206

\[ {} x^{\prime }-x = \cos \left (t \right )-\sin \left (t \right ) \]

17207

\[ {} 2 x^{\prime }+6 x = t \,{\mathrm e}^{-3 t} \]

17208

\[ {} x^{\prime }+x = 2 \sin \left (t \right ) \]

17209

\[ {} x^{\prime \prime } = 0 \]

17210

\[ {} x^{\prime \prime } = 1 \]

17211

\[ {} x^{\prime \prime } = \cos \left (t \right ) \]

17212

\[ {} x^{\prime \prime }+x^{\prime } = 0 \]

17213

\[ {} x^{\prime \prime }+x^{\prime } = 0 \]

17214

\[ {} x^{\prime \prime }-x^{\prime } = 1 \]

17215

\[ {} x^{\prime \prime }+x = t \]

17216

\[ {} x^{\prime \prime }+6 x^{\prime } = 12 t +2 \]

17217

\[ {} x^{\prime \prime }-2 x^{\prime }+2 x = 2 \]

17218

\[ {} x^{\prime \prime }+4 x^{\prime }+4 x = 4 \]

17219

\[ {} 2 x^{\prime \prime }-2 x^{\prime } = \left (t +1\right ) {\mathrm e}^{t} \]

17220

\[ {} x^{\prime \prime }+x = 2 \cos \left (t \right ) \]

17221

\[ {} y^{\prime } = \frac {x^{4}}{y} \]

17222

\[ {} y^{\prime } = \frac {x^{2} \left (x^{3}+1\right )}{y} \]

17223

\[ {} y^{\prime }+y^{3} \sin \left (x \right ) = 0 \]

17224

\[ {} y^{\prime } = \frac {7 x^{2}-1}{7+5 y} \]

17225

\[ {} y^{\prime } = \sin \left (2 x \right )^{2} \cos \left (y\right )^{2} \]

17226

\[ {} x y^{\prime } = \sqrt {1-y^{2}} \]

17227

\[ {} y y^{\prime } = \left (x +x y^{2}\right ) {\mathrm e}^{x^{2}} \]

17228

\[ {} y^{\prime } = \frac {x^{2}+{\mathrm e}^{-x}}{y^{2}-{\mathrm e}^{y}} \]

17229

\[ {} y^{\prime } = \frac {x^{2}}{1+y^{2}} \]

17230

\[ {} y^{\prime } = \frac {\sec \left (x \right )^{2}}{y^{3}+1} \]

17231

\[ {} y^{\prime } = 4 \sqrt {x y} \]

17232

\[ {} y^{\prime } = x \left (y-y^{2}\right ) \]

17233

\[ {} y^{\prime } = \left (1-12 x \right ) y^{2} \]

17234

\[ {} y^{\prime } = \frac {3-2 x}{y} \]

17235

\[ {} x +y \,{\mathrm e}^{-x} y^{\prime } = 0 \]

17236

\[ {} r^{\prime } = \frac {r^{2}}{\theta } \]

17237

\[ {} y^{\prime } = \frac {3 x}{y+x^{2} y} \]

17238

\[ {} y^{\prime } = \frac {2 x}{1+2 y} \]

17239

\[ {} y^{\prime } = 2 x y^{2}+4 x^{3} y^{2} \]

17240

\[ {} y^{\prime } = x^{2} {\mathrm e}^{-3 y} \]

17241

\[ {} y^{\prime } = \left (1+y^{2}\right ) \tan \left (2 x \right ) \]

17242

\[ {} y^{\prime } = \frac {x \left (x^{2}+1\right ) y^{5}}{6} \]

17243

\[ {} y^{\prime } = \frac {3 x^{2}-{\mathrm e}^{x}}{2 y-11} \]

17244

\[ {} x^{2} y^{\prime } = y-x y \]

17245

\[ {} y^{\prime } = \frac {{\mathrm e}^{-x}-{\mathrm e}^{x}}{3+4 y} \]

17246

\[ {} 2 y y^{\prime } = \frac {x}{\sqrt {x^{2}-4}} \]

17247

\[ {} \sin \left (2 x \right )+\cos \left (3 y\right ) y^{\prime } = 0 \]

17248

\[ {} y^{2} \sqrt {-x^{2}+1}\, y^{\prime } = \arcsin \left (x \right ) \]

17249

\[ {} y^{\prime } = \frac {3 x^{2}+1}{12 y^{2}-12 y} \]

17250

\[ {} y^{\prime } = \frac {2 x^{2}}{2 y^{2}-6} \]

17251

\[ {} y^{\prime } = 2 y^{2}+x y^{2} \]

17252

\[ {} y^{\prime } = \frac {6-{\mathrm e}^{x}}{3+2 y} \]

17253

\[ {} y^{\prime } = \frac {2 \cos \left (2 x \right )}{10+2 y} \]

