| # |
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]] |
✓ |
✓ |
✓ |
✓ |
0.618 |
|
| \begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.156 |
|
| \begin{align*}
\left (b x +a \right ) y+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.106 |
|
| \begin{align*}
y x -y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.138 |
|
| \begin{align*}
\left (c x +b \right ) y+a y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.193 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-y x -x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.168 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-y x -x^{2}&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.819 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-y x -x^{2}-1&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.173 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-y x -x^{2}-1&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.168 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-y x -x^{2}-2&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.180 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }-y x -x^{2}-4&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.180 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-y x -x^{3}+1&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.787 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-y x -x^{3}-x^{2}&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.179 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-y x -x^{3}+2&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.175 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-y x -x^{3}+2&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.177 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }-y x -x^{3}+2&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.184 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }-y x -x^{3}+2&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.186 |
|
| \begin{align*}
y^{\prime \prime }-8 y^{\prime }-y x -x^{3}+2&=0 \\
\end{align*} | [[_2nd_order, _linear, _nonhomogeneous]] | ✓ | ✓ | ✓ | ✗ | 0.184 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-y x -x^{4}+3&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.180 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-y x -x^{3}&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.684 |
|
| \begin{align*}
y^{\prime \prime }-y x -x^{3}+2&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.776 |
|
| \begin{align*}
y^{\prime \prime }-y x -x^{6}+64&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.040 |
|
| \begin{align*}
y^{\prime \prime }-y x -x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.460 |
|
| \begin{align*}
y^{\prime \prime }-y x -x^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.690 |
|
| \begin{align*}
y^{\prime \prime }-y x -x^{3}&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.462 |
|
| \begin{align*}
y^{\prime \prime }-y x -x^{6}-x^{3}+42&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.125 |
|
| \begin{align*}
y^{\prime \prime }+\left (a x +b \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.198 |
|
| \begin{align*}
4 y^{\prime \prime }+9 y x&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.441 |
|
| \begin{align*}
y^{\prime \prime }-\left (a x +b \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.138 |
|
| \begin{align*}
y^{\prime \prime }+a y^{\prime }+\left (b x +c \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.214 |
|
| \begin{align*}
x^{\prime \prime }+\left (t +1\right ) x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.134 |
|
| \begin{align*}
y^{\prime \prime }+t y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.152 |
|
| \begin{align*}
y^{\prime \prime }-t y&=\frac {1}{\pi } \\
\end{align*} |
unknown |
✓ |
✓ |
✓ |
✓ |
0.636 |
|
| \begin{align*}
y^{\prime \prime }+2 y x&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.486 |
|
| \begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.170 |
|
| \begin{align*}
y^{\prime \prime }+y x&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.655 |
|
| \begin{align*}
y^{\prime \prime }+y x&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} | [[_Emden, _Fowler]] | ✓ | ✓ | ✓ | ✓ | 0.338 |
|
| \begin{align*}
y^{\prime \prime }-2 y&=t y \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.125 |
|