|
# |
ODE |
Mathematica |
Maple |
Sympy |
|
\[
{} y^{\prime \prime }+b \left (t \right ) y^{\prime }+c \left (t \right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime } = \sin \left (y\right )-\cos \left (x \right )
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{3} y^{\prime }-\sin \left (y\right ) = 1
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{\prime \prime }-2 {x^{\prime }}^{2}+x^{\prime }-2 x = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{\prime \prime }+{\mathrm e}^{-x^{\prime }}-x = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{\prime \prime }-x^{\prime }+x-x^{2} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left [x^{\prime }\left (t \right ) = \cos \left (x \left (t \right )\right )^{2} \cos \left (y \left (t \right )\right )^{2}+\sin \left (x \left (t \right )\right )^{2} \cos \left (y \left (t \right )\right )^{2}, y^{\prime }\left (t \right ) = -\frac {\sin \left (2 x \left (t \right )\right ) \sin \left (2 y \left (t \right )\right )}{2}\right ]
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime } = \sqrt {1-t^{2}-y^{2}}
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime } = \frac {\ln \left (t y\right )}{1-t^{2}+y^{2}}
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime } = \left (t^{2}+y^{2}\right )^{{3}/{2}}
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} {\mathrm e}^{x} \sin \left (y\right )+3 y-\left (3 x -{\mathrm e}^{x} \sin \left (y\right )\right ) y^{\prime } = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \frac {4 x^{3}}{y^{2}}+\frac {12}{y}+3 \left (\frac {x}{y^{2}}+4 y\right ) y^{\prime } = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 2-y \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )-x \left (t \right )^{2}]
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left [x^{\prime }\left (t \right ) = x \left (t \right )-x \left (t \right )^{2}-x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = \frac {y \left (t \right )}{2}-\frac {y \left (t \right )^{2}}{4}-\frac {3 x \left (t \right ) y \left (t \right )}{4}\right ]
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -\left (x \left (t \right )-y \left (t \right )\right ) \left (1-x \left (t \right )-y \left (t \right )\right ), y^{\prime }\left (t \right ) = x \left (t \right ) \left (2+y \left (t \right )\right )]
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} [x^{\prime }\left (t \right ) = y \left (t \right ) \left (2-x \left (t \right )-y \left (t \right )\right ), y^{\prime }\left (t \right ) = -x \left (t \right )-y \left (t \right )-2 x \left (t \right ) y \left (t \right )]
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} [x^{\prime }\left (t \right ) = \left (2+x \left (t \right )\right ) \left (y \left (t \right )-x \left (t \right )\right ), y^{\prime }\left (t \right ) = y \left (t \right )-x \left (t \right )^{2}-y \left (t \right )^{2}]
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-\frac {x \left (t \right )^{3}}{5}-\frac {y \left (t \right )}{5}\right ]
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left [x^{\prime }\left (t \right ) = x \left (t \right ) \left (1-x \left (t \right )-y \left (t \right )\right ), y^{\prime }\left (t \right ) = y \left (t \right ) \left (\frac {3}{4}-y \left (t \right )-\frac {x \left (t \right )}{2}\right )\right ]
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+y^{\prime }+y+y^{3} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+\mu \left (1-y^{2}\right ) y^{\prime }+y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+\cos \left (t \right ) y^{\prime }+3 y \ln \left (t \right ) = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (x +3\right ) y^{\prime \prime }+x y^{\prime }+y \ln \left (x \right ) = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (x -2\right ) y^{\prime \prime }+y^{\prime }+\left (x -2\right ) \tan \left (x \right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+y+\frac {y^{3}}{5} = \cos \left (w t \right )
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+\frac {y^{\prime }}{5}+y+\frac {y^{3}}{5} = \cos \left (w t \right )
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} t y^{\prime \prime \prime }+\sin \left (t \right ) y^{\prime \prime }+8 y = \cos \left (t \right )
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+4 t^{2} y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime \prime }+t y^{\prime \prime }+t^{2} y^{\prime }+t^{2} y = \ln \left (t \right )
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (x -4\right ) y^{\prime \prime \prime \prime }+\left (1+x \right ) y^{\prime \prime }+\tan \left (x \right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (x^{2}-2\right ) y^{\left (6\right )}+x^{2} y^{\prime \prime }+3 y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} t y^{\prime \prime \prime }+\sin \left (t \right ) y^{\prime \prime }+4 y = \cos \left (t \right )
