5.1.13 Problems 1201 to 1288

Table 5.25: Problems not solved by Mathematica

#

ODE

Mathematica

Maple

Sympy

22717

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

22732

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

22921

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

23008

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

23010

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

23015

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

23222

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

23237

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

23257

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

23262

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

23272

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

23304

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

23323

\[ {} 2 x -3 y+\left (7 y^{2}+x^{2}\right ) y^{\prime } = 0 \]

23327

\[ {} x y+1+y^{2} y^{\prime } = 0 \]

23357

\[ {} y^{\prime \prime }+y y^{\prime \prime \prime \prime } = 5 \]

23362

\[ {} 2 y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }+x y = 0 \]

23364

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

23373

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

23394

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

23403

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

23405

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

23406

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

23407

\[ {} \left (x^{3}-1\right ) y^{\prime \prime \prime }-3 y^{\prime \prime }+4 x y = 0 \]

23411

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

23413

\[ {} 2 x y^{\prime \prime }-7 \cos \left (x \right ) y^{\prime }+y = {\mathrm e}^{-x} \]

23414

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

23415

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

23416

\[ {} \left (x^{2}-4\right ) y^{\prime \prime }+3 x^{3} y^{\prime }+\frac {4 y}{x -1} = 0 \]

23470

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

23532

\[ {} x \left (1-3 x \ln \left (x \right )\right ) y^{\prime \prime }+\left (1+9 x^{2} \ln \left (x \right )\right ) y^{\prime }-\left (3+9 x \right ) y = 0 \]

23534

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

23585

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

23588

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

23669

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

23673

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

23870

\[ {} y^{\prime \prime }+9 y = 0 \]

23873

\[ {} y^{\prime \prime }+9 y = 0 \]

23912

\[ {} [x^{\prime }\left (t \right ) = 5 x \left (t \right )-6 y \left (t \right )+x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = 6 x \left (t \right )-7 y \left (t \right )-x \left (t \right ) y \left (t \right )] \]

23913

\[ {} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right )+\left (x \left (t \right )^{2}+y \left (t \right )^{2}\right )^{2}, y^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right )+\left (x \left (t \right )^{2}-y \left (t \right )^{2}\right )^{5}] \]

23914

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

23916

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

23931

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

23933

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

23934

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

23976

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

23984

\[ {} y^{\prime } = \frac {x y+3}{5 x -y} \]

23987

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

24001

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

24004

\[ {} \frac {8 x^{4} y+12 y^{2} x^{3}+2}{2 x +3 y}+\frac {\left (2 x^{5}+3 x^{4} y+3\right ) y^{\prime }}{x^{2} y^{4}+1} = 0 \]

24017

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

24020

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

24159

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

24263

\[ {} \left (2 a^{2}-r^{2}\right ) r^{\prime } = r^{3} \sin \left (\theta \right ) \]

24311

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

24321

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

24336

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

24337

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

24343

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

24688

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

24919

\[ {} {y^{\prime }}^{2}+4 x^{4} y^{\prime }-12 x^{4} y = 0 \]

24930

\[ {} y = x^{6} {y^{\prime }}^{3}-x y^{\prime } \]

24935

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

24937

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

24957

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

24960

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

24970

\[ {} {y^{\prime }}^{4}+x y^{\prime }-3 y = 0 \]

24973

\[ {} 16 x {y^{\prime }}^{2}+8 y y^{\prime }+y^{6} = 0 \]

24975

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

25020

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

25022

\[ {} {y^{\prime \prime }}^{3} = 12 y^{\prime } \left (x y^{\prime \prime }-2 y^{\prime }\right ) \]

25126

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

25145

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

25147

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

25150

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

25261

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

25262

\[ {} y^{\left (5\right )}+t y^{\prime \prime }-3 y = 0 \]

25299

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

25301

\[ {} y^{\prime \prime }+\sqrt {y^{\prime }}+y = t \]

25302

\[ {} y^{\prime \prime }+\sqrt {t}\, y^{\prime }+y = \sqrt {t} \]

25304

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

25329

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

25330

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

25331

\[ {} y^{\prime \prime }+\sqrt {t}\, y^{\prime }-\sqrt {t -3}\, y = 0 \]

25332

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

25334

\[ {} y^{\prime \prime }+a_{1} \left (t \right ) y^{\prime }+a_{0} \left (t \right ) y = f \left (t \right ) \]

25353

\[ {} t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y = 0 \]

25478

\[ {} [y_{1}^{\prime }\left (t \right ) = t \sin \left (y_{1} \left (t \right )\right )-y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )+t \cos \left (y_{2} \left (t \right )\right )] \]

25512

\[ {} [y_{1}^{\prime }\left (t \right ) = 3 \sec \left (t \right ) y_{1} \left (t \right )+5 \sec \left (t \right ) y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -\sec \left (t \right ) y_{1} \left (t \right )-3 \sec \left (t \right ) y_{2} \left (t \right )] \]