5.3.56 Problems 5501 to 5600

Table 5.157: Problems not solved by Sympy

#

ODE

Mathematica

Maple

Sympy

15209

\[ {} m x^{\prime \prime } = f \left (x^{\prime }\right ) \]

15212

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

15213

\[ {} x^{3} y^{\prime \prime }-x y^{\prime }+y = 0 \]

15217

\[ {} -y y^{\prime }-x {y^{\prime }}^{2}+x y y^{\prime \prime } = 0 \]

15220

\[ {} 6 y^{\prime \prime } y^{\prime \prime \prime \prime }-5 {y^{\prime \prime \prime }}^{2} = 0 \]

15223

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

15224

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

15231

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

15235

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

15237

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

15239

\[ {} y^{\prime \prime }+x^{2} y = 0 \]

15240

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

15241

\[ {} y y^{\prime }+y^{\prime \prime } = 1 \]

15242

\[ {} y^{\left (5\right )}-y^{\prime \prime \prime \prime }+y^{\prime } = 2 x^{2}+3 \]

15243

\[ {} y^{\prime \prime }+y y^{\prime \prime \prime \prime } = 1 \]

15244

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

15245

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

15246

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

15248

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

15251

\[ {} 2 y^{\prime \prime }+3 y^{\prime }+4 x^{2} y = 1 \]

15255

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

15256

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

15257

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

15258

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

15259

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

15260

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

15265

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

15266

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

15267

\[ {} \left (x^{2}+1\right ) y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y = 0 \]

15268

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

15269

\[ {} \sin \left (x \right ) y^{\prime \prime }+x y^{\prime }+7 y = 1 \]

15270

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

15271

\[ {} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \]

15272

\[ {} x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (x^{2}+1\right ) y = 0 \]

15273

\[ {} y^{\prime \prime }+\frac {k x}{y^{4}} = 0 \]

15274

\[ {} y^{\prime \prime }+2 x y^{\prime }+2 y = 0 \]

15275

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

15276

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

15277

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

15278

\[ {} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0 \]

15279

\[ {} x^{2} y^{\prime \prime }+x^{2} y^{\prime }+2 \left (1-x \right ) y = 0 \]

15280

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

15281

\[ {} \ln \left (x^{2}+1\right ) y^{\prime \prime }+\frac {4 x y^{\prime }}{x^{2}+1}+\frac {\left (-x^{2}+1\right ) y}{\left (x^{2}+1\right )^{2}} = 0 \]

15282

\[ {} x y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 0 \]

15283

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

15284

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

15285

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

15286

\[ {} x y^{\prime \prime }+\left (6 x y^{2}+1\right ) y^{\prime }+2 y^{3}+1 = 0 \]

15287

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

15288

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

15289

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

15290

\[ {} \left (1-y\right ) y^{\prime \prime }-{y^{\prime }}^{2} = 0 \]

15291

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

15292

\[ {} y^{\prime \prime }+\frac {2 x y^{\prime }}{2 x -1}-\frac {4 x y}{\left (2 x -1\right )^{2}} = 0 \]

15293

\[ {} \left (x^{2}+2 x \right ) y^{\prime \prime }+\left (x^{2}+x +10\right ) y^{\prime } = \left (25-6 x \right ) y \]

15294

\[ {} y^{\prime \prime }+\frac {y^{\prime }}{1+x}-\frac {\left (x +2\right ) y}{x^{2} \left (1+x \right )} = 0 \]

15295

\[ {} \left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x^{2}+4 x -3\right ) y^{\prime }+8 x y = 0 \]

15296

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

15297

\[ {} \left (2 \sin \left (x \right )-\cos \left (x \right )\right ) y^{\prime \prime }+\left (7 \sin \left (x \right )+4 \cos \left (x \right )\right ) y^{\prime }+10 y \cos \left (x \right ) = 0 \]

15298

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

15299

\[ {} y^{\prime \prime }+\left (2 x +5\right ) y^{\prime }+\left (4 x +8\right ) y = {\mathrm e}^{-2 x} \]

15350

\[ {} y^{\prime \prime }-2 y^{\prime } = \left \{\begin {array}{cc} 4 & 0\le t <1 \\ 6 & 1\le t \end {array}\right . \]

15351

\[ {} y^{\prime \prime }-3 y^{\prime }+2 y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ 1 & 1\le t <2 \\ -1 & 2\le t \end {array}\right . \]

15352

\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t <2 \\ -1 & 2\le t \end {array}\right . \]

15365

\[ {} y^{\prime \prime \prime }-5 y^{\prime \prime }+y^{\prime }-y = -t^{2}+2 t -10 \]

15369

\[ {} t^{2} y^{\prime \prime }-6 t y^{\prime }+y \sin \left (2 t \right ) = \ln \left (t \right ) \]

15370

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

15371

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

15372

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

15405

\[ {} [x^{\prime }\left (t \right ) = -3 x \left (t \right )-3 y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )+2 z \left (t \right )+29 \,{\mathrm e}^{-t}, z^{\prime }\left (t \right ) = 5 x \left (t \right )+y \left (t \right )+z \left (t \right )+39 \,{\mathrm e}^{t}] \]

15411

\[ {} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \]

15415

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

15423

\[ {} x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y = 0 \]

15424

\[ {} x^{2} y^{\prime \prime }+y^{\prime }-2 y = 0 \]

15427

\[ {} y^{\prime \prime }-x^{2} y = 0 \]

15433

\[ {} n \left (n +1\right ) y-2 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0 \]

15434

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

15437

\[ {} y^{\prime \prime }-4 y^{\prime }+4 y = \left \{\begin {array}{cc} t & 0\le t \le 3 \\ t +2 & 3<t \end {array}\right . \]

15439

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

15444

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

15447

\[ {} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }-a^{2} y = 0 \]

15470

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

15474

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

15484

\[ {} y^{\prime }+\frac {n y}{x} = a \,x^{-n} \]

15493

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

15494

\[ {} y-3 x^{2}-\left (4 y-x \right ) y^{\prime } = 0 \]

15496

\[ {} \frac {y^{2}}{\left (x -y\right )^{2}}-\frac {1}{x}+\left (\frac {1}{y}-\frac {x^{2}}{\left (x -y\right )^{2}}\right ) y^{\prime } = 0 \]

15497

\[ {} 6 x y^{2}+4 x^{3}+3 \left (2 x^{2} y+y^{2}\right ) y^{\prime } = 0 \]

15498

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

15501

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

15502

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

15507

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

15509

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

15510

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

15518

\[ {} -{y^{\prime }}^{2}+{y^{\prime }}^{3}+y y^{\prime \prime } = 0 \]

15520

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

15523

\[ {} y^{\prime } y^{\prime \prime \prime }-3 {y^{\prime \prime }}^{2} = 0 \]

15558

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

15562

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

15575

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