| # | ODE | Mathematica | Maple | Sympy |
| \[
{} 4 x y^{\prime \prime }+2 y^{\prime }+y = \frac {x +6}{x^{2}}
\]
|
✗ |
✓ |
✗ |
|
| \[
{} -y+x y^{\prime }+\left (1-x \right ) y^{\prime \prime } = \left (x -1\right )^{2} {\mathrm e}^{x}
\]
|
✗ |
✓ |
✗ |
|
| \[
{} 2 x^{2} \left (2-\ln \left (x \right )\right ) y^{\prime \prime }+x \left (4-\ln \left (x \right )\right ) y^{\prime }-y = \frac {\left (2-\ln \left (x \right )\right )^{2}}{\sqrt {x}}
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+\frac {2 y^{\prime }}{x}-y = 4 \,{\mathrm e}^{x}
\]
|
✗ |
✓ |
✗ |
|
| \[
{} x^{3} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-x^{2} y^{\prime }+x y = 2 \ln \left (x \right )
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-2 \left (1-x \right ) y = -2+2 x
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime \prime }+x \sin \left (y\right ) = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \left [x^{\prime }\left (t \right ) = \frac {y \left (t \right )+t}{x \left (t \right )+y \left (t \right )}, y^{\prime }\left (t \right ) = \frac {x \left (t \right )-t}{x \left (t \right )+y \left (t \right )}\right ]
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \left [x^{\prime }\left (t \right ) = \frac {y \left (t \right )+t}{x \left (t \right )+y \left (t \right )}, y^{\prime }\left (t \right ) = \frac {t +x \left (t \right )}{x \left (t \right )+y \left (t \right )}\right ]
\]
|
✗ |
✓ |
✗ |
|
| \[
{} [x^{\prime \prime }\left (t \right ) = x \left (t \right )^{2}+y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right ) x^{\prime }\left (t \right )+x \left (t \right )]
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime } = \frac {t \left (4-y\right ) y}{3}
\]
|
✗ |
✓ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )+4, y^{\prime }\left (t \right ) = -2 x \left (t \right )+\sin \left (t \right ) y \left (t \right )]
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y = \frac {k \left (y y^{\prime }+x \right )}{\sqrt {1+{y^{\prime }}^{2}}}
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y = -3 \,{\mathrm e}^{x^{2}} \sin \left (2 x \right )
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = {\mathrm e}^{y} y^{\prime }
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-f \left (x \right ) y^{\prime }+\left (f \left (x \right )-1\right ) y = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }+\left (x +3\right ) y = 3 \,{\mathrm e}^{-x}
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime } y^{\prime \prime \prime }-3 {y^{\prime \prime }}^{2}+3 y^{\prime \prime } {y^{\prime }}^{2}-2 {y^{\prime }}^{4}-x {y^{\prime }}^{5} = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{2} y^{\prime \prime \prime }-\left (3 y y^{\prime }+2 x y^{2}\right ) y^{\prime \prime }+\left (2 {y^{\prime }}^{2}+2 y y^{\prime } x +3 x^{2} y^{2}\right ) y^{\prime }+x^{3} y^{3} = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} {y^{\prime }}^{3}-4 y y^{\prime } x +8 y^{2} = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} {y^{\prime }}^{3}+m {y^{\prime }}^{2} = a \left (y+m x \right )
\]
|
✗ |
✓ |
✗ |
|
| \[
{} {\mathrm e}^{3 x} \left (y^{\prime }-1\right )+{\mathrm e}^{2 y} {y^{\prime }}^{3} = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \left (1-y^{2}+\frac {y^{4}}{x^{2}}\right ) {y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+\frac {y^{2}}{x^{2}} = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{2}-2 y y^{\prime } x +{y^{\prime }}^{2} \left (x^{2}-1\right ) = m^{2}
\]
|
✗ |
✓ |
✗ |
|
| \[
{} x^{5} y^{\prime \prime }+3 x^{3} y^{\prime }+\left (3-6 x \right ) x^{2} y = x^{4}+2 x -5
\]
|
✗ |
✓ |
✗ |
|
| \[
{} {y^{\prime }}^{2}-y y^{\prime \prime } = n \sqrt {{y^{\prime }}^{2}+a^{2} {y^{\prime \prime }}^{2}}
\]
|
✗ |
✓ |
✗ |
|
| \[
{} {x^{\prime }}^{2} = k^{2} \left (1-{\mathrm e}^{-\frac {2 g x}{k^{2}}}\right )
\]
|
✗ |
✓ |
✗ |
|
| \[
{} x^{2} {y^{\prime }}^{3}+y \left (x^{2} y+1\right ) {y^{\prime }}^{2}+y^{2} y^{\prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} x +y^{\prime } y \left (2 {y^{\prime }}^{2}+3\right ) = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y y^{\prime \prime }+\sqrt {{y^{\prime }}^{2}+a^{2} {y^{\prime \prime }}^{2}} = {y^{\prime }}^{2}
