| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.059 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime \prime }-6 y^{\prime }+5 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.060 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.047 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-5 y^{\prime }-2 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.056 |
|
| \begin{align*}
y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+48 y^{\prime \prime }+16 y^{\prime }-96 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.067 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.032 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }&=\sin \left (x \right )+24 \\
\end{align*} |
[[_high_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.139 |
|
| \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }&=10+42 \,{\mathrm e}^{3 x} \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.129 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime }&=1 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 4 \\
y^{\prime \prime }\left (0\right ) &= 4 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.119 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.105 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.118 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.118 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime \prime }+8 x^{2} y^{\prime \prime \prime }+8 y^{\prime \prime } x -8 y^{\prime }&=0 \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.302 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.225 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.283 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.233 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }+6 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.284 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-5 y&=x \\
\end{align*} | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✓ | 0.348 |
|
| \begin{align*}
y^{\prime \prime }+y&={\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.294 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.359 |
|
| \begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.280 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.345 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }+4 y&=x \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.766 |
|
| \begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+4 y&=\sin \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
y^{\prime }\left (\frac {\pi }{2}\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.107 |
|
| \begin{align*}
y^{\prime \prime }+y&={\mathrm e}^{-x} \\
y \left (2\right ) &= 0 \\
y^{\prime }\left (2\right ) &= -2 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.536 |
|
| \begin{align*}
y^{\prime \prime }-y&=\cos \left (x \right ) \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (2\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.569 |
|
| \begin{align*}
y^{\prime \prime }&=\tan \left (x \right ) \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
3.684 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }&=\ln \left (x \right ) \\
y \left (1\right ) &= {\mathrm e} \\
y^{\prime }\left (1\right ) &= {\mathrm e}^{-1} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
2.770 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=2 x -1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.295 |
|
| \begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.289 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=\cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.317 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }-y&={\mathrm e}^{x} \sin \left (x \right ) x \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.467 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=\sec \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.772 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=x \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {2}{x} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.609 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=\tan \left (x \right )^{2} \\
\end{align*} | [[_2nd_order, _linear, _nonhomogeneous]] | ✓ | ✓ | ✓ | ✓ | 0.527 |
|
| \begin{align*}
y^{\prime \prime }-y&=3 \,{\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.181 |
|
| \begin{align*}
y^{\prime \prime }+y&=-8 \sin \left (3 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.191 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=x^{2}+2 x +2 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.364 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=\frac {x -1}{x^{2}} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.956 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.953 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=-3 \cos \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.388 |
|
| \begin{align*}
y^{\prime }+y&=\cos \left (x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.619 |
|
| \begin{align*}
y^{\prime \prime }&=-3 y \\
y \left (0\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.592 |
|
| \begin{align*}
y^{\prime \prime }+\sin \left (y\right )&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
38.317 |
|
| \begin{align*}
y^{\prime }&=2 y x \\
\end{align*} Series expansion around \(x=0\). |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.287 |
|
| \begin{align*}
y^{\prime }&=2 y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.816 |
|
| \begin{align*}
y^{\prime }+y&=1 \\
\end{align*} Series expansion around \(x=0\). |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.263 |
|
| \begin{align*}
y^{\prime }+y&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.438 |
|
| \begin{align*}
y^{\prime }-y&=2 \\
\end{align*} Series expansion around \(x=0\). |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.254 |
|
| \begin{align*}
y^{\prime }-y&=2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.394 |
|
| \begin{align*}
y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.214 |
|
| \begin{align*}
y^{\prime }+y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.443 |
|
| \begin{align*}
y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.214 |
|
| \begin{align*}
y^{\prime }-y&=0 \\
\end{align*} | [_quadrature] | ✓ | ✓ | ✓ | ✓ | 0.391 |
|
| \begin{align*}
y^{\prime }-y&=x^{2} \\
\end{align*} Series expansion around \(x=0\). |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.271 |
|
| \begin{align*}
y^{\prime }-y&=x^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.532 |
|
| \begin{align*}
y^{\prime } x&=y \\
\end{align*} Series expansion around \(x=0\). |
[_separable] |
✓ |
✓ |
✓ |
✗ |
0.166 |
|
| \begin{align*}
y^{\prime } x&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.724 |
|
| \begin{align*}
x^{2} y^{\prime }&=y \\
\end{align*} Series expansion around \(x=0\). |
[_separable] |
✗ |
✗ |
✓ |
✗ |
0.046 |
|
| \begin{align*}
x^{2} y^{\prime }&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.858 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=x^{2} \\
\end{align*} Series expansion around \(x=0\). |
[_linear] |
✓ |
✓ |
✓ |
✗ |
0.205 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.964 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.013 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{\sqrt {-x^{2}+1}} \\
\end{align*} Series expansion around \(x=0\). |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.286 |
|
| \begin{align*}
y^{\prime }&=1+y \\
\end{align*} Series expansion around \(x=0\). |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.243 |
|
| \begin{align*}
y^{\prime }&=x -y \\
y \left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.278 |
|
| \begin{align*}
y^{\prime }&=x -y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.963 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| \begin{align*}
y x -y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.466 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime } x -y&=x \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.444 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-x^{2} y&=1 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.536 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.476 |
|
| \begin{align*}
y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✓ | 0.446 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.378 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.296 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-y x&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.368 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-y x&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.323 |
|
| \begin{align*}
y^{\prime \prime }+\left (p +\frac {1}{2}-\frac {x^{2}}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.500 |
|
| \begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.292 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +p^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.680 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime } x +2 y p&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| \begin{align*}
x^{3} \left (x -1\right ) y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+3 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✗ |
0.108 |
|
| \begin{align*}
x^{2} \left (x^{2}-1\right ) y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.247 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (-x +2\right ) y^{\prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _missing_y]] |
✗ |
✗ |
✓ |
✗ |
0.112 |
|
| \begin{align*}
\left (1+3 x \right ) x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.581 |
|
| \begin{align*}
y^{\prime \prime }+y \sin \left (x \right )&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.574 |
|
| \begin{align*}
y^{\prime \prime } x +y \sin \left (x \right )&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.654 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y \sin \left (x \right )&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.991 |
|
| \begin{align*}
x^{3} y^{\prime \prime }+y \sin \left (x \right )&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.661 |
|
| \begin{align*}
x^{4} y^{\prime \prime }+y \sin \left (x \right )&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✗ |
0.091 |
|
| \begin{align*}
x^{3} y^{\prime \prime }+\left (-1+\cos \left (2 x \right )\right ) y^{\prime }+2 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.647 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+\left (2 x^{4}-5 x \right ) y^{\prime }+\left (3 x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✓ | 0.819 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +4 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.733 |
|
| \begin{align*}
x^{3} y^{\prime \prime }-4 x^{2} y^{\prime }+3 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✗ |
0.540 |
|
| \begin{align*}
4 y^{\prime \prime } x +3 y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.876 |
|
| \begin{align*}
2 y^{\prime \prime } x +\left (-x +3\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| \begin{align*}
2 y^{\prime \prime } x +\left (x +1\right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.880 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+y^{\prime } x -\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.872 |
|