| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }&=3 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.944 |
|
| \begin{align*}
y^{\prime \prime }-7 y^{\prime }&=\left (x -1\right )^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.884 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }&={\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.799 |
|
| \begin{align*}
y^{\prime \prime }+7 y^{\prime }&={\mathrm e}^{-7 x} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.796 |
|
| \begin{align*}
y^{\prime \prime }-8 y^{\prime }+16 y&=\left (1-x \right ) {\mathrm e}^{4 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.438 |
|
| \begin{align*}
y^{\prime \prime }-10 y^{\prime }+25 y&={\mathrm e}^{5 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.410 |
|
| \begin{align*}
4 y^{\prime \prime }-3 y^{\prime }&=x \,{\mathrm e}^{\frac {3 x}{4}} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.954 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{x}+{\mathrm e}^{-2 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.368 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }&={\mathrm e}^{4 x} x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.888 |
|
| \begin{align*}
y^{\prime \prime }+25 y&=\cos \left (5 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.445 |
|
| \begin{align*}
y^{\prime \prime }+y&=-\cos \left (x \right )+\sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.456 |
|
| \begin{align*}
y^{\prime \prime }+16 y&=\sin \left (4 x +\alpha \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.625 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+8 y&={\mathrm e}^{2 x} \left (\cos \left (2 x \right )+\sin \left (2 x \right )\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.438 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+8 y&={\mathrm e}^{2 x} \left (\sin \left (2 x \right )-\cos \left (2 x \right )\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.431 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+13 y&={\mathrm e}^{-3 x} \cos \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.421 |
|
| \begin{align*}
y^{\prime \prime }+k^{2} y&=k \sin \left (x k +\alpha \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.165 |
|
| \begin{align*}
y^{\prime \prime }+k^{2} y&=k \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
5.878 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=\sin \left (2 x \right ) \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.790 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }&=2 \cos \left (4 x \right )^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.118 |
|
| \begin{align*}
y^{\prime \prime \prime }+y&=x \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.097 |
|
| \begin{align*}
y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y&=1 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.102 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime }&=2 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.089 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }&=3 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.086 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y&=1 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.089 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y^{\prime }&=2 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.103 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y^{\prime \prime }&=3 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.093 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }&=4 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.096 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+4 y^{\prime \prime }&=1 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.103 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+y^{\prime \prime }&={\mathrm e}^{4 x} \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.105 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+y^{\prime \prime }&={\mathrm e}^{-x} \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.115 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+y^{\prime \prime }&=x \,{\mathrm e}^{-x} \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.117 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y&=\sin \left (2 x \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.132 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y&=\cos \left (x \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.121 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y&=\sin \left (2 x \right ) x \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.158 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+2 n^{2} y^{\prime \prime }+n^{4} y&=a \sin \left (x n +\alpha \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.740 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-2 n^{2} y^{\prime \prime }+n^{4} y&=\cos \left (x n +\alpha \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.146 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }+y&=\sin \left (x \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.118 |
|
| \begin{align*}
y-4 y^{\prime }+6 y^{\prime \prime }-4 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&={\mathrm e}^{x} \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.117 |
|
| \begin{align*}
y-4 y^{\prime }+6 y^{\prime \prime }-4 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=x \,{\mathrm e}^{x} \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.144 |
|
| \begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=-2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.368 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.896 |
|
| \begin{align*}
y^{\prime \prime }+9 y-9&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.781 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }&=1 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.076 |
|
| \begin{align*}
5 y^{\prime \prime \prime }-7 y^{\prime \prime }-3&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.092 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+6&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.101 |
|
| \begin{align*}
3 y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }&=2 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.096 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y&=1 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.096 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.428 |
|
| \begin{align*}
y^{\prime \prime }+8 y^{\prime }&=8 x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.944 |
|
| \begin{align*}
y^{\prime \prime }-2 k y^{\prime }+k^{2} y&={\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.404 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=8 \,{\mathrm e}^{-2 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.443 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&=9 \,{\mathrm e}^{-3 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.369 |
|
| \begin{align*}
7 y^{\prime \prime }-y^{\prime }&=14 x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.895 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }&=3 x \,{\mathrm e}^{-3 x} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.957 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=10 \left (1-x \right ) {\mathrm e}^{-2 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.412 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=x +1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.361 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\left (x^{2}+x \right ) {\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.480 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }-2 y&=8 \sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.431 |
|
| \begin{align*}
y^{\prime \prime }+y&=4 \cos \left (x \right ) x \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.473 |
|
| \begin{align*}
y^{\prime \prime }-2 m y^{\prime }+m^{2} y&=\sin \left (x n \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| \begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&=\sin \left (2 x \right ) {\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| \begin{align*}
y^{\prime \prime }+a^{2} y&=2 \cos \left (x m \right )+3 \sin \left (x m \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }&={\mathrm e}^{x} \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.003 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }&=4 \,{\mathrm e}^{x} \left (\cos \left (x \right )+\sin \left (x \right )\right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.112 |
|
| \begin{align*}
5 y+4 y^{\prime }+y^{\prime \prime }&=10 \,{\mathrm e}^{-2 x} \cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.424 |
|
| \begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-2 x} \left (2 x +\sin \left (2 x \right )\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.507 |
|
| \begin{align*}
4 y^{\prime \prime }+8 y^{\prime }&=x \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.098 |
|
| \begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=x \,{\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.378 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=x^{2} {\mathrm e}^{4 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.376 |
|
| \begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=\left (x^{2}+x \right ) {\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.388 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=x^{2}+x \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.116 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y&={\mathrm e}^{x} \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.129 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=x^{3} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.433 |
|
| \begin{align*}
5 y^{\prime \prime }-6 y^{\prime }+5 y&=13 \,{\mathrm e}^{x} \cosh \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+y^{\prime \prime }&=x^{2}+x \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.112 |
|
| \begin{align*}
y^{\left (5\right )}-y^{\prime \prime \prime \prime }&=x \,{\mathrm e}^{x}-1 \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.163 |
|
| \begin{align*}
y^{\prime \prime }+y&=x^{2} \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.532 |
|
| \begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{-x} \cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.556 |
|
| \begin{align*}
-4 y^{\prime }+y^{\prime \prime \prime }&=x \,{\mathrm e}^{2 x}+\sin \left (x \right )+x^{2} \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.404 |
|
| \begin{align*}
y^{\prime \prime \prime }-y&=\sin \left (x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.110 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=\cos \left (x \right ) {\mathrm e}^{-x}+x \,{\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.467 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y&=\cos \left (x \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.117 |
|
| \begin{align*}
y^{\prime \prime }+y&=2 \sin \left (2 x \right ) \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.720 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=x \sin \left (x \right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y&=x \,{\mathrm e}^{x}+\frac {\cos \left (x \right )}{2} \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=\cos \left (x \right )^{2}+{\mathrm e}^{x}+x^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.372 |
|
| \begin{align*}
y^{\left (5\right )}+4 y^{\prime \prime \prime }&={\mathrm e}^{x}+3 \sin \left (2 x \right )+1 \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.654 |
|
| \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&={\mathrm e}^{x} \cos \left (2 x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.121 |
|
| \begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime }+4 y&={\mathrm e}^{x} \cos \left (x \right )+x^{2}+\sin \left (2 x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
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3.225 |
|