| # |
ODE |
CAS classification |
Solved |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-9 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.112 |
|
| \begin{align*}
4 y^{\prime \prime }-4 y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.122 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.112 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime \prime }-\left (x +2\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.113 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
0.119 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
0.129 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.190 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-9 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.093 |
|
| \begin{align*}
4 y^{\prime \prime }-4 y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.105 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.100 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime \prime }-\left (x +2\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.101 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
0.099 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
0.108 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.181 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.100 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+2 t y^{\prime }-2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.099 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+3 t y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.113 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.109 |
|
| \begin{align*}
x y^{\prime \prime }-y^{\prime }+4 x^{3} y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.235 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.105 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-\left (x -\frac {3}{16}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.121 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.112 |
|
| \begin{align*}
\left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y&=\left (2 x +1\right )^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.313 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-y&=\frac {4}{x^{2}} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.248 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }+y&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.257 |
|
| \begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=\frac {1}{1+{\mathrm e}^{-x}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.338 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=7 x^{{3}/{2}} {\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.317 |
|
| \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&=4 \sqrt {x}\, {\mathrm e}^{x} \left (1+4 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.373 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&={\mathrm e}^{x} \sec \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.345 |
|
| \begin{align*}
y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y&=8 \,{\mathrm e}^{-x \left (x +2\right )} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.320 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-4 y&=-6 x -4 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.283 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 x \left (x -1\right ) y^{\prime }+\left (x^{2}-2 x +2\right ) y&=x^{3} {\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.335 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x \left (2 x -1\right ) y^{\prime }+\left (x^{2}-x -1\right ) y&={\mathrm e}^{x} x^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.318 |
|
| \begin{align*}
\left (1-2 x \right ) y^{\prime \prime }+2 y^{\prime }+\left (2 x -3\right ) y&=\left (4 x^{2}-4 x +1\right ) {\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.332 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=4 x^{4} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.297 |
|
| \begin{align*}
2 x y^{\prime \prime }+\left (1+4 x \right ) y^{\prime }+\left (2 x +1\right ) y&=3 \sqrt {x}\, {\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.330 |
|
| \begin{align*}
x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=-{\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.337 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }-4 x \left (x +1\right ) y^{\prime }+\left (2 x +3\right ) y&=4 x^{{5}/{2}} {\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.333 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y&=4 x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.280 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.134 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.132 |
|
| \begin{align*}
x^{2} \ln \left (x \right )^{2} y^{\prime \prime }-2 x \ln \left (x \right ) y^{\prime }+\left (2+\ln \left (x \right )\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.138 |
|
| \begin{align*}
4 x y^{\prime \prime }+2 y^{\prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.155 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.141 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-\left (2 a -1\right ) x y^{\prime }+a^{2} y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.159 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.132 |
|
| \begin{align*}
x y^{\prime \prime }-\left (1+4 x \right ) y^{\prime }+\left (4 x +2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.141 |
|
| \begin{align*}
4 x^{2} \sin \left (x \right ) y^{\prime \prime }-4 x \left (\sin \left (x \right )+x \cos \left (x \right )\right ) y^{\prime }+\left (2 x \cos \left (x \right )+3 \sin \left (x \right )\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.178 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.148 |
|
| \begin{align*}
\left (2 x +1\right ) x y^{\prime \prime }-2 \left (2 x^{2}-1\right ) y^{\prime }-4 \left (x +1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.144 |
|
| \begin{align*}
\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.139 |
|
| \begin{align*}
x y^{\prime \prime }-\left (1+4 x \right ) y^{\prime }+\left (4 x +2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.130 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=4 x^{4} \\
y \left (-1\right ) &= 7 \\
y^{\prime }\left (-1\right ) &= -8 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.390 |
