| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.697 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-30 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.620 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.827 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.356 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.635 |
|
| \begin{align*}
y^{\prime \prime }-7 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
6.218 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.823 |
|
| \begin{align*}
3 y+2 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.803 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }-5 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.723 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+\frac {y}{4}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.862 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.245 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-9 y^{\prime \prime }+20 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.227 |
|
| \begin{align*}
y^{\prime }-5 y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.813 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+2 y^{\prime }+36 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.224 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+7 y^{\prime \prime }-4 y^{\prime }+6 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.253 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+24 y^{\prime \prime }+32 y^{\prime }+16 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.247 |
|
| \begin{align*}
y^{\left (5\right )}-y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }-y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.251 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+32 y^{\prime \prime }-64 y^{\prime }+64 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.255 |
|
| \begin{align*}
y^{\left (6\right )}-5 y^{\prime \prime \prime \prime }+16 y^{\prime \prime \prime }-16 y^{\prime }-32 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.323 |
|
| \begin{align*}
2 y-y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.216 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.213 |
|
| \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.223 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.223 |
|
| \begin{align*}
y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.239 |
|
| \begin{align*}
-y-2 y^{\prime }+2 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.238 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+16 y^{\prime }+32 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.264 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.228 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }+y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.255 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=4 x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.989 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.989 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=\sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.053 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=2 x \,{\mathrm e}^{-x} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.441 |
|
| \begin{align*}
y^{\prime \prime }&=9 x^{2}+2 x -1 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.974 |
|
| \begin{align*}
y^{\prime }-5 y&=2 \,{\mathrm e}^{x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.638 |
|
| \begin{align*}
y^{\prime }-5 y&=\sin \left (x \right ) \left (-1+x \right )+\left (x +1\right ) \cos \left (x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.673 |
|
| \begin{align*}
y^{\prime }-5 y&=3 \,{\mathrm e}^{x}-2 x +1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.344 |
|
| \begin{align*}
y^{\prime }-5 y&={\mathrm e}^{x} x^{2}-x \,{\mathrm e}^{5 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.369 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=x^{2}-1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.281 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.254 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=4 \cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.352 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.266 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=x \,{\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.286 |
|
| \begin{align*}
y^{\prime }-y&={\mathrm e}^{x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.531 |
|
| \begin{align*}
y^{\prime }-y&=x \,{\mathrm e}^{2 x}+1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.401 |
|
| \begin{align*}
y^{\prime }-y&=\sin \left (x \right )+\cos \left (2 x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.451 |
|
| \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&={\mathrm e}^{x}+1 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.457 |
|
| \begin{align*}
y^{\prime \prime \prime }+y&=\sec \left (x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.229 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.274 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.999 |
|
| \begin{align*}
y^{\prime }+\frac {4 y}{x}&=x^{4} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
14.934 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }&=5 x \\
\end{align*} |
[[_high_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.359 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x^{5}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.305 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.981 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=\sin \left (2 x \right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.746 |
|
| \begin{align*}
y^{\prime \prime }-\frac {y}{x}&=x^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.020 |
|
| \begin{align*}
y^{\prime \prime }+2 y x&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.362 |
|
| \begin{align*}
y^{\prime \prime \prime }&=12 \\
\end{align*} |
[[_3rd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.313 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=4 x^{2} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.708 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.705 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+8 y&=\sin \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.922 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\
y \left (\pi \right ) &= 0 \\
y^{\prime }\left (\pi \right ) &= 0 \\
y^{\prime \prime }\left (\pi \right ) &= 1 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.543 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.704 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.724 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.273 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.493 |
|
| \begin{align*}
y^{\prime \prime }+y&=x \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.343 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=\sin \left (2 x \right )^{2} \\
y \left (\pi \right ) &= 0 \\
y^{\prime }\left (\pi \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.677 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (2\right ) &= 0 \\
y^{\prime }\left (2\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
4.799 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=\cos \left (2 x \right )+\sin \left (2 x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.823 |
|
| \begin{align*}
\left (x^{2}-4\right ) y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=1\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.724 |
|
| \begin{align*}
\left (x^{2}-4\right ) y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=2\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
14.037 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+7 x \left (x +1\right ) y^{\prime }-3 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.382 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✗ |
0.736 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y x&=0 \\
\end{align*}
Series expansion around \(x=1\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.425 |
|
| \begin{align*}
\left (x -2\right ) y^{\prime \prime }+3 \left (x^{2}-3 x +2\right ) y^{\prime }+\left (x -2\right )^{2} x y&=0 \\
\end{align*}
Series expansion around \(x=2\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.670 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.249 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+y x&=0 \\
\end{align*}
Series expansion around \(x=-1\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
16.421 |
|
| \begin{align*}
x^{3} y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✗ |
✓ |
✗ |
0.570 |
|
| \begin{align*}
x^{3} y^{\prime \prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✗ |
1.658 |
|
| \begin{align*}
{\mathrm e}^{x} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
6.492 |
|
| \begin{align*}
\left (x +1\right )^{3} y^{\prime \prime }+\left (x^{2}-1\right ) \left (x +1\right ) y^{\prime }+\left (-1+x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=-1\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✗ |
0.819 |
|
| \begin{align*}
x^{4} \left (x^{2}-4\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+\left (x^{2}-3 x +2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=2\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.068 |
|
| \begin{align*}
2 y-y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Hermite] |
✓ |
✓ |
✓ |
✓ |
1.682 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.143 |
|
| \begin{align*}
y^{\prime \prime }-\left (x -2\right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=2\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.869 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime } x +\left (2 x -1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=-1\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.745 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime } x +\left (2 x -1\right ) y&=0 \\
y \left (-1\right ) &= 2 \\
y^{\prime }\left (-1\right ) &= -2 \\
\end{align*}
Series expansion around \(x=-1\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.362 |
|
| \begin{align*}
y^{\prime \prime }-2 y x&=0 \\
y \left (2\right ) &= 1 \\
y^{\prime }\left (2\right ) &= 6 \\
\end{align*}
Series expansion around \(x=2\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.885 |
|
| \begin{align*}
y^{\prime \prime }+y x&=2 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.677 |
|
| \begin{align*}
\left (x^{2}+4\right ) y^{\prime \prime }+y x&=2+x \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.526 |
|
| \begin{align*}
y^{\prime \prime }+\left (-1+x \right ) y&={\mathrm e}^{x} \\
\end{align*}
Series expansion around \(x=1\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.681 |
|
| \begin{align*}
n \left (n +1\right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
1.651 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.302 |
|
| \begin{align*}
y^{\prime \prime }-y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.360 |
|
| \begin{align*}
y^{\prime \prime }-y x&=0 \\
\end{align*}
Series expansion around \(x=1\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.885 |
|
| \begin{align*}
y^{\prime \prime }-x^{2} y^{\prime }+\left (2+x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=-2\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.503 |
|
| \begin{align*}
\left (x^{2}+4\right ) y^{\prime \prime }+y&=x \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.493 |
|
| \begin{align*}
y^{\prime \prime }-\left (-1+x \right ) y^{\prime }&=x^{2}-2 x \\
\end{align*}
Series expansion around \(x=1\). |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
1.658 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime } x&={\mathrm e}^{-x} \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
1.509 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime } x +x^{2} y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.984 |
|