| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y^{\prime \prime }-x y^{\prime }-2 x y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+\lambda y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+\lambda y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+4 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-x^{2} y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y \,{\mathrm e}^{2 x} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \sin \left (x \right ) y^{\prime \prime }-y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+x y = \sin \left (x \right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-y^{\prime } \sin \left (x \right )-x y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }+\cos \left (y\right ) = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime }-y \,{\mathrm e}^{x} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime }-y \tan \left (x \right ) = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \sin \left (x \right ) y^{\prime \prime }+x^{2} y^{\prime }-y \,{\mathrm e}^{x} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \sinh \left (x \right ) y^{\prime \prime }+x^{2} y^{\prime }-y \,{\mathrm e}^{x} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \sinh \left (x \right ) y^{\prime \prime }+x^{2} y^{\prime }-\sin \left (x \right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} {\mathrm e}^{3 x} y^{\prime \prime }+y^{\prime } \sin \left (x \right )+\frac {2 y}{x^{2}+4} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+\frac {\left ({\mathrm e}^{x}+1\right ) y}{-{\mathrm e}^{x}+1} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x^{2}-4\right ) y^{\prime \prime }+\left (x^{2}+x -6\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime \prime }+\left (-{\mathrm e}^{x}+1\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \sin \left (\pi \,x^{2}\right ) y^{\prime \prime }+x^{2} y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }-y \,{\mathrm e}^{x} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime }+y \,{\mathrm e}^{2 x} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime }+y \cos \left (x \right ) = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime }+y \ln \left (x \right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-y \,{\mathrm e}^{x} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+3 x y^{\prime }-y \,{\mathrm e}^{x} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime \prime }-3 x y^{\prime }+\sin \left (x \right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y \ln \left (x \right ) = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \sqrt {x}\, y^{\prime \prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+\left (6 x^{2}+2 x +1\right ) y^{\prime }+\left (2+12 x \right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime }-y \,{\mathrm e}^{x} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime }+\sqrt {x^{2}+1}\, y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \cos \left (x \right ) y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime }+\sqrt {2 x^{2}+1}\, y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-y \,{\mathrm e}^{x} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y \cos \left (x \right ) = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y^{\prime } \sin \left (x \right )+y \cos \left (x \right ) = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \sqrt {x}\, y^{\prime \prime }+y^{\prime }+x y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x -3\right )^{2} y^{\prime \prime }-2 \left (x -3\right ) y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x -1\right )^{2} y^{\prime \prime }-5 \left (x -1\right ) y^{\prime }+9 y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x +2\right )^{2} y^{\prime \prime }+\left (x +2\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 3 \left (x -2\right )^{2} y^{\prime \prime }-4 \left (x -5\right ) y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x -5\right )^{2} y^{\prime \prime }+\left (x -5\right ) y^{\prime }+4 y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }+\frac {x y^{\prime }}{x -2}+\frac {2 y}{x +2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (-x^{4}+x^{3}\right ) y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+827 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+\frac {y^{\prime }}{x -3}+\frac {y}{x -4} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+\frac {y^{\prime }}{\left (x -3\right )^{2}}+\frac {y}{\left (x -4\right )^{2}} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+\left (\frac {1}{x}-\frac {1}{3}\right ) y^{\prime }+\left (\frac {1}{x}-\frac {1}{4}\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (4 x^{2}-1\right ) y^{\prime \prime }+\left (4-\frac {2}{x}\right ) y^{\prime }+\frac {\left (-x^{2}+1\right ) y}{x^{2}+1} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x^{2}+4\right )^{2} y^{\prime \prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 4 x^{2} y^{\prime \prime }+\left (1-4 x \right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (4 x -4\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (-9 x^{4}+x^{2}\right ) y^{\prime \prime }-6 x y^{\prime }+10 y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+\frac {y}{1-x} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+\frac {y^{\prime }}{x}+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (1-\frac {1}{x^{2}}\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 2 x^{2} y^{\prime \prime }+\left (-2 x^{3}+5 x \right ) y^{\prime }+\left (-x^{2}+1\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-\left (2 x^{2}+5 x \right ) y^{\prime }+\left (9+4 x \right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (-3 x^{3}+3 x^{2}\right ) y^{\prime \prime }-\left (5 x^{2}+4 x \right ) y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+4 x y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 4 x^{2} y^{\prime \prime }+8 x^{2} y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+\left (-x^{4}+x \right ) y^{\prime }+3 x^{3} y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (9 x^{3}+9 x^{2}\right ) y^{\prime \prime }+\left (27 x^{2}+9 x \right ) y^{\prime }+\left (8 x -1\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x -3\right ) y^{\prime \prime }+\left (x -3\right ) y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+\frac {2 y^{\prime }}{x +2}+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 4 y^{\prime \prime }+\frac {\left (4 x -3\right ) y}{\left (x -1\right )^{2}} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x -3\right )^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }-3 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (-x^{2}+2\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-2 x^{2} y^{\prime }+\left (x^{2}-2\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+\frac {y^{\prime }}{x}+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+\left (4 x^{2}+5 x \right ) y^{\prime }+\left (x^{2}+1\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-\left (2 x^{2}+5 x \right ) y^{\prime }+9 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x y^{\prime }+\left (4 x^{3}-4\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 4 x^{2} y^{\prime \prime }+8 x y^{\prime }+\left (1-4 x \right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }-\left (2 x +1\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime \prime }+4 y^{\prime }+\frac {12 y}{\left (x +2\right )^{2}} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime \prime }+4 y^{\prime }+\frac {12 y}{\left (x +2\right )^{2}} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x -3\right ) y^{\prime \prime }+\left (x -3\right ) y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+3 y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 4 x^{2} y^{\prime \prime }+\left (1-4 x \right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+\frac {y^{\prime }}{x}+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+4 x y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (4 x -4\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+7 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x -2\right ) y^{\prime \prime }+y^{\prime }-y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x^{2}-4\right ) y^{\prime \prime }+16 \left (x +2\right ) y^{\prime }-y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+3 y^{\prime }-18 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-11 y^{\prime }+30 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{-x}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (-2-2 x \right ) y^{\prime \prime }+2 y^{\prime }+4 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (2+3 x \right ) y^{\prime \prime }+3 x y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (3 x +1\right ) y^{\prime \prime }-3 y^{\prime }-2 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (-x^{2}+2\right ) y^{\prime \prime }+2 \left (x -1\right ) y^{\prime }+4 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-x y^{\prime }+4 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (2 x^{2}+2\right ) y^{\prime \prime }+2 x y^{\prime }-3 y = 0
\]
|
✓ |
✓ |
✓ |
|