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y y^{\prime \prime }+\sqrt {{y^{\prime }}^{2}+a^{2} {y^{\prime \prime }}^{2}} = {y^{\prime }}^{2}
\]
|
✗ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime } \left (x \cos \left (x \right )-2 \sin \left (x \right )\right )+\left (x^{2}+2\right ) y^{\prime } \sin \left (x \right )-2 y \left (x \sin \left (x \right )+\cos \left (x \right )\right ) = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} {y^{\prime }}^{3}+m {y^{\prime }}^{2} = a \left (y+m x \right )
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime } = \tan \left (x -\frac {y^{\prime }}{1+{y^{\prime }}^{2}}\right )
\]
|
✗ |
✓ |
✗ |
|
| \[
{} {\mathrm e}^{3 x} \left (y^{\prime }-1\right )+{\mathrm e}^{2 y} {y^{\prime }}^{3} = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \left (1-y^{2}+\frac {y^{4}}{x^{2}}\right ) {y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+\frac {y^{2}}{x^{2}} = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} {y^{\prime }}^{3}-4 y y^{\prime } x +8 y^{2} = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} x^{2} {y^{\prime }}^{3}+\left (y+2 x \right ) y y^{\prime }+y^{2} = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+\left (1+\frac {2 \cot \left (x \right )}{x}-\frac {2}{x^{2}}\right ) y = x \cos \left (x \right )
\]
|
✗ |
✓ |
✗ |
|
| \[
{} 3 x^{2}-y+\left (4 y^{3}-x \right ) y^{\prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} x^{\prime \prime }-2 x^{\prime } \left (x-1\right ) = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} x^{\prime \prime \prime }+a x^{\prime \prime }+b x^{\prime }+c x = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} x^{\prime \prime \prime }-3 x^{\prime }+k x = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-7 x \left (t \right ) y \left (t \right )-a x \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right )+4 x \left (t \right ) y \left (t \right )-a y \left (t \right )]
\]
|
✗ |
✓ |
✗ |
|
| \[
{} x^{\prime \prime } = x^{3}-x
\]
|
✗ |
✓ |
✗ |
|
| \[
{} x^{\prime \prime } = x^{3}-x
\]
|
✗ |
✓ |
✗ |
|
| \[
{} x^{\prime \prime } = x^{3}-x
\]
|
✗ |
✓ |
✗ |
|
| \[
{} x^{\prime \prime } = x-x^{3}
\]
|
✗ |
✓ |
✗ |
|
| \[
{} x^{\prime \prime }+x+8 x^{7} = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} x^{\prime \prime }+x+\frac {x^{2}}{3} = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} x^{\prime \prime }-x+3 x^{2} = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} x^{\prime \prime }-x+3 x^{2} = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} x^{\prime \prime }-x+3 x^{2} = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} x^{\prime \prime }+6 x^{5} = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} x^{\prime \prime }+\lambda x-x^{3} = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} x^{\prime \prime }+4 x^{3} = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} -x^{\prime \prime } = 2 x-x^{2}
\]
|
✗ |
✓ |
✗ |
|
| \[
{} -x^{\prime \prime } = \arctan \left (x\right )
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \frac {x^{2}}{y}+y^{2}-\left (\frac {x^{3}}{y^{2}}+x y+y^{2}\right ) y^{\prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} x u^{\prime \prime }-\left (x^{2} {\mathrm e}^{x}+1\right ) u^{\prime }-x^{2} {\mathrm e}^{x} u = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \frac {x^{2}}{y}+y^{2}-\left (\frac {x^{3}}{y^{2}}+x y+y^{2}\right ) y^{\prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = {\mathrm e}^{y} y^{\prime }
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y {y^{\prime }}^{2}-\left (x y+x +y^{2}\right ) y^{\prime }+x^{2}+x y = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )^{2}, y^{\prime }\left (t \right ) = x \left (t \right )^{2}-y \left (t \right )]
\]
|
✗ |
✓ |
✗ |
|
| \[
{} 3 x^{2}-2 x y+\left (4 y^{3}-x^{2}\right ) y^{\prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} 2 {y^{\prime }}^{3}+3 {y^{\prime }}^{2} = x +y
\]
|
✗ |
✓ |
✗ |
|
| \[
{} 2 x +y y^{\prime } \left (4 {y^{\prime }}^{2}+6\right ) = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime \prime }+y^{\prime } = {\mathrm e}^{t}
\]
|
✗ |
✓ |
✗ |
|
| \[
