| # |
ODE |
CAS classification |
Solved |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime \prime }+y x&=\sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.873 |
|
| \begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.447 |
|
| \begin{align*}
\left (b x +a \right ) y+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.158 |
|
| \begin{align*}
y x -y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.402 |
|
| \begin{align*}
\left (c x +b \right ) y+a y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.517 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-y x -x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.357 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-y x -x^{2}&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.513 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-y x -x^{2}-1&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.345 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-y x -x^{2}-1&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.342 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-y x -x^{2}-2&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.344 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }-y x -x^{2}-4&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.349 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-y x -x^{3}+1&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.194 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-y x -x^{3}-x^{2}&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.359 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-y x -x^{3}+2&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.350 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-y x -x^{3}+2&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.351 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }-y x -x^{3}+2&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.345 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }-y x -x^{3}+2&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.358 |
|
| \begin{align*}
y^{\prime \prime }-8 y^{\prime }-y x -x^{3}+2&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.374 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-y x -x^{4}+3&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.363 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-y x -x^{3}&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.078 |
|
| \begin{align*}
y^{\prime \prime }-y x -x^{3}+2&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.868 |
|
| \begin{align*}
y^{\prime \prime }-y x -x^{6}+64&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.493 |
|
| \begin{align*}
y^{\prime \prime }-y x -x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.862 |
|
| \begin{align*}
y^{\prime \prime }-y x -x^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
5.979 |
|
| \begin{align*}
y^{\prime \prime }-y x -x^{3}&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.364 |
|
| \begin{align*}
y^{\prime \prime }-y x -x^{6}-x^{3}+42&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.743 |
|
| \begin{align*}
y^{\prime \prime }+\left (a x +b \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.132 |
|
| \begin{align*}
4 y^{\prime \prime }+9 y x&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.320 |
|
| \begin{align*}
y^{\prime \prime }-\left (a x +b \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.238 |
|
| \begin{align*}
y^{\prime \prime }+a y^{\prime }+\left (b x +c \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.509 |
|
| \begin{align*}
x^{\prime \prime }+\left (1+t \right ) x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.243 |
|
| \begin{align*}
y^{\prime \prime }+t y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.213 |
|
| \begin{align*}
y^{\prime \prime }-t y&=\frac {1}{\pi } \\
\end{align*} |
unknown |
✓ |
✓ |
✓ |
✓ |
0.969 |
|
| \begin{align*}
y^{\prime \prime }+2 y x&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.821 |
|
| \begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.596 |
|
| \begin{align*}
y^{\prime \prime }+y x&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.831 |
|
| \begin{align*}
y^{\prime \prime }+y x&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.908 |
|
| \begin{align*}
y^{\prime \prime }-2 y&=t y \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.142 |
|