| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
\left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.283 |
|
| \begin{align*}
2 y-x y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[_Hermite] |
✓ |
✓ |
✓ |
✗ |
0.211 |
|
| \begin{align*}
\left (x +2\right ) y^{\prime \prime }+x y^{\prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.263 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }-6 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.212 |
|
| \begin{align*}
\left (x^{2}+2\right ) y^{\prime \prime }+3 x y^{\prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.294 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.237 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.255 |
|
| \begin{align*}
2 x y^{\prime \prime }-y^{\prime }+2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.181 |
|
| \begin{align*}
2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y&=0 \\
\end{align*} |
[_Laguerre] |
✓ |
✓ |
✓ |
✗ |
0.244 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (2 x -1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.184 |
|
| \begin{align*}
x y^{\prime \prime }+2 y^{\prime }-y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.102 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.100 |
|
| \begin{align*}
x y^{\prime \prime }+\left (-6+x \right ) y^{\prime }-3 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.275 |
|
| \begin{align*}
x^{4} y^{\prime \prime }+\lambda y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.248 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-25\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.280 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.125 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.257 |
|
| \begin{align*}
x y^{\prime \prime }+3 y^{\prime }+x^{3} y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.276 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.113 |
|
| \begin{align*}
16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.281 |
|
| \begin{align*}
y x -x^{2} y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.243 |
|
| \begin{align*}
x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y&=0 \\
\end{align*} |
[_Laguerre] |
✓ |
✓ |
✓ |
✗ |
0.240 |
|
| \begin{align*}
y^{\prime \prime }+x y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.218 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
0.259 |
|
| \begin{align*}
y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.103 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+30 y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
0.335 |
|
| \begin{align*}
x y^{\prime \prime }+2 y^{\prime }+y x&=0 \\
\end{align*} |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.107 |
|
| \begin{align*}
x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.200 |
|
| \begin{align*}
2 x \left (x -1\right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✓ |
✗ |
0.219 |
|
| \begin{align*}
x y^{\prime \prime }+2 y^{\prime }+4 y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.114 |
|
| \begin{align*}
x y^{\prime \prime }+\left (-2 x +2\right ) y^{\prime }+\left (x -2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.107 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+6 x y^{\prime }+\left (4 x^{2}+6\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.115 |
|
| \begin{align*}
x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.195 |
|
| \begin{align*}
x \left (1-x \right ) y^{\prime \prime }+\left (\frac {1}{2}+2 x \right ) y^{\prime }-2 y&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✓ |
✗ |
0.260 |
|
| \begin{align*}
4 \left (t^{2}-3 t +2\right ) y^{\prime \prime }-2 y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.232 |
|
| \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*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.268 |
|
| \begin{align*}
3 t \left (t +1\right ) y^{\prime \prime }+t y^{\prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.238 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\frac {\left (x +\frac {3}{4}\right ) y}{4}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.162 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (x^{2}-1\right ) y}{4}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.124 |
|
| \begin{align*}
x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.195 |
|
| \begin{align*}
y-\left (x +1\right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[_Laguerre] |
✓ |
✓ |
✓ |
✗ |
0.233 |
|
| \begin{align*}
x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.273 |
|
| \begin{align*}
x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-x^{2}+1\right ) y^{\prime }-2 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.277 |
|
| \begin{align*}
2 x y^{\prime \prime }+\left (x -2\right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.233 |
|
| \begin{align*}
x y^{\prime \prime }+2 y^{\prime }+y x&=0 \\
\end{align*} |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.107 |
|
| \begin{align*}
y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{4}+2 x -1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.114 |
|
| \begin{align*}
u^{\prime \prime }+2 u^{\prime }+u&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.112 |
|
| \begin{align*}
u^{\prime \prime }-\left (2 x +1\right ) u^{\prime }+\left (x^{2}+x -1\right ) u&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.119 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.182 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.112 |
|
| \begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (x +1\right )^{2}}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.186 |