{} [w^{\prime \prime }\left (t \right )+y \left (t \right )+z \left (t \right ) = -1, w \left (t \right )+y^{\prime \prime }\left (t \right )-z \left (t \right ) = 0, -w \left (t \right )-y^{\prime }\left (t \right )+z^{\prime \prime }\left (t \right ) = 0]
\]
|
✗ |
✓ |
✗ |
|
| \[
{} {| y^{\prime }|}+1 = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime } = \frac {1}{x^{2}+y^{2}}
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime } = \frac {1}{x^{2}+y^{2}}
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime } = \frac {x -2 y}{y-2 x}
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime } = \frac {1}{x^{2}-y^{2}}
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime } = \frac {1}{x^{2}+4 y^{2}}
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = {y^{\prime }}^{2} \left (2+x y^{\prime }-4 y^{2} y^{\prime }\right )
\]
|
✗ |
✓ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right )+3 y^{\prime }\left (t \right ) = x \left (t \right ) y \left (t \right ), 3 x^{\prime }\left (t \right )-y^{\prime }\left (t \right ) = \sin \left (t \right )]
\]
|
✗ |
✓ |
✗ |
|
| \[
{} [t^{2} y^{\prime \prime }\left (t \right )+t z^{\prime }\left (t \right )+z \left (t \right ) = t, t y^{\prime }\left (t \right )+z \left (t \right ) = \ln \left (t \right )]
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{4}+\left (x^{2}-3 y\right ) y^{\prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime }+\sqrt {y} = 3 x
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \left (1+a \cos \left (2 x \right )\right ) y^{\prime \prime }+\lambda y = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } \cos \left (x \right )+y = \sin \left (x \right )
\]
|
✗ |
✓ |
✗ |
|
| \[
{} x \left (1-3 x \ln \left (x \right )\right ) y^{\prime \prime }+\left (1+9 x^{2} \ln \left (x \right )\right ) y^{\prime }-\left (3+9 x \right ) y = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} x \left (1-2 x \ln \left (x \right )\right ) y^{\prime \prime }+\left (1+4 x^{2} \ln \left (x \right )\right ) y^{\prime }-\left (4 x +2\right ) y = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} x \left (1-2 x \ln \left (x \right )\right ) y^{\prime \prime }+\left (1+4 x^{2} \ln \left (x \right )\right ) y^{\prime }-\left (4 x +2\right ) y = {\mathrm e}^{2 x} \left (1-2 x \ln \left (x \right )\right )^{2}
\]
|
✗ |
✓ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )-x \left (t \right )^{2}+y \left (t \right )^{2}, y^{\prime }\left (t \right ) = -y \left (t \right )+2 x \left (t \right ) y \left (t \right )]
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \sec \left (x -2 y\right )^{2}+\cos \left (3 y+x \right )-3 \sin \left (3 x \right )+\left (3 \cos \left (3 y+x \right )-2 \sec \left (x -2 y\right )^{2}\right ) y^{\prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \left (2 a^{2}-r^{2}\right ) r^{\prime } = r^{3} \sin \left (\theta \right )
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \frac {1}{\left (1-x y\right )^{2}}+\left (y^{2}+\frac {x^{2}}{\left (1-x y\right )^{2}}\right ) y^{\prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y \left (x^{3} y^{3}+2 x^{2}-y\right )+x^{3} \left (x y^{3}-2\right ) y^{\prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y = x^{6} {y^{\prime }}^{3}-x y^{\prime }
\]
|
✗ |
✓ |
✗ |
|
| \[
{} 2 {y^{\prime }}^{3}+x y^{\prime }-2 y = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} {y^{\prime }}^{3}+2 x y^{\prime }-y = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{2} {y^{\prime }}^{3}-x y^{\prime }+y = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{3} {y^{\prime }}^{3}-x y^{\prime }+y = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} {y^{\prime }}^{4}+x y^{\prime }-3 y = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} 16 x {y^{\prime }}^{2}+8 y y^{\prime }+y^{6} = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} {y^{\prime }}^{3}-2 x y^{\prime }+y = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} {y^{\prime \prime }}^{2}-2 y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime }+x^{2} = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} {y^{\prime \prime }}^{3} = 12 y^{\prime } \left (x y^{\prime \prime }-2 y^{\prime }\right )
\]
|
✗ |
✓ |
✗ |
|