17254

\[ {} y^{\prime } = 2 \left (1+x \right ) \left (1+y^{2}\right ) \]

17255

\[ {} y^{\prime } = \frac {t y \left (4-y\right )}{3} \]

17256

\[ {} y^{\prime } = \frac {t y \left (4-y\right )}{t +1} \]

17257

\[ {} y^{\prime } = \frac {a y+b}{c y+d} \]

17258

\[ {} y^{\prime }+4 y = t +{\mathrm e}^{-2 t} \]

17259

\[ {} y^{\prime }-2 y = t^{2} {\mathrm e}^{2 t} \]

17260

\[ {} y^{\prime }+y = t \,{\mathrm e}^{-t}+1 \]

17261

\[ {} y^{\prime }+\frac {y}{t} = 5+\cos \left (2 t \right ) \]

17262

\[ {} y^{\prime }-2 y = 3 \,{\mathrm e}^{t} \]

17263

\[ {} t y^{\prime }+2 y = \sin \left (t \right ) \]

17264

\[ {} y^{\prime }+2 t y = 16 t \,{\mathrm e}^{-t^{2}} \]

17265

\[ {} \left (t^{2}+1\right ) y^{\prime }+4 t y = \frac {1}{\left (t^{2}+1\right )^{2}} \]

17266

\[ {} 2 y^{\prime }+y = 3 t \]

17267

\[ {} t y^{\prime }-y = t^{3} {\mathrm e}^{-t} \]

17268

\[ {} y^{\prime }+y = 5 \sin \left (2 t \right ) \]

17269

\[ {} 2 y^{\prime }+y = 3 t^{2} \]

17270

\[ {} y^{\prime }-y = 2 t \,{\mathrm e}^{2 t} \]

17271

\[ {} y^{\prime }+2 y = t \,{\mathrm e}^{-2 t} \]

17272

\[ {} t y^{\prime }+4 y = t^{2}-t +1 \]

17273

\[ {} y^{\prime }+\frac {2 y}{t} = \frac {\cos \left (t \right )}{t^{2}} \]

17274

\[ {} y^{\prime }-2 y = {\mathrm e}^{2 t} \]

17275

\[ {} t y^{\prime }+2 y = \sin \left (t \right ) \]

17276

\[ {} t^{3} y^{\prime }+4 t^{2} y = {\mathrm e}^{-t} \]

17277

\[ {} t y^{\prime }+\left (t +1\right ) y = t \]

17278

\[ {} y^{\prime }-\frac {y}{3} = 3 \cos \left (t \right ) \]

17279

\[ {} 2 y^{\prime }-y = {\mathrm e}^{\frac {t}{3}} \]

17280

\[ {} 3 y^{\prime }-2 y = {\mathrm e}^{-\frac {\pi t}{2}} \]

17281

\[ {} t y^{\prime }+\left (t +1\right ) y = 2 t \,{\mathrm e}^{-t} \]

17282

\[ {} t y^{\prime }+2 y = \frac {\sin \left (t \right )}{t} \]

17283

\[ {} \sin \left (t \right ) y^{\prime }+\cos \left (t \right ) y = {\mathrm e}^{t} \]

17284

\[ {} y^{\prime }+\frac {y}{2} = 2 \cos \left (t \right ) \]

17285

\[ {} y^{\prime }+\frac {4 y}{3} = 1-\frac {t}{4} \]

17286

\[ {} y^{\prime }+\frac {y}{4} = 3+2 \cos \left (2 t \right ) \]

17287

\[ {} y^{\prime }-y = 1+3 \sin \left (t \right ) \]

17288

\[ {} y^{\prime }-\frac {3 y}{2} = 3 t +3 \,{\mathrm e}^{t} \]

17289

\[ {} y^{\prime }-6 y = t^{6} {\mathrm e}^{6 t} \]

17290

\[ {} y^{\prime }+\frac {y}{t} = 3 \cos \left (2 t \right ) \]

17291

\[ {} t y^{\prime }+2 y = \sin \left (t \right ) \]

17292

\[ {} 2 y^{\prime }+y = 3 t^{2} \]

17293

\[ {} \left (t -3\right ) y^{\prime }+\ln \left (t \right ) y = 2 t \]

17294

\[ {} t \left (t -4\right ) y^{\prime }+y = 0 \]

17295

\[ {} y^{\prime }+\tan \left (t \right ) y = \sin \left (t \right ) \]

17296

\[ {} \left (-t^{2}+4\right ) y^{\prime }+2 t y = 3 t^{2} \]

17297

\[ {} \left (-t^{2}+4\right ) y^{\prime }+2 t y = 3 t^{2} \]

17298

\[ {} \ln \left (t \right ) y^{\prime }+y = \cot \left (t \right ) \]

17299

\[ {} y^{\prime } = \frac {t -y}{2 t +5 y} \]

17300

\[ {} y^{\prime } = \sqrt {1-t^{2}-y^{2}} \]