|
| \begin{align*}
\left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.260 |
|
| \begin{align*}
\left (x +1\right )^{2} y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }-\left (x^{2}+2 x -1\right ) y&=\left (x +1\right )^{3} {\mathrm e}^{x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.473 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y&=x^{2} \\
y \left (1\right ) &= {\frac {5}{4}} \\
y^{\prime }\left (1\right ) &= {\frac {3}{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.359 |
|
| \begin{align*}
\left (x^{2}-4\right ) y^{\prime \prime }+4 x y^{\prime }+2 y&=x +2 \\
y \left (0\right ) &= -{\frac {1}{3}} \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.450 |
|
| \begin{align*}
y^{\prime \prime }-\frac {2 \left (t +1\right ) y^{\prime }}{t^{2}+2 t -1}+\frac {2 y}{t^{2}+2 t -1}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.155 |
|
| \begin{align*}
y^{\prime \prime }-4 t y^{\prime }+\left (4 t^{2}-2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.143 |
|
| \begin{align*}
\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
0.163 |
|
| \begin{align*}
\left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.141 |
|
| \begin{align*}
\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+6 y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
0.174 |
|
| \begin{align*}
\left (2 t +1\right ) y^{\prime \prime }-4 \left (t +1\right ) y^{\prime }+4 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.158 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.164 |
|
| \begin{align*}
t y^{\prime \prime }-\left (1+3 t \right ) y^{\prime }+3 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.156 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.132 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.143 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.148 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
0.151 |
|
| \begin{align*}
y^{\prime \prime }-\frac {y^{\prime }}{x}+4 x^{2} y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.148 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.137 |
|
| \begin{align*}
y^{\prime \prime }+y&=\csc \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.304 |
|
| \begin{align*}
x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+2 y&=8 x^{2} {\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.336 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=8 x^{4} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.306 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=15 \,{\mathrm e}^{3 x} \sqrt {x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.358 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=4 \,{\mathrm e}^{2 x} \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+y&=\sqrt {x}\, \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.290 |
|
| \begin{align*}
\left (2-x \right ) x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.109 |
|
| \begin{align*}
2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.098 |
|
| \begin{align*}
x y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+\left (x +2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.107 |
|
| \begin{align*}
3 x y^{\prime \prime }-2 \left (3 x -1\right ) y^{\prime }+\left (3 x -2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.107 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.112 |
|
| \begin{align*}
x \left (x +1\right ) y^{\prime \prime }-\left (x -1\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.114 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.164 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.159 |
|
| \begin{align*}
y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.158 |
|
| \begin{align*}
y-\left (x +1\right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[_Laguerre] |
✓ |
✓ |
✓ |
✗ |
0.162 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
0.176 |
|
| \begin{align*}
y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.213 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.155 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.158 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.195 |
|
| \begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.183 |
|
| \begin{align*}
x y^{\prime \prime }+3 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.166 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.172 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
0.184 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.178 |
|
| \begin{align*}
y^{\prime \prime }-\frac {x y^{\prime }}{x -1}+\frac {y}{x -1}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.174 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.178 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.182 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.184 |
|
| \begin{align*}
y^{\prime \prime }-y&=3 \,{\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.320 |
|
| \begin{align*}
y^{\prime \prime }+y&=-8 \sin \left (3 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime } t +x&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.254 |
|
| \begin{align*}
x^{\prime \prime }-x^{\prime } t +x&=0 \\
\end{align*} |
[_Hermite] |
✓ |
✓ |
✓ |
✗ |
0.285 |
|
| \begin{align*}
x^{\prime \prime }-2 a x^{\prime }+a^{2} x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.231 |
|
| \begin{align*}
x^{\prime \prime }-\frac {\left (t +2\right ) x^{\prime }}{t}+\frac {\left (t +2\right ) x}{t^{2}}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.233 |
|
| \begin{align*}
t^{2} x^{\prime \prime }+x^{\prime } t +\left (t^{2}-\frac {1}{4}\right ) x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.229 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.228 |
|
| \begin{align*}
\left (x +1\right )^{2} y^{\prime \prime }-3 \left (x +1\right ) y^{\prime }+3 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.244 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
0.231 |
|
| \begin{align*}
\left (x^{2}-x +1\right ) y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.243 |
|
| \begin{align*}
\left (2 x +1\right ) y^{\prime \prime }-4 \left (x +1\right ) y^{\prime }+4 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.258 |
|
| \begin{align*}
