| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
\left (x^{2}-9\right )^{2} y^{\prime \prime }+\left (x +3\right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.774 |
|
| \begin{align*}
y^{\prime \prime }-\frac {y^{\prime }}{x}+\frac {y}{\left (x -1\right )^{3}}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
5.382 |
|
| \begin{align*}
\left (x^{3}+4 x \right ) y^{\prime \prime }-2 x y^{\prime }+6 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.702 |
|
| \begin{align*}
x^{2} \left (x -5\right )^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}-25\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.480 |
|
| \begin{align*}
\left (x^{2}+x -6\right ) y^{\prime \prime }+\left (x +3\right ) y^{\prime }+\left (x -2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| \begin{align*}
x \left (x^{2}+1\right )^{2} y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.282 |
|
| \begin{align*}
x^{3} \left (x^{2}-25\right ) \left (x -2\right )^{2} y^{\prime \prime }+3 x \left (x -2\right ) y^{\prime }+7 \left (5+x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✗ |
0.267 |
|
| \begin{align*}
\left (x^{3}-2 x^{2}+3 x \right )^{2} y^{\prime \prime }+x \left (x -3\right )^{2} y^{\prime }-\left (x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.256 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+5 \left (x +1\right ) y^{\prime }+\left (x^{2}-x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.735 |
|
| \begin{align*}
x y^{\prime \prime }+\left (x +3\right ) y^{\prime }+7 x^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.346 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.016 |
|
| \begin{align*}
x y^{\prime \prime }+y^{\prime }+10 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.908 |
|
| \begin{align*}
2 x y^{\prime \prime }-y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.085 |
|
| \begin{align*}
2 x y^{\prime \prime }+5 y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.872 |
|
| \begin{align*}
4 x y^{\prime \prime }+\frac {y^{\prime }}{2}+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.075 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.869 |
|
| \begin{align*}
3 x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.107 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-\left (x -\frac {2}{9}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.937 |
|
| \begin{align*}
2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Laguerre] |
✓ |
✓ |
✓ |
✓ |
1.115 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {4}{9}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.860 |
|
| \begin{align*}
9 x^{2} y^{\prime \prime }+9 x^{2} y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.007 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (2 x -1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.984 |
|
| \begin{align*}
x y^{\prime \prime }+2 y^{\prime }-y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.899 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.915 |
|
| \begin{align*}
x y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Laguerre, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.402 |
|
| \begin{align*}
y^{\prime \prime }+\frac {3 y^{\prime }}{x}-2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.315 |
|
| \begin{align*}
x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.942 |
|
| \begin{align*}
x y^{\prime \prime }+y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.898 |
|
| \begin{align*}
x y^{\prime \prime }+\left (-6+x \right ) y^{\prime }-3 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.431 |
|
| \begin{align*}
x \left (x -1\right ) y^{\prime \prime }+3 y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.095 |
|
| \begin{align*}
x^{4} y^{\prime \prime }+\lambda y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✗ |
✓ |
✗ |
0.282 |
|
| \begin{align*}
x^{3} y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✗ |
✗ |
✓ |
✗ |
0.161 |
|
| \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]] |
✗ |
✗ |
✓ |
✗ |
0.370 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{9}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.865 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
4.116 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-25\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.927 |
|
| \begin{align*}
16 x^{2} y^{\prime \prime }+16 x y^{\prime }+\left (16 x^{2}-1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.875 |
|
| \begin{align*}
x y^{\prime \prime }+y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.716 |
|
| \begin{align*}
y^{\prime }+x y^{\prime \prime }+\left (x -\frac {4}{x}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Bessel] |
✓ |
✓ |
✓ |
✓ |
4.115 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (9 x^{2}-4\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.089 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.925 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (25 x^{2}-\frac {4}{9}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.874 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}-64\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
4.999 |
|
| \begin{align*}
x y^{\prime \prime }+2 y^{\prime }+4 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.401 |
|
| \begin{align*}
x y^{\prime \prime }+3 y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
3.196 |
|
| \begin{align*}
x y^{\prime \prime }-y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
3.417 |
|
| \begin{align*}
x y^{\prime \prime }-5 y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✗ |
3.273 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.868 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+\left (16 x^{2}+1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.744 |
