| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }&=4 y \\
\end{align*}
Series expansion around \(x=0\). |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.381 |
|
| \begin{align*}
2 y^{\prime }+3 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.378 |
|
| \begin{align*}
y^{\prime }+2 y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.388 |
|
| \begin{align*}
y^{\prime }&=y x \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.371 |
|
| \begin{align*}
\left (x -2\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.394 |
|
| \begin{align*}
\left (2 x -1\right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.411 |
|
| \begin{align*}
2 \left (x +1\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.399 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| \begin{align*}
2 \left (x -1\right ) y^{\prime }&=3 y \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.397 |
|
| \begin{align*}
y^{\prime \prime }&=y \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.282 |
|
| \begin{align*}
y^{\prime \prime }&=4 y \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.294 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.315 |
|
| \begin{align*}
y^{\prime \prime }+y&=x \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.344 |
|
| \begin{align*}
x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✓ |
✓ |
✓ |
✗ |
0.267 |
|
| \begin{align*}
2 x y^{\prime }&=y \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✓ |
✓ |
✓ |
✗ |
0.268 |
|
| \begin{align*}
x^{2} y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✗ |
✗ |
✓ |
✗ |
0.058 |
|
| \begin{align*}
x^{3} y^{\prime }&=2 y \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✗ |
✗ |
✓ |
✗ |
0.076 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.326 |
|
| \begin{align*}
y^{\prime \prime }-4 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.336 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.368 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.373 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.869 |
|
| \begin{align*}
y^{\prime \prime }&=y^{\prime }+y \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.401 |
|
| \begin{align*}
y^{\prime }&=1+y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.246 |
|
| \begin{align*}
y^{\prime \prime \prime }&=y \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= -1 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.095 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.352 |
|
| \begin{align*}
\left (x^{2}+2\right ) y^{\prime \prime }+4 x y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.410 |
|
| \begin{align*}
y^{\prime \prime }+x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+6 x y^{\prime }+4 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| \begin{align*}
\left (x^{2}-3\right ) y^{\prime \prime }+2 x y^{\prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.363 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
0.336 |
|
| \begin{align*}
\left (x^{2}+3\right ) y^{\prime \prime }-7 x y^{\prime }+16 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.412 |
|
| \begin{align*}
\left (-x^{2}+2\right ) y^{\prime \prime }-x y^{\prime }+16 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.412 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+8 x y^{\prime }+12 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
0.416 |
|
| \begin{align*}
3 y^{\prime \prime }+x y^{\prime }-4 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.354 |
|
| \begin{align*}
5 y^{\prime \prime }-2 x y^{\prime }+10 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.376 |
|
| \begin{align*}
y^{\prime \prime }-x^{2} y^{\prime }-3 y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.356 |
|
| \begin{align*}
y^{\prime \prime }+x^{2} y^{\prime }+2 y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| \begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.282 |
|
| \begin{align*}
y^{\prime \prime }+x^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.281 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.368 |
|
| \begin{align*}
y^{\prime \prime }+x y^{\prime }-2 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.333 |
|
| \begin{align*}
y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*}
Series expansion around \(x=1\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.402 |
|
| \begin{align*}
\left (-x^{2}+2 x \right ) y^{\prime \prime }-6 \left (x -1\right ) y^{\prime }-4 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*}
Series expansion around \(x=1\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.481 |
|
| \begin{align*}
\left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y&=0 \\
y \left (3\right ) &= 2 \\
y^{\prime }\left (3\right ) &= 0 \\
\end{align*}
Series expansion around \(x=3\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.402 |
|
| \begin{align*}
\left (4 x^{2}+16 x +17\right ) y^{\prime \prime }&=8 y \\
y \left (-2\right ) &= 1 \\
y^{\prime }\left (-2\right ) &= 0 \\
\end{align*}
Series expansion around \(x=-2\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| \begin{align*}
\left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y&=0 \\
y \left (-3\right ) &= 0 \\
y^{\prime }\left (-3\right ) &= 2 \\
\end{align*}
Series expansion around \(x=-3\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| \begin{align*}
y^{\prime \prime }+\left (x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.382 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }+2 y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.470 |
|
| \begin{align*}
y^{\prime \prime }+x^{2} y^{\prime }+x^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.385 |
|
| \begin{align*}
\left (x^{3}+1\right ) y^{\prime \prime }+x^{4} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.377 |
|
| \begin{align*}
y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}+1\right ) 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]] |
✓ |
✓ |