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+7 t^{2} y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime \prime }+t y^{\prime \prime }+5 t^{2} y^{\prime }+2 t^{3} y = \ln \left (t \right )
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (x -1\right ) y^{\prime \prime \prime \prime }+\left (x +5\right ) y^{\prime \prime }+\tan \left (x \right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (x^{2}-25\right ) y^{\left (6\right )}+x^{2} y^{\prime \prime }+5 y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y = {y^{\prime }}^{2}-x y^{\prime }+\frac {x^{3}}{2}
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime } y^{\prime \prime }-x^{2} y y^{\prime }-x y^{2} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x \left (x^{2} y^{\prime }+2 x y\right ) y^{\prime \prime }+4 x {y^{\prime }}^{2}+8 x y y^{\prime }+4 y^{2}-1 = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime } = x +y^{2}
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+2 y^{\prime }+y^{2} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (x \,{\mathrm e}^{y}+y-x^{2}\right ) y^{\prime \prime } = 2 x y-{\mathrm e}^{y}-x
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{\prime \prime }+\left (5 x^{4}-9 x^{2}\right ) x^{\prime }+x^{5} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} v^{\prime \prime } = \left (\frac {1}{v}+{v^{\prime }}^{4}\right )^{{1}/{3}}
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \sqrt {y^{\prime }+y} = \left (y^{\prime \prime }+2 x \right )^{{1}/{4}}
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime \prime } y^{\prime }-3 {y^{\prime \prime }}^{2}+3 y^{\prime \prime } {y^{\prime }}^{2}-2 {y^{\prime }}^{4}-x {y^{\prime }}^{5} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (1+y^{2}\right ) y^{\prime \prime }-2 y {y^{\prime }}^{2}-2 \left (1+y^{2}\right ) y^{\prime } = y^{2} \left (1+y^{2}\right )
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime } y^{\prime \prime }-x^{2} y y^{\prime } = x y^{2}
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (y^{2}+2 x^{2} y^{\prime }\right ) y^{\prime \prime }+2 {y^{\prime }}^{2} \left (x +y\right )+x y^{\prime }+y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (x^{3}+x +1\right ) y^{\prime \prime \prime }+\left (6 x +3\right ) y^{\prime \prime }+6 y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+\frac {y^{\prime }}{x^{{1}/{3}}}+\left (\frac {1}{4 x^{{2}/{3}}}-\frac {1}{6 x^{{1}/{3}}}-\frac {6}{x^{2}}\right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime }+\frac {y \ln \left (y\right )}{x} = \frac {y}{x^{2}}-\ln \left (y\right )^{2}
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}-h^{2}\right ) y^{\prime }-x y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (x^{2} y^{\prime }+y^{2}\right ) \left (x y^{\prime }+y\right ) = \left (y^{\prime }+1\right )^{2}
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{5} y^{\left (6\right )}+x^{4} y^{\left (5\right )}+x y^{\prime }+y = \ln \left (x \right )
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{2}+\left (2 x y-1\right ) y^{\prime }+x y^{\prime \prime }+x^{2} y^{\prime \prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime } = \sqrt {m \,x^{2} {y^{\prime }}^{3}+n y^{2}}
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+4 y^{2}-6 y = x^{4} {y^{\prime }}^{2}
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} 4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{3}+6 x^{2}+4\right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (x y \sin \left (x y\right )+\cos \left (x y\right )\right ) y+\left (x y \sin \left (x y\right )-\cos \left (x y\right )\right ) y^{\prime } = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} 3 x^{2} y^{4}+2 x y+\left (2 x^{3} y^{2}-x^{2}\right ) y^{\prime } = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} 3 y {y^{\prime }}^{2}-2 x y y^{\prime }+4 y^{2}-x^{2} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y+3 x y^{\prime }+2 y {y^{\prime }}^{2}+\left (x^{2}+2 y^{2} y^{\prime }\right ) y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (y^{2}+2 x^{2} y^{\prime }\right ) y^{\prime \prime }+2 {y^{\prime }}^{2} \left (x +y\right )+x y^{\prime }+y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime }-y y^{\prime \prime } = n \sqrt {{y^{\prime }}^{2}+a^{2} y^{\prime \prime }}
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x y^{\prime \prime }+2 y^{\prime } = x^{2} y^{\prime }-y^{2}
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+\left (1+\frac {2 \cot \left (x \right )}{x}-\frac {2}{x^{2}}\right ) y = x \cos \left (x \right )
\]
|
✗ |
✗ |
✗ |
|