|
| \begin{align*}
x y^{\prime \prime }+3 y^{\prime }+x^{3} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.961 |
|
| \begin{align*}
9 x^{2} y^{\prime \prime }+9 x y^{\prime }+\left (x^{6}-36\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.891 |
|
| \begin{align*}
y^{\prime \prime }-x^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.404 |
|
| \begin{align*}
x y^{\prime \prime }+y^{\prime }-7 x^{3} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.800 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.388 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.935 |
|
| \begin{align*}
16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.978 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (16 x^{4}+3\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.959 |
|
| \begin{align*}
2 x y^{\prime \prime }+y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.119 |
|
| \begin{align*}
y^{\prime \prime }-x y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.475 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime \prime }+3 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.593 |
|
| \begin{align*}
y x -x^{2} y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| \begin{align*}
x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Laguerre] |
✓ |
✓ |
✓ |
✓ |
1.138 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.770 |
|
| \begin{align*}
y^{\prime \prime }+x y^{\prime }+2 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.497 |
|
| \begin{align*}
\left (x +2\right ) y^{\prime \prime }+3 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=y \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.385 |
|
| \begin{align*}
y^{\prime }&=-2 y x \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.459 |
|
| \begin{align*}
x y^{\prime }-3 y&=k \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✓ |
✓ |
✓ |
✗ |
0.464 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.379 |
|
| \begin{align*}
y x -y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.610 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }+x^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.575 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
0.507 |
|
| \begin{align*}
y^{\prime \prime }+\left (x^{2}+1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.471 |
|
| \begin{align*}
y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| \begin{align*}
y^{\prime }+4 y&=1 \\
y \left (0\right ) &= {\frac {5}{4}} \\
\end{align*}
Series expansion around \(x=0\). |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.467 |
|
| \begin{align*}
y^{\prime \prime }+3 x y^{\prime }+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]] |
✓ |
✓ |
✓ |
✓ |
0.545 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+30 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= {\frac {15}{8}} \\
\end{align*}
Series expansion around \(x=0\). |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
0.579 |
|
| \begin{align*}
\left (x -2\right ) y^{\prime }&=y x \\
y \left (0\right ) &= 4 \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| \begin{align*}
\left (x -2\right )^{2} y^{\prime \prime }+\left (x +2\right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.687 |
|
| \begin{align*}
x y^{\prime \prime }+2 y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.918 |
|
| \begin{align*}
x y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.004 |
|
| \begin{align*}
x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.010 |
|
| \begin{align*}
x y^{\prime \prime }+2 x^{3} y^{\prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.661 |
|
| \begin{align*}
y^{\prime \prime }+\left (x -1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| \begin{align*}
x y^{\prime \prime }+y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.746 |
|
| \begin{align*}
2 x \left (x -1\right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Jacobi] |
✓ |
✓ |
✓ |
✓ |
1.174 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.928 |
|
| \begin{align*}
x y^{\prime \prime }+\left (-2 x +2\right ) y^{\prime }+\left (x -2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.160 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+6 x y^{\prime }+\left (4 x^{2}+6\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.969 |
|
| \begin{align*}
x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.040 |
|
| \begin{align*}
2 x \left (1-x \right ) y^{\prime \prime }-\left (1+6 x \right ) y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.391 |
|
| \begin{align*}
x \left (1-x \right ) y^{\prime \prime }+\left (\frac {1}{2}+2 x \right ) y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Jacobi] |
✓ |
✓ |
✓ |
✓ |
1.224 |
|
| \begin{align*}
4 x y^{\prime \prime }+y^{\prime }+8 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.060 |
|
| \begin{align*}
4 \left (t^{2}-3 t +2\right ) y^{\prime \prime }-2 y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.771 |
|
| \begin{align*}
2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| \begin{align*}
3 t \left (t +1\right ) y^{\prime \prime }+t y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.853 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {4}{49}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.920 |
|
| \begin{align*}
x y^{\prime \prime }+y^{\prime }+\frac {y}{4}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.963 |
|
| \begin{align*}
y^{\prime \prime }+\left ({\mathrm e}^{-2 x}-\frac {1}{9}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.917 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\frac {\left (x +\frac {3}{4}\right ) y}{4}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.996 |
|