5.8.7 Problems 601 to 700

Table 5.229: Problems not solved by any CAS

#

ODE

Mathematica

Maple

Sympy

17066

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

17073

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

17074

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

17124

\[ {} 4 x \left (x^{2}+y^{2}\right )-5 y+4 y \left (x^{2}+y^{2}-5 x \right ) y^{\prime } = 0 \]

17149

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

17334

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

17344

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

17348

\[ {} \frac {1}{t^{2}+1}-y^{2}-2 t y y^{\prime } = 0 \]

17349

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

17491

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

17958

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

18018

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

18461

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

18463

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

18466

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

18470

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

18541

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

18666

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

18667

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

18668

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

18689

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

18705

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

18823

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

18824

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

18825

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

18826

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

18827

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

18829

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

18831

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

18833

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

18836

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

18847

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

18848

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

18849

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

18971

\[ {} y^{\prime \prime }+y+\frac {y^{3}}{5} = \cos \left (w t \right ) \]

18972

\[ {} y^{\prime \prime }+\frac {y^{\prime }}{5}+y+\frac {y^{3}}{5} = \cos \left (w t \right ) \]

19081

\[ {} t y^{\prime \prime \prime }+\sin \left (t \right ) y^{\prime \prime }+8 y = \cos \left (t \right ) \]

19082

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

19083

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

19084

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

19085

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

19087

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

19088

\[ {} t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+7 t^{2} y = 0 \]

19089

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

19090

\[ {} \left (x -1\right ) y^{\prime \prime \prime \prime }+\left (x +5\right ) y^{\prime \prime }+y \tan \left (x \right ) = 0 \]

19091

\[ {} \left (x^{2}-25\right ) y^{\left (6\right )}+x^{2} y^{\prime \prime }+5 y = 0 \]

19253

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

19268

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

19269

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

19329

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

19330

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

19508

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

19773

\[ {} x^{\prime \prime }+\left (5 x^{4}-9 x^{2}\right ) x^{\prime }+x^{5} = 0 \]

19822

\[ {} v^{\prime \prime } = \left (\frac {1}{v}+{v^{\prime }}^{4}\right )^{{1}/{3}} \]

19824

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

19899

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

20237

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

20267

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

20269

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

20294

\[ {} y^{\prime \prime }+\frac {y^{\prime }}{x^{{1}/{3}}}+\left (\frac {1}{4 x^{{2}/{3}}}-\frac {1}{6 x^{{1}/{3}}}-\frac {6}{x^{2}}\right ) y = 0 \]

20397

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

20593

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

20596

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

20646

\[ {} x^{5} y^{\left (6\right )}+x^{4} y^{\left (5\right )}+x y^{\prime }+y = \ln \left (x \right ) \]

20650

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

20701

\[ {} x^{2} y^{\prime \prime } = \sqrt {m \,x^{2} {y^{\prime }}^{3}+n y^{2}} \]

20704

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

20735

\[ {} 4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{3}+6 x^{2}+4\right ) y = 0 \]

20809

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

20811

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

20846

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

20884

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

20885

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

20893

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

20897

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

20937

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

21105

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

21155

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

21157

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

21160

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

21192

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

21210

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

21222

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

21223

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

21272

\[ {} x^{\prime \prime }+\frac {\left (t^{5}+1\right ) x}{t^{4}+5} = 0 \]

21273

\[ {} x^{\prime \prime }+\sqrt {t^{6}+3 t^{5}+1}\, x = 0 \]

21275

\[ {} x^{\prime \prime }-p \left (t \right ) x = q \left (t \right ) \]

21276

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

21310

\[ {} x^{\left (5\right )}+x = 0 \]

21385

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

21432

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

21440

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

21441

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

21442

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

21443

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

21582

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

21665

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

21850

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

21895

\[ {} [x^{\prime }\left (t \right ) = x \left (t \right )+4 y \left (t \right )-y \left (t \right )^{2}, y^{\prime }\left (t \right ) = 6 x \left (t \right )-y \left (t \right )+2 x \left (t \right ) y \left (t \right )] \]

21896

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