| # | ODE | Mathematica | Maple | Sympy |
| \[
{} \left (x \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+y \cos \left (x \right ) = x
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime }-3 y^{\prime }+\frac {3 y}{x} = x +2
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (1+x \right ) y^{\prime \prime }-\left (3 x +4\right ) y^{\prime }+3 y = \left (2+3 x \right ) {\mathrm e}^{3 x}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime }+2 y^{\prime }+4 x y = 4
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime } = \frac {-x^{2}+1}{x}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = \frac {2}{x^{3}}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime \prime }-y^{\prime } = -\frac {2}{x}-\ln \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (1-x \right ) y^{\prime \prime }-4 x y^{\prime }+5 y = \cos \left (x \right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+y = \sec \left (\ln \left (x \right )\right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y+x y^{\prime }+y^{\prime \prime } = 2 x \,{\mathrm e}^{x}-1
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime }+x y^{\prime }-y = x^{2}+2 x
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{2}+2 x
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -y+x y^{\prime }+x^{3} y^{\prime \prime } = \cos \left (\frac {1}{x}\right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x \left (1+x \right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }-y = x +\frac {1}{x}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 x y^{\prime \prime }+\left (x -2\right ) y^{\prime }-y = x^{2}-1
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (4 x +3\right ) y^{\prime }-y = x +\frac {1}{x}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-x y^{\prime }+y = x \left (1-\ln \left (x \right )\right )^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime }+2 y^{\prime }+x y = \sec \left (x \right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+\frac {y}{4} = -\frac {x^{2}}{2}+\frac {1}{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (\cos \left (x \right )+\sin \left (x \right )\right ) y^{\prime \prime }-2 \cos \left (x \right ) y^{\prime }+\left (\cos \left (x \right )-\sin \left (x \right )\right ) y = \left (\cos \left (x \right )+\sin \left (x \right )\right )^{2} {\mathrm e}^{2 x}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (\cos \left (x \right )-\sin \left (x \right )\right ) y^{\prime \prime }-2 y^{\prime } \sin \left (x \right )+y \left (\cos \left (x \right )+\sin \left (x \right )\right ) = \left (\cos \left (x \right )-\sin \left (x \right )\right )^{2}
\]
|
✓ |
✗ |
✗ |
|
| \[
{} p \,x^{2} u^{\prime \prime }+q x u^{\prime }+r u = f \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = x^{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 1
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }-4 \pi y = x
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+{\mathrm e}^{x} y^{\prime } = {\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime \prime }-2 y^{\prime } = x^{3}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime \prime }+y^{\prime } = 4 x
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime \prime }-3 y^{\prime } = 5 x
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = \left (x^{2}-1\right )^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x^{2}+x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-\left (x +2\right ) y = x \left (1+x \right )^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -y+x y^{\prime }+\left (1-x \right ) y^{\prime \prime } = \left (1-x \right )^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y-y^{\prime } \left (1+x \right )+x y^{\prime \prime } = x^{2} {\mathrm e}^{2 x}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = x \,{\mathrm e}^{-x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {2}{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} t y^{\prime \prime }-y^{\prime } = 2 t^{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 2 y^{\prime \prime }+t y^{\prime }-2 y = 10
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime } = y^{\prime }+x^{5}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime \prime }+y^{\prime }+x = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -x^{2} y^{\prime }+x^{3} y^{\prime \prime } = -x^{2}+3
\]
|
✓ |
✓ |
✓ |
|
| \[
{} t y^{\prime \prime }+4 y^{\prime } = t^{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-x y^{\prime }-x y-x = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-x y^{\prime }-x y-2 x = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-x y^{\prime }-x y-3 x = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-x y^{\prime }-x y-x^{2}-x = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-x y^{\prime }-x y-x^{3}+2 = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-x y^{\prime }-x y-x^{4}-6 = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-x y^{\prime }-x y-x^{5}+24 = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-x y^{\prime }-x y-x = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-x y^{\prime }-x y-x^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-x y^{\prime }-x y-x^{3} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-a x y^{\prime }-b x y-c x = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{3} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-y^{\prime }-x y-x = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-y^{\prime }-x y-x^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-y^{\prime }-x y-x^{2}-1 = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-y^{\prime }-x y-x^{2}-1 = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-2 y^{\prime }-x y-x^{2}-2 = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-4 y^{\prime }-x y-x^{2}-4 = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-y^{\prime }-x y-x^{3}+1 = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-2 y^{\prime }-x y-x^{3}-x^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-y^{\prime }-x y-x^{3}+2 = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-2 y^{\prime }-x y-x^{3}+2 = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-4 y^{\prime }-x y-x^{3}+2 = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-6 y^{\prime }-x y-x^{3}+2 = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-8 y^{\prime }-x y-x^{3}+2 = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-y^{\prime }-x y-x^{4}+3 = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-y^{\prime }-x y-x^{3} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-x y-x^{3}+2 = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-x y-x^{6}+64 = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-x y-x = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-x y-x^{2} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-x y-x^{3} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-x y-x^{6}-x^{3}+42 = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-x^{2} y-x^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-x^{2} y-x^{3} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-x^{2} y-x^{4} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-x^{2} y-x^{4}+2 = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-2 x^{2} y-x^{4}+1 = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-x^{3} y-x^{3} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-x^{3} y-x^{4} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-x^{2} y^{\prime }-x^{2} y-x^{2} = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-x^{3} y^{\prime }-x^{3} y-x^{3} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }-x y^{\prime }-x y-x = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-x^{2} y^{\prime }-x y-x^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-x^{2} y^{\prime }-x^{2} y-x^{3}-x^{2} = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-x^{2} y^{\prime }-x^{3} y-x^{4}-x^{2} = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-\frac {y^{\prime }}{x}-x y-x^{2}-\frac {1}{x} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{2} y-x^{3}-\frac {1}{x} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{3} y-x^{4}-\frac {1}{x} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-x^{3} y^{\prime }-x y-x^{3}-x^{2} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }-x^{3} y^{\prime }-x^{2} y-x^{3} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-x^{3} y^{\prime }-x^{3} y-x^{4}-x^{3} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y = 1
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y = x
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }-4 y = x
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 4 x^{2} y^{\prime \prime }+y = 8 \sqrt {x}\, \left (\ln \left (x \right )+1\right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \frac {x y^{\prime \prime }}{1-x}+y = \frac {1}{1-x}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \frac {x y^{\prime \prime }}{1-x}+y = \cos \left (x \right )
\]
|
✓ |
✓ |
✗ |
|