| # | ODE | Mathematica | Maple | Sympy |
| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (1-x \right ) x y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (2 x^{2}+2 x \right ) y^{\prime \prime }+\left (5 x +1\right ) y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x^{2}-1\right ) y^{\prime \prime }+\left (5 x +4\right ) y^{\prime }+4 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x^{2}-x -6\right ) y^{\prime \prime }+\left (5+3 x \right ) y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (1-x \right ) x y^{\prime \prime }+\left (1-3 x \right ) y^{\prime }-y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} n \left (n +1\right ) y-2 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (-n^{2}+x^{2}\right ) y = 0
\]
|
✓ |
✗ |
✓ |
|
| \[
{} \left (-x^{2}+x \right ) y^{\prime \prime }+4 y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{4} y^{\prime \prime }+x y^{\prime }+y = \frac {1}{x}
\]
|
✓ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (2 x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} n \left (n +1\right ) y-2 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime } = y
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime } = 2 x y-x^{3}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime } \left (1+x \right ) = p y
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime } = \sqrt {x^{2}+y^{2}}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime } = y-x
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime } \left (1+x \right ) = p y
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+9 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+2 x^{2} y^{\prime }+x y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-x y^{\prime }+3 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime \prime }-x y^{\prime }+y = {\mathrm e}^{x}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-x y^{\prime }-y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (-x^{2}+1\right ) y^{\prime \prime }+\frac {3 y^{\prime }}{x +2}+\frac {\left (1-x \right )^{2} y}{x +3} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \frac {y^{\prime \prime }}{x}+\frac {3 \left (x -4\right ) y^{\prime }}{x +6}+\frac {x^{2} \left (x -2\right ) y}{x -1} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+x y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} \left (x -2\right ) y^{\prime \prime }+4 \left (x -2\right ) y^{\prime }+3 y = 0
\]
|
✓ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+x y = 0
\]
|
✓ |
✗ |
✓ |
|
| \[
{} x^{2} \left (x -2\right ) y^{\prime \prime }+4 \left (x -2\right ) y^{\prime }+3 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 4 x y^{\prime \prime }+2 y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+\frac {y}{4 x^{2}} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime \prime }+2 y^{\prime }+x y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+\frac {y^{\prime }}{2 x}-\frac {\left (1+x \right ) y}{2 x^{2}} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-1\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 2 x \left (1+x \right ) y^{\prime \prime }+3 y^{\prime } \left (1+x \right )-y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-x \left (1+x \right ) y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime \prime }-\left (x +4\right ) y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 n y-2 x y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-x y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime } = {\mathrm e}^{x}+x \cos \left (y\right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime } = y^{3}+x^{3}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} u^{\prime } = u^{3}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} t x^{\prime \prime } = x
\]
|
✓ |
✓ |
✓ |
|
| \[
{} t x^{\prime \prime } = x^{\prime }
\]
|
✓ |
✓ |
✓ |
|
| \[
{} t x^{\prime \prime } = t x+1
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{\prime \prime }+t x^{\prime }+x = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 4 t^{2} x^{\prime \prime }+4 t x^{\prime }-x = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} t^{2} x^{\prime \prime }+3 t x^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} t^{2} x^{\prime \prime }-3 t x^{\prime }+\left (4-t \right ) x = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} t^{2} x^{\prime \prime }+t x^{\prime }+x t^{2} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+2 y^{\prime }+x y = 0
\]
|
✓ |
✗ |
✗ |
|
| \[
{} 2 y-x y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 2 x^{2} y^{\prime \prime }+7 x \left (1+x \right ) y^{\prime }-3 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x^{2}-4\right ) y^{\prime \prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x^{2}-4\right ) y^{\prime \prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+x y^{\prime }+\left (x^{2}+2\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x -1\right ) y^{\prime \prime }+x y^{\prime }+\frac {y}{x} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x -1\right ) y^{\prime \prime }+x y^{\prime }+\frac {y}{x} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x -1\right ) y^{\prime \prime }+x y^{\prime }+\frac {y}{x} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+x y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime }-y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+x y^{\prime }+\left (x^{2}+2\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+y^{\prime }+y = 0
\]
|
✓ |
✗ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime } = x y^{2}-y^{\prime }
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{\prime \prime }-s x = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime } = x^{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime } = y
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+4 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 2 y-x y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-x y^{\prime }-y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -4 y-6 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x^{2}+4\right ) y^{\prime \prime }+x y = x +2
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-\left (x -2\right ) y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+\left (x -1\right )^{2} y^{\prime }-4 \left (x -1\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+\left (x -1\right ) y = {\mathrm e}^{x}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x^{2}+2\right ) y^{\prime \prime }+\left (2 x +\frac {2}{x}\right ) y^{\prime }+2 x^{2} y = \frac {4 x^{2}+2 x +10}{x^{4}}
\]
|
✓ |
✗ |
✗ |
|
| \[
{} -2 y+2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -2 y+2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+x y^{\prime }+\left (2 x -1\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x^{2}-1\right ) y^{\prime \prime }+3 x y^{\prime }+x y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+x y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+\lambda \left (\lambda +1\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -b y a +\left (c -\left (1+a +b \right ) x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+x y^{\prime }+\left (2 x -1\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \cos \left (x \right ) u^{\prime \prime }+\sin \left (x \right ) u^{\prime }+\left (\cos \left (x \right )+\sin \left (x \right )\right ) u = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{\prime }+x^{2} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime } = y^{2} {\mathrm e}^{x}-{y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+3 y^{\prime }+\left (-x^{2}+1\right ) y = \frac {-x^{2}+x}{1+x}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x \left (x -1\right )^{2} \left (x +2\right ) y^{\prime \prime }+x^{2} y^{\prime }-\left (x^{3}+2 x -1\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{4} \left (x^{2}+1\right ) \left (x -1\right )^{2} y^{\prime \prime }+4 x^{3} \left (x -1\right ) y^{\prime }+\left (1+x \right ) y = 0
\]
|
✓ |
✓ |
✗ |
|