| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
\left (x^{2}-2 x +10\right ) y^{\prime \prime }+y^{\prime } x -4 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.229 |
|
| \begin{align*}
2 y-y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} |
[_Hermite] |
✓ |
✓ |
✓ |
✗ |
0.157 |
|
| \begin{align*}
\left (2+x \right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.211 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }-6 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.174 |
|
| \begin{align*}
\left (x^{2}+2\right ) y^{\prime \prime }+3 y^{\prime } x -y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.264 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.178 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.277 |
|
| \begin{align*}
2 y^{\prime \prime } x -y^{\prime }+2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.134 |
|
| \begin{align*}
2 y^{\prime \prime } x -\left (2 x +3\right ) y^{\prime }+y&=0 \\
\end{align*} |
[_Laguerre] |
✓ |
✓ |
✓ |
✗ |
0.246 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (2 x -1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.144 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }-y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.080 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.081 |
|
| \begin{align*}
y^{\prime \prime } x +\left (x -6\right ) y^{\prime }-3 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.231 |
|
| \begin{align*}
x^{4} y^{\prime \prime }+\lambda y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.204 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-25\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.223 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (36 x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.108 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.211 |
|
| \begin{align*}
y^{\prime \prime } x +3 y^{\prime }+x^{3} y&=0 \\
\end{align*} | [[_Emden, _Fowler]] | ✓ | ✓ | ✓ | ✓ | 0.228 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.090 |
|
| \begin{align*}
16 x^{2} y^{\prime \prime }+32 y^{\prime } x +\left (x^{4}-12\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.243 |
|
| \begin{align*}
y x -x^{2} y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.223 |
|
| \begin{align*}
y^{\prime \prime } x -\left (2+x \right ) y^{\prime }+2 y&=0 \\
\end{align*} |
[_Laguerre] |
✓ |
✓ |
✓ |
✗ |
0.184 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.181 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
0.192 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.078 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +30 y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
0.266 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\
\end{align*} |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.072 |
|
| \begin{align*}
y^{\prime \prime } x +\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.148 |
|
| \begin{align*}
2 x \left (x -1\right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✓ |
✗ |
0.176 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }+4 y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.108 |
|
| \begin{align*}
y^{\prime \prime } x +\left (-2 x +2\right ) y^{\prime }+\left (x -2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.086 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+6 y^{\prime } x +\left (4 x^{2}+6\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.090 |
|
| \begin{align*}
y^{\prime \prime } x +\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.142 |
|
| \begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\left (\frac {1}{2}+2 x \right ) y^{\prime }-2 y&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✓ |
✗ |
0.226 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.223 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.222 |
|
| \begin{align*}
3 t \left (t +1\right ) y^{\prime \prime }+t y^{\prime }-y&=0 \\
\end{align*} | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✗ | 0.240 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\frac {\left (x +\frac {3}{4}\right ) y}{4}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.150 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\frac {\left (x^{2}-1\right ) y}{4}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.100 |
|
| \begin{align*}
y^{\prime \prime } x +\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.130 |
|
| \begin{align*}
y-\left (x +1\right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[_Laguerre] |
✓ |
✓ |
✓ |
✗ |
0.177 |
|
| \begin{align*}
y^{\prime \prime } x +3 y^{\prime }+4 x^{3} y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.210 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.245 |
|
| \begin{align*}
2 y^{\prime \prime } x +\left (x -2\right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.190 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\
\end{align*} |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.076 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.098 |
|
| \begin{align*}
u^{\prime \prime }+2 u^{\prime }+u&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.095 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.091 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.139 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.078 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.136 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime } x -y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.186 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime } x -y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.155 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime } x -y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.150 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime } x -y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.154 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime } x -y x&=0 \\
\end{align*} | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✗ | 0.154 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime } x -y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.151 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime } x -y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.152 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime } x -y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.152 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime } x -y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.146 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime } x -y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.154 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime } x -y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.151 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\
\end{align*} |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.069 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+3 y^{\prime } x -y x&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.144 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.198 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.939 |
|
| \begin{align*}
y^{\prime \prime } x +\left (x +1\right ) y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.197 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.235 |
|
| \begin{align*}
2 x^{2} \left (2+x \right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.175 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.078 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.082 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x -\left (x^{2}+\frac {5}{4}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.196 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.085 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +4 x^{4} y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.212 |
|
| \begin{align*}
y^{\prime \prime }&=\left (x^{2}+3\right ) y \\
\end{align*} | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✗ | 0.173 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime } x +\left (x^{2}+1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.075 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.076 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.091 |
|
| \begin{align*}
y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.067 |
|
| \begin{align*}
y^{\prime \prime }&=\frac {2 y}{x^{2}} \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.115 |
|
| \begin{align*}
y^{\prime \prime }&=\frac {6 y}{x^{2}} \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.115 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.191 |
|
| \begin{align*}
y^{\prime \prime }&=\frac {20 y}{x^{2}} \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.119 |
|
| \begin{align*}
y^{\prime \prime }&=\frac {12 y}{x^{2}} \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.113 |
|
| \begin{align*}
y^{\prime \prime }-\frac {y}{4 x^{2}}&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.167 |
|
| \begin{align*}
y^{\prime \prime } x -\left (2 x +2\right ) y^{\prime }+\left (2+x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.141 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y}{x^{2}}&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.188 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.448 |
|
| \begin{align*}
\left (x^{2}-x \right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.171 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.382 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.401 |
|
| \begin{align*}
y^{\prime \prime }&=\left (\frac {6}{x^{2}}-1\right ) y \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.222 |
|
| \begin{align*}
y^{\prime \prime }&=\left (\frac {x^{2}}{4}-\frac {11}{2}\right ) y \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.220 |
|
| \begin{align*}
y^{\prime \prime }&=\left (\frac {1}{x}-\frac {3}{16 x^{2}}\right ) y \\
\end{align*} | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✓ | 0.125 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.241 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
130.405 |
|
| \begin{align*}
y^{\prime \prime }&=-\frac {y}{4 x^{2}} \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.128 |
|
| \begin{align*}
y^{\prime \prime }&=\left (x^{2}+3\right ) y \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.166 |
|
| \begin{align*}
x^{2} y^{\prime \prime }&=2 y \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.118 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.077 |
|