✓ |
✓ |
0.419 |
|
| \begin{align*}
y^{\prime \prime }+{\mathrm e}^{-x} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.557 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.624 |
|
| \begin{align*}
x y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
1.437 |
|
| \begin{align*}
y^{\prime \prime }-2 x y^{\prime }+2 \alpha y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.419 |
|
| \begin{align*}
x y^{\prime \prime }+\left (-x^{3}+x \right ) y^{\prime }+y \sin \left (x \right )&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.737 |
|
| \begin{align*}
x y^{\prime \prime }+x^{2} y^{\prime }+\left ({\mathrm e}^{x}-1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\cos \left (x \right ) y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✗ |
0.271 |
|
| \begin{align*}
3 x^{3} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (-x^{2}+1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✗ |
0.132 |
|
| \begin{align*}
x \left (x +1\right ) y^{\prime \prime }+2 y^{\prime }+3 y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.009 |
|
| \begin{align*}
x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.779 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+6 \sin \left (x \right ) y^{\prime }+6 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.713 |
|
| \begin{align*}
\left (2 x^{3}+6 x^{2}\right ) y^{\prime \prime }+21 x y^{\prime }+9 \left (x^{2}-1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.954 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime \prime }+x y^{\prime }+x^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.444 |
|
| \begin{align*}
\left (1-x \right )^{2} y^{\prime \prime }+\left (2 x -2\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.489 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+12 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
0.402 |
|
| \begin{align*}
\left (x -2\right )^{3} y^{\prime \prime }+3 \left (x -2\right )^{2} y^{\prime }+x^{3} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.573 |
|
| \begin{align*}
\left (x^{2}-4\right ) y^{\prime \prime }+\left (x -2\right ) y^{\prime }+\left (x +2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| \begin{align*}
\left (x^{2}-9\right )^{2} y^{\prime \prime }+\left (x^{2}+9\right ) y^{\prime }+\left (x^{2}+4\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.661 |
|
| \begin{align*}
\left (x -2\right )^{2} y^{\prime \prime }-\left (x^{2}-4\right ) y^{\prime }+\left (x +2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| \begin{align*}
x^{3} \left (1-x \right ) y^{\prime \prime }+\left (3 x +2\right ) y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✗ |
0.153 |
|
| \begin{align*}
4 x y^{\prime \prime }+2 y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.856 |
|
| \begin{align*}
2 x y^{\prime \prime }+3 y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.834 |
|
| \begin{align*}
2 x y^{\prime \prime }-y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.843 |
|
| \begin{align*}
3 x y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.852 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+x y^{\prime }-\left (2 x^{2}+1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.730 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+x y^{\prime }-\left (-2 x^{2}+3\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.728 |
|
| \begin{align*}
6 x^{2} y^{\prime \prime }+7 x y^{\prime }-\left (x^{2}+2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.728 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }+2 x y^{\prime }+x^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.690 |
|
| \begin{align*}
2 x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.848 |
|
| \begin{align*}
2 x y^{\prime \prime }+\left (-2 x^{2}+1\right ) y^{\prime }-4 y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.749 |
|
| \begin{align*}
x y^{\prime \prime }+2 y^{\prime }+9 y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.735 |
|
| \begin{align*}
x y^{\prime \prime }+2 y^{\prime }-4 y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| \begin{align*}
4 x y^{\prime \prime }+8 y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| \begin{align*}
x y^{\prime \prime }-y^{\prime }+4 x^{3} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.688 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-4 x^{2}+3\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (2 x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.892 |
|
| \begin{align*}
\left (5 x^{3}+2 x^{2}\right ) y^{\prime \prime }+\left (-x^{2}+3 x \right ) y^{\prime }-\left (x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.999 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.754 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
✗ |
✓ |
✗ |
0.200 |
|
| \begin{align*}
x^{3} y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
✗ |
✓ |
✗ |
0.112 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.767 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Bessel] |
✓ |
✓ |
✓ |
✓ |
1.750 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (1-x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.659 |
|
| \begin{align*}
x \left (x -1\right ) \left (x +1\right )^{2} y^{\prime \prime }+2 x \left (x -3\right ) \left (x +1\right ) y^{\prime }-2 \left (x -1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.751 |
|
| \begin{align*}
x \left (1-x \right ) y^{\prime \prime }+\left (\gamma -\left (\alpha +\beta +1\right ) x \right ) y^{\prime }-\alpha \beta y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Jacobi] |
✓ |
✓ |
✓ |
✗ |
1.247 |
|
| \begin{align*}
x y^{\prime \prime }+\left (-x +3\right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.852 |
|
| \begin{align*}
x y^{\prime \prime }+\left (5-x \right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.856 |
|
| \begin{align*}
x y^{\prime \prime }+\left (5+3 x \right ) y^{\prime }+3 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.865 |
|