| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y-2 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{x} \arcsin \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+3 y^{\prime }+2 y = \frac {{\mathrm e}^{-x}}{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y-2 y^{\prime }+y^{\prime \prime } = x \ln \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-6 x y^{\prime }+10 y = 3 x^{4}+6 x^{3}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (1+x \right )^{2} y^{\prime \prime }-2 y^{\prime } \left (1+x \right )+2 y = 1
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x^{2}+2 x \right ) y^{\prime \prime }-2 y^{\prime } \left (1+x \right )+2 y = \left (x +2\right )^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y = x^{3}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x \left (x -2\right ) y^{\prime \prime }-\left (x^{2}-2\right ) y^{\prime }+2 \left (x -1\right ) y = 3 x^{2} \left (x -2\right )^{2} {\mathrm e}^{x}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (2 x +1\right ) \left (1+x \right ) y^{\prime \prime }+2 x y^{\prime }-2 y = \left (2 x +1\right )^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \sin \left (x \right )^{2} y^{\prime \prime }-2 \sin \left (x \right ) \cos \left (x \right ) y^{\prime }+\left (\cos \left (x \right )^{2}+1\right ) y = \sin \left (x \right )^{3}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y = x^{2} {\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }-4 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+3 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+13 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 3 x^{2} y^{\prime \prime }-4 x y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-5 x y^{\prime }+10 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-10 x y^{\prime }-8 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-6 x y^{\prime }+18 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 4 x -6
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 2 x^{3}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 4 \ln \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 2 x \ln \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 4 \sin \left (\ln \left (x \right )\right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -2 y+2 x y^{\prime }-x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = x^{3}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }-10 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-2 y = 4 x -8
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = -6 x^{3}+4 x^{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 10 x^{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 2 x^{3}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-6 y = \ln \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x +2\right )^{2} y^{\prime \prime }-\left (x +2\right ) y^{\prime }-3 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (2 x -3\right )^{2} y^{\prime \prime }-6 \left (2 x -3\right ) y^{\prime }+12 y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y+x y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+8 x y^{\prime }-4 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}+1\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-4\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+x y^{\prime }+\left (2+3 x \right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-x y^{\prime }+\left (3 x -2\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+x y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x -1\right ) y^{\prime \prime }-\left (3 x -2\right ) y^{\prime }+2 x y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x^{3}-1\right ) y^{\prime \prime }+x^{2} y^{\prime }+x y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x +3\right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-x y^{\prime }-y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+x y^{\prime }-2 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+2 x y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (2 x^{2}-3\right ) y^{\prime \prime }-2 x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }-y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime \prime }+y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} n \left (n +1\right ) y-2 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x^{2}-3 x \right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x^{3}+x^{2}\right ) y^{\prime \prime }+\left (x^{2}-2 x \right ) y^{\prime }+4 y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x^{4}-2 x^{3}+x^{2}\right ) y^{\prime \prime }+2 \left (x -1\right ) y^{\prime }+x^{2} y = 0
\]
|
✓ |
✗ |
✗ |
|
| \[
{} \left (x^{5}+x^{4}-6 x^{3}\right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y = 0
\]
|
✓ |
✗ |
✗ |
|
| \[
{} 2 x^{2} y^{\prime \prime }+x y^{\prime }+y \left (x^{2}-1\right ) = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 2 x^{2} y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}-3\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+\frac {8}{9}\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+\left (2 x^{2}+\frac {5}{9}\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{9}\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 2 x y^{\prime \prime }+y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 3 x y^{\prime \prime }-\left (x -2\right ) y^{\prime }-2 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime \prime }+2 y^{\prime }+x y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+\left (x^{4}+x \right ) y^{\prime }-y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime \prime }-y^{\prime } \left (x^{2}+2\right )+x y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (2 x^{2}-x \right ) y^{\prime \prime }+\left (-2+2 x \right ) y^{\prime }+\left (-2 x^{2}+3 x -2\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+\frac {3 y}{4} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x -1\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }-3 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+8 y \left (x^{2}-1\right ) = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\frac {3 y}{4} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime \prime }+y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 2 x y^{\prime \prime }+6 y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+1\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}-3\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-2 x \left (t \right )-4 y \left (t \right ) = {\mathrm e}^{t}, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-y \left (t \right ) = {\mathrm e}^{4 t}]
\]
|
✓ |
✓ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right ) = -2 t, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-3 x \left (t \right )-y \left (t \right ) = t^{2}]
\]
|
✓ |
✓ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-3 y \left (t \right ) = {\mathrm e}^{t}, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+x \left (t \right ) = {\mathrm e}^{3 t}]
\]
|
✓ |
✓ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-2 y \left (t \right ) = 2 \,{\mathrm e}^{t}, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-3 x \left (t \right )-4 y \left (t \right ) = {\mathrm e}^{2 t}]
\]
|
✓ |
✓ |
✗ |
|
| \[
{} [2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-y \left (t \right ) = {\mathrm e}^{-t}, x^{\prime }\left (t \right )+2 x \left (t \right )+y^{\prime }\left (t \right )+y \left (t \right ) = {\mathrm e}^{t}]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-3 x \left (t \right )-y \left (t \right ) = t, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-4 x \left (t \right )-y \left (t \right ) = {\mathrm e}^{t}]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-6 y \left (t \right ) = {\mathrm e}^{3 t}, x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )-2 x \left (t \right )-6 y \left (t \right ) = t]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-3 y \left (t \right ) = 3 t, x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )-2 x \left (t \right )-3 y \left (t \right ) = 1]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 y \left (t \right ) = \sin \left (t \right ), x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-y \left (t \right ) = 0]
\]
|
✓ |
✓ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right )-y^{\prime }\left (t \right )-2 x \left (t \right )+4 y \left (t \right ) = t, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-y \left (t \right ) = 1]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+x \left (t \right )+5 y \left (t \right ) = 4 t, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 x \left (t \right )+2 y \left (t \right ) = 2]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )+5 y \left (t \right ) = t^{2}, x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )-2 x \left (t \right )+4 y \left (t \right ) = 2 t +1]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+x \left (t \right )+y \left (t \right ) = t^{2}+4 t, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 x \left (t \right )+2 y \left (t \right ) = 2 t^{2}-2 t]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [3 x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )-x \left (t \right )+y \left (t \right ) = t -1, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right ) = t +2]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [2 x^{\prime }\left (t \right )+4 y^{\prime }\left (t \right )+x \left (t \right )-y \left (t \right ) = 3 \,{\mathrm e}^{t}, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 x \left (t \right )+2 y \left (t \right ) = {\mathrm e}^{t}]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-y \left (t \right ) = -2 t, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+x \left (t \right )-y \left (t \right ) = t^{2}]
\]
|
✓ |
✓ |
✓ |
|