| # | ODE | Mathematica | Maple | Sympy |
| \[
{} -x^{\prime \prime }+x = {\mathrm e}^{-x^{2}}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} -x^{\prime \prime } = \frac {1}{\sqrt {1+x^{2}}}-x
\]
|
✗ |
✗ |
✗ |
|
| \[
{} -x^{\prime \prime } = 2 x-x^{2}
\]
|
✗ |
✓ |
✗ |
|
| \[
{} -x^{\prime \prime } = \arctan \left (x\right )
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime \prime }+{y^{\prime }}^{2} = 1
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x +2\right ) y^{\prime \prime }+{y^{\prime }}^{2} = 1
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \frac {{y^{\prime \prime }}^{2}}{{y^{\prime }}^{2}}+\frac {y y^{\prime \prime }}{y^{\prime }}-y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } \cos \left (y\right )+\left (\cos \left (y\right )-y^{\prime } \sin \left (y\right )\right ) y^{\prime }-2 x y = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime \prime }-{y^{\prime }}^{3}-y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime } = x y^{\prime \prime }+{y^{\prime \prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 y y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 y y^{\prime \prime } = {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = {\mathrm e}^{y} y^{\prime }
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-\frac {2 {y^{\prime }}^{2}}{y}-y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 1+{y^{\prime }}^{2}+y y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{\prime \prime } = 4 x^{3}-4 x
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{\prime \prime }+\sin \left (x\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{\prime \prime } = x^{2}-4 x+\lambda
\]
|
✓ |
✓ |
✗ |
|
| \[
{} s^{2} t^{\prime \prime }+s t t^{\prime } = s
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime \prime } = 1+y^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} {y^{\prime \prime }}^{2}-3 y y^{\prime }+x y = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} {r^{\prime \prime }}^{2}+r^{\prime \prime }+y r^{\prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} {y^{\prime \prime }}^{{3}/{2}}+y = x
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+2 x y^{\prime }+y = 4 x y^{2}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y y^{\prime }+y^{\prime \prime } = x^{2}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+x y = \sin \left (y^{\prime \prime }\right )
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+y^{2} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 1+{y^{\prime }}^{2}+2 y y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 y y^{\prime }+x {y^{\prime }}^{2}+x y y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+x {y^{\prime }}^{2} = 1
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } y^{\prime \prime } = 1
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y y^{\prime \prime } = y^{\prime }
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+{y^{\prime }}^{2} = 1
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = \left (1+y\right ) y^{\prime }
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 1+{y^{\prime }}^{2}+y y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = -\frac {4}{y^{3}}
\]
|
✓ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime } = \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime \prime }+{y^{\prime }}^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime \prime } = {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = {y^{\prime }}^{2} \left (2+x y^{\prime }-4 y^{2} y^{\prime }\right )
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (1-y^{2}\right ) y^{\prime \prime } = y^{\prime }
\]
|
✓ |
✓ |
✗ |
|
| \[
{} T^{\prime \prime }+{T^{\prime }}^{3} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime } {y^{\prime }}^{2}-x^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime } = {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-\tan \left (x \right ) y^{\prime }-\frac {\tan \left (x \right ) y}{x} = \frac {y^{3}}{x^{3}}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime } = y^{\prime } \left (y^{\prime }+y\right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = \frac {1+{y^{\prime }}^{2}}{2 y}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-2 y^{\prime }-2 y y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-\frac {2 y^{\prime }}{y^{3}} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = \frac {1+{y^{\prime }}^{2}}{y}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = y^{\prime } \left (1+{y^{\prime }}^{2}\right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+\cos \left (y\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime }+y^{\prime \prime } = 2
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 3 y y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime }+x {y^{\prime }}^{2}-y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime } = x {y^{\prime }}^{3}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (2+3 y\right ) y^{\prime \prime } = {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = x {y^{\prime }}^{3}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y y^{\prime \prime }+{y^{\prime }}^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{2} y^{\prime \prime }+{y^{\prime }}^{3} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (1+y\right ) y^{\prime \prime } = {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 a y^{\prime \prime }+{y^{\prime }}^{3} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime } = 2 {y^{\prime }}^{3} y
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -{y^{\prime }}^{2}+{y^{\prime }}^{3}+y y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} {y^{\prime }}^{3}+y y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-x {y^{\prime }}^{2} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-x {y^{\prime }}^{2} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+{\mathrm e}^{-2 y} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+{\mathrm e}^{-2 y} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 y^{\prime \prime } = \sin \left (2 y\right )
\]
|
✓ |
✗ |
✗ |
|
| \[
{} 2 y^{\prime \prime } = \sin \left (2 y\right )
\]
|
✓ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime } = {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime } = {\mathrm e}^{x} {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 2 y^{\prime \prime } = {y^{\prime }}^{3} \sin \left (2 x \right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} {y^{\prime }}^{2}+x^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime } = \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime \prime } = {y^{\prime }}^{2} \left (1-y^{\prime } \sin \left (y\right )-\cos \left (y\right ) y y^{\prime }\right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (1+y^{2}\right ) y^{\prime \prime }+{y^{\prime }}^{3}+y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (1+{y^{\prime }}^{2}+y y^{\prime \prime }\right )^{2} = \left (1+{y^{\prime }}^{2}\right )^{3}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime } = y^{\prime } \left (2 x -y^{\prime }\right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime } = \left (3 x -2 y^{\prime }\right ) y^{\prime }
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime \prime } = y^{\prime } \left (2-3 x y^{\prime }\right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{4} y^{\prime \prime } = y^{\prime } \left (y^{\prime }+x^{3}\right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime } = 2 x +\left (x^{2}-y^{\prime }\right )^{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} {y^{\prime \prime }}^{2}-2 y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime }+x^{2} = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime }-x y^{\prime \prime }+{y^{\prime \prime }}^{2} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} {y^{\prime \prime }}^{3} = 12 y^{\prime } \left (x y^{\prime \prime }-2 y^{\prime }\right )
\]
|
✗ |
✓ |
✗ |
|
| \[
{} 3 y y^{\prime } y^{\prime \prime } = -1+{y^{\prime }}^{3}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 4 y {y^{\prime }}^{2} y^{\prime \prime } = 3+{y^{\prime }}^{4}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-y y^{\prime } = 6
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+\sin \left (y\right ) = 0
\]
|
✓ |
✓ |
✗ |
|