| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&=\frac {1}{1+{\mathrm e}^{-x}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.532 |
|
| \begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{-x} \sin \left ({\mathrm e}^{-x}\right )+\cos \left ({\mathrm e}^{-x}\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.117 |
|
| \begin{align*}
y^{\prime \prime }-y&=\frac {1}{\left (1+{\mathrm e}^{-x}\right )^{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.487 |
|
| \begin{align*}
y^{\prime \prime }+2 y&={\mathrm e}^{x}+2 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.326 |
|
| \begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{x} \sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=x^{2}+\sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.353 |
|
| \begin{align*}
y^{\prime \prime }-9 y&=x +{\mathrm e}^{2 x}-\sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.507 |
|
| \begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }&=x^{2}+4 x +8 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.095 |
|
| \begin{align*}
y^{\prime \prime }+y&=-2 \sin \left (x \right )+4 \cos \left (x \right ) x \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.450 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y&=2 x^{2}-4 x -1+2 x^{2} {\mathrm e}^{2 x}+5 x \,{\mathrm e}^{2 x}+{\mathrm e}^{2 x} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.317 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&={\mathrm e}^{3 x}+6 \,{\mathrm e}^{x}-3 \,{\mathrm e}^{-2 x}+5 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.428 |
|
| \begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.270 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{x}+x \,{\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.356 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y&=\sin \left (2 x \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.101 |
|
| \begin{align*}
y^{\prime \prime \prime }+y&=\cos \left (x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.094 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=\sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.285 |
|
| \begin{align*}
y^{\prime \prime }+5 y&=\cos \left (\sqrt {5}\, x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.372 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y&={\mathrm e}^{x}+{\mathrm e}^{-x}+\sin \left (x \right ) \\
\end{align*} | [[_3rd_order, _linear, _nonhomogeneous]] | ✓ | ✓ | ✓ | ✓ | 0.835 |
|
| \begin{align*}
y^{\prime \prime }-y&=x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.218 |
|
| \begin{align*}
y^{\prime \prime }+2 y&=x^{3}+x^{2}+{\mathrm e}^{-2 x}+\cos \left (3 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.943 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-y&={\mathrm e}^{x} \cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.283 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=\frac {{\mathrm e}^{2 x}}{x^{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| \begin{align*}
y^{\prime \prime }-y&=x \,{\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.257 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&={\mathrm e}^{-2 x} \sec \left (x \right )^{2} \left (1+2 \tan \left (x \right )\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.464 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x +\ln \left (x \right ) x^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.289 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=\ln \left (x \right )^{2}-\ln \left (x^{2}\right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.997 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }&=x +\sin \left (\ln \left (x \right )\right ) \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.295 |
|
| \begin{align*}
-y+y^{\prime } x +x^{3} y^{\prime \prime \prime }&=3 x^{4} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.254 |
|
| \begin{align*}
\left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y&=\ln \left (x +1\right )^{2}+x -1 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.394 |
|
| \begin{align*}
-12 y-2 \left (2 x +1\right ) y^{\prime }+\left (2 x +1\right )^{2} y^{\prime \prime }&=6 x \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.839 |
|
| \begin{align*}
y^{\prime \prime } x -\left (2+x \right ) y^{\prime }+2 y&=0 \\
\end{align*} |
[_Laguerre] |
✓ |
✓ |
✓ |
✗ |
0.263 |
|
| \begin{align*}
2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=2 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.954 |
|
| \begin{align*}
\left (x^{2}+4\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=8 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.924 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+\left (2+x \right ) y&=\left (x^{2}+2 x +1\right ) {\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.326 |
|
