| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+\left (1-\frac {2}{\left (1+3 x \right )^{2}}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.789 |
|
| \begin{align*}
x^{2} u^{\prime \prime }-3 u^{\prime } x +13 u&=0 \\
u \left (1\right ) &= -1 \\
u^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.190 |
|
| \begin{align*}
y^{\prime }&=\frac {y+x^{2}+y^{2}}{x} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.836 |
|
| \begin{align*}
\sin \left (x \right )^{2} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }-k^{2} \cos \left (x \right )^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
7.054 |
|
| \begin{align*}
x^{2} \cos \left (x \right ) y^{\prime \prime }+\left (x \sin \left (x \right )-2 \cos \left (x \right )\right ) \left (x y^{\prime }-y\right )&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.274 |
|
| \begin{align*}
y^{\prime }+x \left (-x +y\right )+x^{3} \left (-x +y\right )^{2}&=1 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✓ |
5.305 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x +y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.440 |
|
| \begin{align*}
\frac {x^{2}}{y}+y^{2}-\left (\frac {x^{3}}{y^{2}}+y x +y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✓ |
✗ |
✗ |
20.091 |
|
| \begin{align*}
\left (1-\frac {1}{x}\right ) u^{\prime \prime }+\left (\frac {2}{x}-\frac {2}{x^{2}}-\frac {1}{x^{3}}\right ) u^{\prime }-\frac {u}{x^{4}}&=\frac {2}{x}-\frac {2}{x^{2}}-\frac {2}{x^{3}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.643 |
|
| \begin{align*}
y+\left (1+y^{2} {\mathrm e}^{2 x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
4.024 |
|
| \begin{align*}
x y^{\prime \prime }+\left (x +3\right ) y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.339 |
|
| \begin{align*}
\left (x +2\right ) y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
2.427 |
|
| \begin{align*}
\frac {{y^{\prime \prime }}^{2}}{{y^{\prime }}^{2}}+\frac {y y^{\prime \prime }}{y^{\prime }}-y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
1.570 |
|
| \begin{align*}
\left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x^{2}+4 x -3\right ) y^{\prime }+8 y x&=1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.398 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+7 x y^{\prime }+8 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.879 |
|
| \begin{align*}
n \left (n +1\right ) y-2 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[_Gegenbauer] |
✗ |
✓ |
✓ |
✗ |
195.343 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.398 |
|
| \begin{align*}
y^{\prime \prime }+2 b y^{\prime }+y&=k \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.492 |
|
| \begin{align*}
m y^{\prime \prime }+a y^{\prime }+k y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.616 |
|
| \begin{align*}
y^{\prime \prime }+\omega ^{2} y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= v \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
6.464 |
|
| \begin{align*}
\theta ^{\prime \prime }+4 \theta &=15 \cos \left (3 t \right ) \\
\theta \left (0\right ) &= 0 \\
\theta ^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.084 |
|
| \begin{align*}
y^{\prime }&=\alpha \left (A -y\right ) y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
13.689 |
|
| \begin{align*}
y^{\prime }&=2 y-5 z \\
z^{\prime }&=4 y-2 z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.050 |
|
| \begin{align*}
y^{\prime }-k y&=A \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.347 |
|
| \begin{align*}
L i^{\prime }+R i&=E_{0} \\
i \left (0\right ) &= i_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.156 |
|
| \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]] |
✗ |
✗ |
✓ |
✗ |
0.472 |
|
| \begin{align*}
2 y-x y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Hermite] |
✓ |
✓ |
✓ |
✓ |
0.560 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.396 |
|
| \begin{align*}
\left (x^{2}-4\right ) y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=1\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.920 |
|
| \begin{align*}
\left (x^{2}-4\right ) y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=2\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
6.227 |
|
| \begin{align*}
y^{\prime \prime }+x y^{\prime }+\left (x^{2}+2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.645 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime \prime }+x y^{\prime }+\frac {y}{x}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
7.148 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime \prime }+x y^{\prime }+\frac {y}{x}&=0 \\
\end{align*}
Series expansion around \(x=1\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.362 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime \prime }+x y^{\prime }+\frac {y}{x}&=0 \\
\end{align*}
Series expansion around \(x=2\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.104 |
|
| \begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.473 |
|
| \begin{align*}
y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| \begin{align*}
y^{\prime \prime }+x y^{\prime }+\left (x^{2}+2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.548 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✗ |
0.429 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.034 |
|
| \begin{align*}
y^{\prime \prime }&=x y^{2}-y^{\prime } \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
[NONE] |
✓ |
✓ |
✓ |
✗ |
0.418 |
|
| \begin{align*}
x^{\prime \prime }-s x&=0 \\
\end{align*}
Series expansion around \(t=0\). |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
0.598 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.516 |
|
| \begin{align*}
y^{\prime }&=x^{2} \\
y \left (2\right ) &= 1 \\
\end{align*}
Series expansion around \(x=2\). |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| \begin{align*}
y^{\prime }&=y \\
y \left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.461 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.444 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.542 |
|
| \begin{align*}
2 y-x y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Hermite] |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| \begin{align*}
y^{\prime \prime }-x y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.754 |
|
| \begin{align*}
\left (x^{2}+4\right ) y^{\prime \prime }+y x&=x +2 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.757 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| \begin{align*}
