| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y^{\prime \prime }+y^{\prime } = x +{\mathrm e}^{-x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y^{\prime }-2 y = \ln \left (x \right )+1
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+3 y^{\prime }-4 y = 12 \,{\mathrm e}^{2 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{2 x}}{\left ({\mathrm e}^{x}+1\right )^{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+i y = \cosh \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+4 y = x -4
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-4 y^{\prime }-5 y = x^{2} {\mathrm e}^{-x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-y^{\prime }-y = \sinh \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y = \cot \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y = 1
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+4 y = 8
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+4 y^{\prime }-5 y = 20
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y^{\prime } = -\cos \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-2 y^{\prime }-3 y = 27 x^{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-2 y^{\prime }-3 y = -6 x^{2}-8 x +4
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+4 y = 15 \,{\mathrm e}^{x}-8 x
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+4 y = 15 \,{\mathrm e}^{x}-8 x^{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y^{\prime }-2 y = 12 \,{\mathrm e}^{2 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y^{\prime }-2 y = 12 \,{\mathrm e}^{-2 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-4 y = 2+{\mathrm e}^{2 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-y^{\prime }-2 y = 6 x +6 \,{\mathrm e}^{-x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-4 y^{\prime }+3 y = 20 \cos \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-4 y^{\prime }+3 y = 2 \cos \left (x \right )+4 \sin \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y+2 y^{\prime }+y^{\prime \prime } = 7+75 \sin \left (2 x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 5 y+4 y^{\prime }+y^{\prime \prime } = 50 x +13 \,{\mathrm e}^{3 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y = \cos \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 4 y-4 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{2 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -y+y^{\prime \prime } = {\mathrm e}^{-x} \left (2 \sin \left (x \right )+4 \cos \left (x \right )\right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -y+y^{\prime \prime } = 8 x \,{\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -y+y^{\prime \prime } = 10 \sin \left (x \right )^{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y = 12 \cos \left (x \right )^{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+4 y = 4 \sin \left (x \right )^{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y = 10 \,{\mathrm e}^{2 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-4 y = 2-8 x
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+3 y^{\prime } = -18 x
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 5 y+4 y^{\prime }+y^{\prime \prime } = 10 \,{\mathrm e}^{-3 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{\prime \prime }+4 x^{\prime }+5 x = 10
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{\prime \prime }+4 x^{\prime }+5 x = 8 \sin \left (t \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y+2 y^{\prime }+y^{\prime \prime } = x
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y+2 y^{\prime }+y^{\prime \prime } = x
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 4 y^{\prime \prime }+y = 2
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 2 y^{\prime \prime }-5 y^{\prime }-3 y = -9 x^{2}-1
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y^{\prime } = 1+x
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y = x^{3}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+y = 2 \cos \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y^{\prime } = 2-2 x
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+9 y = \sin \left (3 x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+a^{2} y = \sin \left (b x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+a^{2} y = \sin \left (a x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+9 y = 4 \cos \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+9 y = 15 \cos \left (2 x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+9 y = 18 x -3+20 \,{\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-y^{\prime } = 42 \,{\mathrm e}^{4 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-4 y^{\prime }+3 y = {\mathrm e}^{2 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+6 y^{\prime }+14 y = 42 \,{\mathrm e}^{x}-7
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y = {\mathrm e}^{3 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y = 1+4 x
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y = \sin \left (2 x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y = \cos \left (2 x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y = {\mathrm e}^{x}-x +\sin \left (3 x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -y+y^{\prime \prime } = 2 x -3
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -y+y^{\prime \prime } = x +\sin \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -y+y^{\prime \prime } = {\mathrm e}^{2 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -y+y^{\prime \prime } = 16 \,{\mathrm e}^{3 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -y+y^{\prime \prime } = \cos \left (4 x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y^{\prime }+y = 6 \,{\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{-x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y^{\prime }+y = 4-{\mathrm e}^{2 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{-x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{2 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{3 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 4 y^{\prime \prime }-y = {\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 4 y^{\prime \prime }-y = x
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 4 y^{\prime \prime }-y = x +{\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y+2 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y+2 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{2 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y+2 y^{\prime }+y^{\prime \prime } = 7+{\mathrm e}^{x}+{\mathrm e}^{2 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{3 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+4 y^{\prime }+4 y = 12 x \,{\mathrm e}^{-2 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y+2 y^{\prime }+y^{\prime \prime } = 3 x \,{\mathrm e}^{-x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-y^{\prime }-2 y = 18 x \,{\mathrm e}^{-x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-y^{\prime }-2 y = 36 x \,{\mathrm e}^{2 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 4 y-4 y^{\prime }+y^{\prime \prime } = 20-3 x \,{\mathrm e}^{2 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 4 y-4 y^{\prime }+y^{\prime \prime } = 4-8 x +6 x \,{\mathrm e}^{2 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-9 y = 18 x -162 x \,{\mathrm e}^{2 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+4 y^{\prime }+4 y = 4 x -6 \,{\mathrm e}^{-2 x}+3 \,{\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y+2 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{-x}+3 x
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-4 y = 16 x \,{\mathrm e}^{-2 x}+8 x +4
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-4 y = 8 x \,{\mathrm e}^{2 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-9 y = -72 x \,{\mathrm e}^{-3 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y+2 y^{\prime }+y^{\prime \prime } = 48 \,{\mathrm e}^{-x} \cos \left (4 x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+4 y^{\prime }+4 y = 18 \,{\mathrm e}^{-2 x} \cos \left (3 x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x} \sec \left (x \right )^{2} \tan \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+4 y^{\prime }+4 y = -\frac {{\mathrm e}^{-2 x}}{x^{2}}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-2 a y^{\prime }+a^{2} y = {\mathrm e}^{a x}+f^{\prime \prime }\left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+7 y^{\prime }+12 y = {\mathrm e}^{-3 x} \sec \left (x \right )^{2} \left (1+2 \tan \left (x \right )\right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -y+y^{\prime \prime } = {\mathrm e}^{2 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -y+y^{\prime \prime } = {\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|