| # | ODE | Mathematica | Maple | Sympy |
| \[
{} 4 y^{\prime \prime }+8 y^{\prime }+4 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-2 r y^{\prime }+\left (r^{2}-\frac {\alpha ^{2}}{4}\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-2 \left (r +\beta \right ) y^{\prime }+r^{2} y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 5 x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 3 x^{2} y^{\prime \prime }+4 x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+4 x y^{\prime }-4 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x -1\right )^{2} y^{\prime \prime }+5 \left (x -1\right ) y^{\prime }+4 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -3 y+x y^{\prime }+2 x^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+5 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+\frac {7 x y^{\prime }}{2}-\frac {3 y}{2} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x +3\right )^{2} y^{\prime \prime }+3 \left (x +3\right ) y^{\prime }+5 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x -2\right )^{2} y^{\prime \prime }-\left (x -2\right ) y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-6 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+\frac {7 x y^{\prime }}{2}-\frac {3 y}{2} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-\frac {5 y^{\prime }}{x}+\frac {5 y}{x^{2}} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 3 x y^{\prime \prime }-4 y^{\prime }+\frac {5 y}{x} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x -4\right ) y^{\prime \prime }+4 y^{\prime }-\frac {4 y}{x -4} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x +2\right ) y^{\prime \prime }-y^{\prime }+\frac {y}{x +2} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+\frac {5 y^{\prime }}{x -1}+\frac {4 y}{\left (x -1\right )^{2}} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 5 y^{\prime \prime }+\frac {3 y^{\prime }}{x -3}+\frac {3 y}{\left (x -3\right )^{2}} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }-y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+\left (2 x^{2}-x \right ) y^{\prime }-2 x y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{3} y^{\prime \prime }+\left (5 x^{3}-x^{2}\right ) y^{\prime }+2 \left (3 x^{3}-x^{2}\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }-y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (x +2\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime }+\left (x -1\right ) y^{\prime }+\left (3-12 x \right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} \left (1-\ln \left (x \right )\right ) y^{\prime \prime }+x y^{\prime }-y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {9 y}{x^{4}} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-7 x y^{\prime }+7 y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+\frac {y^{\prime }}{x^{{1}/{3}}}+\left (\frac {1}{4 x^{{2}/{3}}}-\frac {1}{6 x^{{4}/{3}}}-\frac {6}{x^{2}}\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x \left (x -2\right ) y^{\prime \prime }-2 \left (x^{2}-3 x +3\right ) y^{\prime }+\left (x^{2}-4 x +6\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x \left (1-3 x \ln \left (x \right )\right ) y^{\prime \prime }+\left (1+9 x^{2} \ln \left (x \right )\right ) y^{\prime }-\left (3+9 x \right ) y = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-\left (1+\frac {3}{2 x}\right ) y^{\prime }+\frac {3 y}{2 x^{2}} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x \left (1-2 x \ln \left (x \right )\right ) y^{\prime \prime }+\left (1+4 x^{2} \ln \left (x \right )\right ) y^{\prime }-\left (4 x +2\right ) y = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 6 y-2 x y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+12 y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+3 y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y-x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+4 y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+9 y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-5 y^{\prime }+6 y = x^{2}+3
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+4 y^{\prime }+4 y = {\mathrm e}^{x}+{\mathrm e}^{-2 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-y^{\prime }-2 y = \cos \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-y = {\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+9 y = \cos \left (3 x \right )-\sin \left (3 x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-13 y^{\prime }+36 y = x \,{\mathrm e}^{4 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = \tan \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-10 y^{\prime }+25 y = x^{2} {\mathrm e}^{5 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+4 x y^{\prime }-10 y = x \ln \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 3 x^{2} y^{\prime \prime }-2 x y^{\prime }-8 y = 5+3 x
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y^{\prime } = {\mathrm e}^{-x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime \prime }-2 y^{\prime }+\frac {\left (x^{2}+2\right ) y}{x} = 4+\tan \left (x \right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+5 y^{\prime } = \sin \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y = x
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-3 y = \cos \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+2 y = {\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-y = {\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y = x +2 \,{\mathrm e}^{-x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-y = {\mathrm e}^{x}+\sin \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{2 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-y = x \,{\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y = x +{\mathrm e}^{-x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-y = {\mathrm e}^{x}+\sin \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{2 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-y = x \,{\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+4 y = 4 x^{3}-8 x^{2}-14 x +7
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y = {\mathrm e}^{x} \left (1+x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-y = x \sin \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{-x} \cos \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 2 y^{\prime \prime }+y^{\prime }-y = {\mathrm e}^{x} \left (x^{2}-1\right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-2 y^{\prime }+y = x \,{\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y = \sin \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+4 y = \sin \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-y^{\prime }-2 y = 2 x \,{\mathrm e}^{-x}+x^{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-y = 4 \cosh \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime } = 3
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+4 x y^{\prime }-4 y = x^{3}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }-8 y = {\mathrm e}^{x} \left (x^{2}+2\right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{x} \sin \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-7 y^{\prime }-8 y = {\mathrm e}^{x} \left (x^{2}+2\right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-5 y^{\prime }+4 y = {\mathrm e}^{2 x} \cos \left (x \right )+{\mathrm e}^{2 x} \sin \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+2 y^{\prime }-3 y = {\mathrm e}^{2 x} \left (x +3\right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y = x +2 \,{\mathrm e}^{-x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-y = x \,{\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{2 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|