|
| \begin{align*}
y^{\prime \prime }-x y^{\prime }-y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.225 |
|
| \begin{align*}
y^{\prime \prime }-x y^{\prime }-y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.204 |
|
| \begin{align*}
y^{\prime \prime }-x y^{\prime }-y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.205 |
|
| \begin{align*}
y^{\prime \prime }-x y^{\prime }-y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.205 |
|
| \begin{align*}
y^{\prime \prime }-x y^{\prime }-y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.204 |
|
| \begin{align*}
y^{\prime \prime }-x y^{\prime }-y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.201 |
|
| \begin{align*}
y^{\prime \prime }-x y^{\prime }-y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.202 |
|
| \begin{align*}
y^{\prime \prime }-x y^{\prime }-y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.192 |
|
| \begin{align*}
y^{\prime \prime }-x y^{\prime }-y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.202 |
|
| \begin{align*}
y^{\prime \prime }-x y^{\prime }-y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.208 |
|
| \begin{align*}
y^{\prime \prime }-x y^{\prime }-y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.205 |
|
| \begin{align*}
x y^{\prime \prime }+2 y^{\prime }+y x&=0 \\
\end{align*} |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.109 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y x&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.178 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.247 |
|
| \begin{align*}
2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.514 |
|
| \begin{align*}
x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.252 |
|
| \begin{align*}
x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.306 |
|
| \begin{align*}
2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.239 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.113 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.101 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }-\left (x^{2}+\frac {5}{4}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.251 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.109 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }+4 x^{4} y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.276 |
|
| \begin{align*}
y^{\prime \prime }&=\left (x^{2}+3\right ) y \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.221 |
|
| \begin{align*}
y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}+1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.104 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.109 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.115 |
|
| \begin{align*}
y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.091 |
|
| \begin{align*}
y^{\prime \prime }&=\frac {2 y}{x^{2}} \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.167 |
|
| \begin{align*}
y^{\prime \prime }&=\frac {6 y}{x^{2}} \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.180 |
|
| \begin{align*}
y^{\prime \prime }&=\left (-\frac {3}{16 x^{2}}-\frac {2}{9 \left (x -1\right )^{2}}+\frac {3}{16 \left (x -1\right ) x}\right ) y \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.142 |
|
| \begin{align*}
y^{\prime \prime }&=\frac {20 y}{x^{2}} \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.182 |
|
| \begin{align*}
y^{\prime \prime }&=\frac {12 y}{x^{2}} \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.173 |
|
| \begin{align*}
y^{\prime \prime }-\frac {y}{4 x^{2}}&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.211 |
|
| \begin{align*}
x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.194 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y}{x^{2}}&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.221 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.604 |
|
| \begin{align*}
\left (x^{2}-x \right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.230 |
|
| \begin{align*}
x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (4 x^{2}+3\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.502 |
|
| \begin{align*}
y^{\prime \prime }&=\frac {\left (4 x^{6}-8 x^{5}+12 x^{4}+4 x^{3}+7 x^{2}-20 x +4\right ) y}{4 x^{4}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.499 |
|
| \begin{align*}
y^{\prime \prime }&=\left (\frac {6}{x^{2}}-1\right ) y \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.274 |
|
| \begin{align*}
y^{\prime \prime }&=\left (\frac {x^{2}}{4}-\frac {11}{2}\right ) y \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.275 |
|
| \begin{align*}
y^{\prime \prime }&=\left (\frac {1}{x}-\frac {3}{16 x^{2}}\right ) y \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.159 |
|
| \begin{align*}
y^{\prime \prime }&=\left (-\frac {3}{16 x^{2}}-\frac {2}{9 \left (x -1\right )^{2}}+\frac {3}{16 \left (x -1\right ) x}\right ) y \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.305 |
|
| \begin{align*}
y^{\prime \prime }&=-\frac {\left (5 x^{2}+27\right ) y}{36 \left (x^{2}-1\right )^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
110.187 |
|
| \begin{align*}
y^{\prime \prime }&=-\frac {y}{4 x^{2}} \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.185 |
|
| \begin{align*}
y^{\prime \prime }&=\left (x^{2}+3\right ) y \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.219 |
|
| \begin{align*}
x^{2} y^{\prime \prime }&=2 y \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.174 |
|
| \begin{align*}
y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.107 |
|