4.5.7 Problems 601 to 648

Table 4.61: Problems not solved by Mathematica nor by Maple

#

ODE

Mathematica

Maple

17546

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

17549

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

17560

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

17561

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

17562

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

17685

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

17686

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

17795

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

17796

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

17797

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

17798

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

17799

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

17801

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

17802

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

17803

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

17804

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

17805

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

17967

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

17982

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

17983

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

18043

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

18044

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

18222

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

18487

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

18536

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

18538

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

18612

\[ {}y^{\prime \prime \prime } y^{\prime }-3 {y^{\prime \prime }}^{2}+3 y^{\prime \prime } {y^{\prime }}^{2}-2 {y^{\prime }}^{4}-x {y^{\prime }}^{5} = 0 \]

18613

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

18952

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

18982

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

18984

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

19009

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

19112

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

19308

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

19311

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

19361

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

19365

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

19417

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

19420

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

19451

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

19525

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

19527

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

19562

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

19600

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

19601

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

19609

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

19613

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

19620

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