5.3.51 Problems 5001 to 5100

Table 5.135: Problems not solved by Sympy

#

ODE

Mathematica

Maple

Sympy

16716

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

16717

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

16718

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

16719

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

16720

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

16721

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

16723

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

16724

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

16725

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

16726

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

16727

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

16743

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

16745

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

16748

\[ {} y^{\prime } = {\mathrm e}^{\frac {y^{\prime }}{y}} \]

16749

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

16753

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

16756

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

16757

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

16758

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

16761

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

16762

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

16763

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

16764

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

16766

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

16767

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

16768

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

16773

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

16775

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

16778

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

16780

\[ {} 8 {y^{\prime }}^{3}-12 {y^{\prime }}^{2} = 27 y-27 x \]

16782

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

16785

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

16787

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

16792

\[ {} 5 x y-4 y^{2}-6 x^{2}+\left (y^{2}-8 x y+\frac {5 x^{2}}{2}\right ) y^{\prime } = 0 \]

16793

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

16796

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

16799

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

16815

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

16819

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

16821

\[ {} \left (5 x -7 y+1\right ) y^{\prime }+x +y-1 = 0 \]

16824

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

16826

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

16834

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

16835

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

16850

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

16852

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

16855

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

16858

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

16860

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

16861

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

16862

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

16863

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

16864

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

16865

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

16866

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

16867

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

16868

\[ {} y^{3} y^{\prime \prime } = -1 \]

16869

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

16870

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

16871

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

16872

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

16984

\[ {} 2 y^{\prime \prime }-3 y^{\prime }-2 y = 5 \,{\mathrm e}^{x} \cosh \left (x \right ) \]

16990

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

17037

\[ {} y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{-x} \left (9 x^{2}+5 x -12\right ) \]

17043

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

17047

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

17054

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

17055

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

17056

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

17057

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

17058

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

17059

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

17060

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

17061

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

17062

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

17064

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

17065

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

17066

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

17067

\[ {} y^{\prime \prime }-y^{\prime }+{\mathrm e}^{2 x} y = x \,{\mathrm e}^{2 x}-1 \]

17068

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

17070

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

17072

\[ {} y^{\prime \prime }+y = \frac {1}{\sqrt {\sin \left (x \right )^{5} \cos \left (x \right )}} \]

17073

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

17080

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

17081

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

17083

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

17084

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

17086

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

17087

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

17088

\[ {} y^{\prime \prime }+\frac {2 y^{\prime }}{x}-y = 4 \,{\mathrm e}^{x} \]

17089

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

17090

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

17094

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

17095

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

17096

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

17097

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

17098

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

17099

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

17100

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

17104

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