y^{\prime \prime }+\left (x -1\right )^{2} y^{\prime }-4 \left (x -1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=1\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.711 |
|
| \begin{align*}
y^{\prime \prime }+\left (x -1\right ) y&={\mathrm e}^{x} \\
\end{align*}
Series expansion around \(x=1\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.724 |
|
| \begin{align*}
\left (x^{2}+2\right ) y^{\prime \prime }+\left (2 x +\frac {2}{x}\right ) y^{\prime }+2 x^{2} y&=\frac {4 x^{2}+2 x +10}{x^{4}} \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✓ |
✗ |
1.076 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.636 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 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]] |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| \begin{align*}
y^{\prime \prime }+x y^{\prime }+\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]] |
✓ |
✓ |
✓ |
✓ |
0.815 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+3 x y^{\prime }+y x&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.729 |
|
| \begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.474 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+\lambda \left (1+\lambda \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
0.949 |
|
| \begin{align*}
-a b y+\left (c -\left (a +b +1\right ) x \right ) y^{\prime }+x \left (1-x \right ) y^{\prime \prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Jacobi] |
✓ |
✓ |
✓ |
✗ |
1.939 |
|
| \begin{align*}
y^{\prime \prime }+x y^{\prime }+\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]] |
✓ |
✓ |
✓ |
✓ |
0.791 |
|
| \begin{align*}
\cos \left (x \right ) u^{\prime \prime }+\sin \left (x \right ) u^{\prime }+\left (\cos \left (x \right )+\sin \left (x \right )\right ) u&=0 \\
u \left (\frac {\pi }{4}\right ) &= 2 \\
u^{\prime }\left (\frac {\pi }{4}\right ) &= 0 \\
\end{align*}
Series expansion around \(x=\frac {\pi }{4}\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.037 |
|
| \begin{align*}
x^{\prime }+x^{2}&=0 \\
x \left (-\frac {1}{2}\right ) &= 0 \\
\end{align*}
Series expansion around \(t=-{\frac {1}{2}}\). |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.320 |
|
| \begin{align*}
y^{\prime \prime }&=y^{2} {\mathrm e}^{x}-{y^{\prime }}^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
[NONE] |
✓ |
✓ |
✓ |
✗ |
0.586 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+\left (-x^{2}+1\right ) y&=\frac {-x^{2}+x}{x +1} \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.971 |
|
| \begin{align*}
x \left (x -1\right )^{2} \left (x +2\right ) y^{\prime \prime }+x^{2} y^{\prime }-\left (x^{3}+2 x -1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
8.177 |
|
| \begin{align*}
x^{4} \left (x^{2}+1\right ) \left (x -1\right )^{2} y^{\prime \prime }+4 x^{3} \left (x -1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=1\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
3.175 |
|
| \begin{align*}
y^{\prime \prime }+p \left (x \right ) y^{\prime }+q \left (x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.325 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+{\mathrm e}^{x} y^{\prime } x +\left (x^{3}-1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
7.933 |
|
| \begin{align*}
8 x^{2} y^{\prime \prime }+10 x y^{\prime }+\left (x -1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.253 |
|
| \begin{align*}
-y+\left (x +1\right ) y^{\prime }+2 x \left (1-x \right ) y^{\prime \prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Jacobi] |
✓ |
✓ |
✓ |
✓ |
1.418 |
|
| \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)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.328 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{2 x}+\frac {y}{4 x}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.339 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (\frac {1}{2} x +x^{2}\right ) y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.398 |
|
| \begin{align*}
18 x^{2} y^{\prime \prime }+3 x \left (5+x \right ) y^{\prime }-\left (10 x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.370 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.235 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.948 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-2 x \right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
6.214 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.137 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.094 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
6.013 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-\left (x +4\right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✗ |
0.467 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.211 |
|
| \begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.480 |
|
| \begin{align*}
2 \left (1-x \right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+\left (x -3-\left (x -1\right )^{2} {\mathrm e}^{x}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=1\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.309 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }-\left (x^{2}+\frac {5}{4}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.101 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+x^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.868 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (1-2 x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.007 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \left (x +3\right ) y^{\prime }+\left (x^{2}+x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.103 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=\infty \). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.063 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.937 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-\lambda y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
0.714 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (-p^{2}+x^{2}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Bessel] |
✓ |
✓ |
✓ |
✗ |
1.261 |
|
| \begin{align*}
-a b y+\left (c -\left (a +b +1\right ) x \right ) y^{\prime }+x \left (1-x \right ) y^{\prime \prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Jacobi] |
✓ |
✓ |
✓ |
✗ |
1.763 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.779 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=x^{3} \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.144 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+8 x y^{\prime }-8 y&=4 \ln \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✗ |
0.062 |
|