| \begin{align*}
y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }-10 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.329 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x \left (2 x +3\right ) y^{\prime }+\left (x^{2}+3 x +3\right ) y&=\left (-x^{2}+6\right ) {\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.328 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+4 x^{3} y^{\prime }+\left (x^{2}+1\right )^{2} y&=0 \\
\end{align*} | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✗ | 0.221 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (-4 x^{2}+x \right ) y^{\prime }+\left (4 x^{2}-2 x +1\right ) y&=\left (x^{2}-x +1\right ) {\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.371 |
|
| \begin{align*}
y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| \begin{align*}
x^{8} y^{\prime \prime }+4 x^{7} y^{\prime }+y&=\frac {1}{x^{3}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.431 |
|
| \begin{align*}
\left (x \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+y \cos \left (x \right )&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.321 |
|
| \begin{align*}
y^{\prime \prime } x -3 y^{\prime }+\frac {3 y}{x}&=2+x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.456 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime \prime }-\left (3 x +4\right ) y^{\prime }+3 y&=\left (3 x +2\right ) {\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.726 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (9 x^{2}+6\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.331 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }+4 y x&=4 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.678 |
|
| \begin{align*}
2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=\frac {-x^{2}+1}{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.931 |
|
| \begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}+1&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
3.269 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x&=\frac {2}{x^{3}} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.750 |
|
| \begin{align*}
-y^{\prime }+y^{\prime \prime } x&=-\frac {2}{x}-\ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.931 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }&=x^{2} \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.102 |
|
| \begin{align*}
{y^{\prime }}^{3}+y y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✗ |
0.362 |
|
| \begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.392 |
|
| \begin{align*}
y y^{\prime \prime }&={y^{\prime }}^{2} \left (1-y^{\prime } \cos \left (y\right )+y y^{\prime } \sin \left (y\right )\right ) \\
\end{align*} | [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_y_y1]] | ✓ | ✓ | ✓ | ✗ | 0.946 |
|
| \begin{align*}
\left (2 x -3\right ) y^{\prime \prime \prime }-\left (6 x -7\right ) y^{\prime \prime }+4 y^{\prime } x -4 y&=8 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.039 |
|
| \begin{align*}
\left (2 x^{3}-1\right ) y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+6 y^{\prime } x&=0 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.286 |
|
| \begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}&=\ln \left (y\right ) y^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.932 |
|
| \begin{align*}
\left (x +2 y\right ) y^{\prime \prime }+2 {y^{\prime }}^{2}+2 y^{\prime }&=2 \\
\end{align*} |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.402 |
|
| \begin{align*}
\left (1+2 y+3 y^{2}\right ) y^{\prime \prime \prime }+6 y^{\prime } \left (y^{\prime \prime }+{y^{\prime }}^{2}+3 y y^{\prime \prime }\right )&=x \\
\end{align*} |
[[_3rd_order, _exact, _nonlinear]] |
✗ |
✓ |
✗ |
✗ |
0.043 |
|
| \begin{align*}
3 x \left (y^{2} y^{\prime \prime \prime }+6 y y^{\prime } y^{\prime \prime }+2 {y^{\prime }}^{3}\right )-3 y \left (y y^{\prime \prime }+2 {y^{\prime }}^{2}\right )&=-\frac {2}{x} \\
\end{align*} |
[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
✗ |
0.065 |
|
| \begin{align*}
y y^{\prime \prime \prime }+3 y^{\prime } y^{\prime \prime }-2 y y^{\prime \prime }-2 {y^{\prime }}^{2}+y^{\prime } y&={\mathrm e}^{2 x} \\
\end{align*} |
[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
✗ |
0.059 |
|
| \begin{align*}
2 \left (1+y\right ) y^{\prime \prime }+2 {y^{\prime }}^{2}+y^{2}+2 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
4.403 |
|
| \begin{align*}
x^{\prime }-y^{\prime }+y&=-{\mathrm e}^{t} \\
x+y^{\prime }-y&={\mathrm e}^{2 t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.587 |
|
| \begin{align*}
x^{\prime }+2 x+y^{\prime }+y&=t \\
5 x+y^{\prime }+3 y&=t^{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.691 |
|
| \begin{align*}
x^{\prime }+x+2 y^{\prime }+7 y&={\mathrm e}^{t}+2 \\
-2 x+y^{\prime }+3 y&={\mathrm e}^{t}-1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.197 |
