| # | ODE | Mathematica | Maple | Sympy |
| \[
{} x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+3 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 4 x^{2} y^{\prime \prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} z^{2} u^{\prime \prime }+\left (3 z +1\right ) u^{\prime }+u = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{\prime \prime }+p \left (t \right ) x^{\prime }+q \left (t \right ) x = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{\prime \prime }+\frac {x^{\prime }}{t}+q \left (t \right ) x = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{\prime \prime }+\frac {\left (t^{5}+1\right ) x}{t^{4}+5} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{\prime \prime }+\sqrt {t^{6}+3 t^{5}+1}\, x = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{\prime \prime }+2 t^{3} x = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{\prime \prime }+p \left (t \right ) x^{\prime }+q \left (t \right ) x = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{\prime \prime }-\frac {t x^{\prime }}{4}+x = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{\prime \prime }-\frac {x^{\prime }}{t} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} t^{2} x^{\prime \prime }-2 x = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} t^{2} x^{\prime \prime }+a t x^{\prime }+x = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} t^{2} x^{\prime \prime }-t x^{\prime }-3 x = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{\prime \prime }-t x^{\prime }+3 x = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} t^{2} x^{\prime \prime }+t x^{\prime }+x t^{2} = 0
\]
|
✗ |
✗ |
✓ |
|
| \[
{} t^{2} x^{\prime \prime }+t x^{\prime }+\left (t^{2}-1\right ) x = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} t^{2} x^{\prime \prime }+t x^{\prime }+\left (-m^{2}+t^{2}\right ) x = 0
\]
|
✓ |
✗ |
✓ |
|
| \[
{} s y^{\prime \prime }+\lambda y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} t^{2} x^{\prime \prime }+t x^{\prime }+x t^{2} = \lambda x
\]
|
✓ |
✗ |
✓ |
|
| \[
{} x u^{\prime \prime }-\left (x^{2} {\mathrm e}^{x}+1\right ) u^{\prime }-x^{2} {\mathrm e}^{x} u = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} u^{\prime \prime }-\left (1+x \right ) u^{\prime }+\left (x -1\right ) u = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} u^{\prime \prime }+\left (\tan \left (x \right )-2 \cos \left (x \right )\right ) u^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} u^{\prime \prime }-3 u^{\prime } x +13 u = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+2 y^{\prime }+\left (1-\frac {2}{\left (3 x +1\right )^{2}}\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} u^{\prime \prime }-3 u^{\prime } x +13 u = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \sin \left (x \right )^{2} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }-k^{2} \cos \left (x \right )^{2} y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} \cos \left (x \right ) y^{\prime \prime }+\left (x \sin \left (x \right )-2 \cos \left (x \right )\right ) \left (x y^{\prime }-y\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime }+\left (x +3\right ) y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }+7 x y^{\prime }+8 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} n \left (n +1\right ) y-2 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime \prime }+y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 2 x y^{\prime \prime }+x^{2} y^{\prime }-\sin \left (x \right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+{\mathrm e}^{x} y^{\prime }+\left (1+x \right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+x y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime \prime }+y^{\prime }+x y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime \prime }+2 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime \prime }+y^{\prime }+x y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (-n^{2}+x^{2}\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 4 x^{2} y^{\prime \prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime } = \frac {\frac {4 x}{25}-\frac {4 y}{25}}{x^{2}}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+4 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (r^{2}+r \right ) R^{\prime \prime }+r R^{\prime }-n \left (n +1\right ) R = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cos \left (x \right )^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime }-y^{\prime }-4 x^{3} y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \sin \left (x \right ) y^{\prime \prime }+\left (3 \sin \left (x \right )^{2}-\cos \left (x \right )\right ) y^{\prime }+2 \sin \left (x \right )^{3} y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }-6 y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+\cos \left (x \right ) y^{\prime }+\left (\sin \left (x \right )+1\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+3\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime }+2 y^{\prime }+x y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} t y^{\prime \prime }-t y^{\prime }+y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+x y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y-x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 y-3 x y^{\prime \prime }+4 y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (1+a \cos \left (2 x \right )\right ) y^{\prime \prime }+\lambda y = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime \prime }-3 y^{\prime }-5 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+\cos \left (x \right ) y^{\prime }+y \,{\mathrm e}^{x} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (x -a \right ) \left (x -b \right ) y^{\prime \prime }+2 \left (2 x -a -b \right ) y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime }+y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime \prime }+4 y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+\frac {y^{\prime }}{x} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+x y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y+x y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y+x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (1-x \right ) y^{\prime \prime }-x y^{\prime }+y \,{\mathrm e}^{x} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+y^{\prime } \sin \left (x \right )+y \,{\mathrm e}^{x} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (x -1\right ) y^{\prime \prime }+3 y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+4 \tan \left (x \right ) y^{\prime }-x y = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (x^{2}-4\right ) y^{\prime \prime }+3 x^{3} y^{\prime }+\frac {4 y}{x -1} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} 5 x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 3 x^{2} y^{\prime \prime }+4 x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+4 x y^{\prime }-4 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x -1\right )^{2} y^{\prime \prime }+5 \left (x -1\right ) y^{\prime }+4 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -3 y+x y^{\prime }+2 x^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+5 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+\frac {7 x y^{\prime }}{2}-\frac {3 y}{2} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x +3\right )^{2} y^{\prime \prime }+3 \left (x +3\right ) y^{\prime }+5 y = 0
\]
|
✓ |
✓ |
✓ |
|