|
| \begin{align*}
x^{\prime }-x+y^{\prime }+3 y&={\mathrm e}^{-t}-1 \\
x^{\prime }+2 x+y^{\prime }+3 y&=1+{\mathrm e}^{2 t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
0.182 |
|
| \begin{align*}
x^{\prime }-x+y^{\prime }+2 y&=1+{\mathrm e}^{t} \\
y^{\prime }+2 y+z^{\prime }+z&={\mathrm e}^{t}+2 \\
x^{\prime }-x+z^{\prime }+z&=3+{\mathrm e}^{t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.687 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime }&=x^{2}-y \\
\end{align*} Series expansion around \(x=0\). |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.220 |
|
| \begin{align*}
y^{\prime } x&=1-x +2 y \\
\end{align*} Series expansion around \(x=1\). | [_linear] | ✓ | ✓ | ✓ | ✗ | 0.248 |
|
| \begin{align*}
y^{\prime } x&=1-x +2 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.823 |
|
| \begin{align*}
y^{\prime }&=2 x^{2}+3 y \\
\end{align*} Series expansion around \(x=0\). |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.247 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=x^{2}-2 x +y \\
\end{align*} Series expansion around \(x=0\). |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.205 |
|
| \begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.210 |
|
| \begin{align*}
y^{\prime \prime }+2 x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.210 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime } x +x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.250 |
|
| \begin{align*}
p \left (1+p \right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| \begin{align*}
y^{\prime \prime }+x^{2} y&=x^{2}+x +1 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.237 |
|
| \begin{align*}
2 \left (x^{3}+x^{2}\right ) y^{\prime \prime }-\left (-3 x^{2}+x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.650 |
|
| \begin{align*}
4 y^{\prime \prime } x +2 \left (1-x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.695 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.587 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.327 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.369 |
|
| \begin{align*}
y^{\prime \prime } x -2 y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.080 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.619 |
|
| \begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| \begin{align*}
2 y^{\prime \prime } x +y^{\prime }-y&=x +1 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.896 |
|
| \begin{align*}
2 x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=\infty \). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| \begin{align*}
x^{3} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=\infty \). | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✓ | 0.617 |
|
| \begin{align*}
z^{\prime \prime }+t z^{\prime }+\left (t^{2}-\frac {1}{9}\right ) z&=0 \\
\end{align*} Series expansion around \(t=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.287 |
|
| \begin{align*}
x \left (-x^{2}+2\right ) y^{\prime \prime }-\left (x^{2}+4 x +2\right ) \left (\left (1-x \right ) y^{\prime }+y\right )&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.835 |
|
| \begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }-\left (2 x +1\right ) \left (-y+y^{\prime } x \right )&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.644 |
|
| \begin{align*}
x^{3} \left (x +1\right ) y^{\prime \prime \prime }-\left (2+4 x \right ) x^{2} y^{\prime \prime }+\left (4+10 x \right ) x y^{\prime }-\left (4+12 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.040 |
|
| \begin{align*}
x^{3} \left (x^{2}+1\right ) y^{\prime \prime \prime }-\left (4 x^{2}+2\right ) x^{2} y^{\prime \prime }+\left (10 x^{2}+4\right ) x y^{\prime }-\left (12 x^{2}+4\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.040 |
|
| \begin{align*}
\left (-x +3\right ) y-x \left (4-x \right ) y^{\prime }+2 \left (-x +2\right ) x^{2} y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.776 |
|
| \begin{align*}
\left (1-x \right ) x^{2} y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.439 |
|
| \begin{align*}
4 x \left (x^{2}+1\right ) y+\left (4 x^{2}+1\right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 \left (x +a \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.886 |
|
| \begin{align*}
y^{\prime \prime } x +\left (x^{3}+1\right ) y^{\prime }+b x y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| \begin{align*}
\left (x -1\right ) \left (x -2\right ) y^{\prime \prime }+\left (4 x -6\right ) y^{\prime }+2 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.385 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime } x +8 y&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.247 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime } x +8 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.214 |
|