\left (x^{3}-x^{2}\right ) y^{\prime \prime }-\left (x^{3}+2 x^{2}-2 x \right ) y^{\prime }+\left (2 x^{2}+2 x -2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.275 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-\left (t^{2}+2 t \right ) y^{\prime }+\left (t +2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.237 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.269 |
|
| \begin{align*}
\left (-t^{2}+t \right ) x^{\prime \prime }+\left (-t^{2}+2\right ) x^{\prime }+\left (2-t \right ) x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.256 |
|
| \begin{align*}
y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*} |
[_Hermite] |
✓ |
✓ |
✓ |
✗ |
0.348 |
|
| \begin{align*}
\tan \left (t \right ) x^{\prime \prime }-3 x^{\prime }+\left (\tan \left (t \right )+3 \cot \left (t \right )\right ) x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.308 |
|
| \begin{align*}
\left (\tan \left (x \right )^{2}-1\right ) y^{\prime \prime }-4 \tan \left (x \right )^{3} y^{\prime }+2 y \sec \left (x \right )^{4}&=\left (\tan \left (x \right )^{2}-1\right ) \left (1-2 \sin \left (x \right )^{2}\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.715 |
|
| \begin{align*}
x^{3} y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.230 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.285 |
|
| \begin{align*}
x y^{\prime \prime }+2 y^{\prime }+y x&=0 \\
\end{align*} |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.258 |
|
| \begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.146 |
|
| \begin{align*}
y^{\prime \prime }-10 y^{\prime }+25 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.151 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-6 x y^{\prime }+12 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.125 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.123 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.127 |
|
| \begin{align*}
y^{\prime \prime }-\left (4+\frac {2}{x}\right ) y^{\prime }+\left (4+\frac {4}{x}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.142 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime \prime }+x y^{\prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.141 |
|
| \begin{align*}
y^{\prime \prime }-\frac {y^{\prime }}{x}-4 x^{2} y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.135 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.379 |
|
| \begin{align*}
x y^{\prime \prime }+\left (2 x +2\right ) y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.139 |
|
| \begin{align*}
\sin \left (x \right )^{2} y^{\prime \prime }-2 \cos \left (x \right ) \sin \left (x \right ) y^{\prime }+\left (\cos \left (x \right )^{2}+1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.143 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.132 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.179 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.364 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&=9 \,{\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.261 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+8 y&={\mathrm e}^{4 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.334 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-y&=\sqrt {x} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.260 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-20 y&=27 x^{5} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.273 |
|
| \begin{align*}
x y^{\prime \prime }+\left (2 x +2\right ) y^{\prime }+2 y&=8 \,{\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.296 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime \prime }+x y^{\prime }-y&=\left (x +1\right )^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.296 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.182 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+8 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.186 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.294 |
|
| \begin{align*}
y^{\prime \prime }+10 y^{\prime }+25 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.188 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -4 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.746 |
|
| \begin{align*}
y^{\prime \prime }+49 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.617 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+4 t y^{\prime }-4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.159 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+6 t y^{\prime }+6 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.169 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.178 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+3 t y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.164 |
|
| \begin{align*}
4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (36 t^{2}-1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.181 |
|
| \begin{align*}
t y^{\prime \prime }+2 y^{\prime }+16 y t&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.183 |
|
| \begin{align*}
y^{\prime \prime }+b y^{\prime }+c y&=0 \\
y \left (\pi \right ) &= 0 \\
y \left (2 \pi \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.796 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-4 t y^{\prime }+\left (t^{2}+6\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.178 |
|
| \begin{align*}
t y^{\prime \prime }+2 y^{\prime }+y t&=0 \\
\end{align*} |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.162 |
|
| \begin{align*}
4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (16 t^{2}-1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.605 |
|
| \begin{align*}
\left (t +1\right )^{2} y^{\prime \prime }-2 \left (t +1\right ) y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.192 |
|
| \begin{align*}
t y^{\prime \prime }+2 y^{\prime }+y t&=0 \\
\end{align*} |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.167 |
|
| \begin{align*}
x^{2} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.211 |
|
| \begin{align*}
y^{\prime \prime }+\left (\tan \left (x \right )-2 \cot \left (x \right )\right ) y^{\prime }+2 \cot \left (x \right )^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.263 |
|
| \begin{align*}
y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cos \left (x \right )^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.858 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-y&=1 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.351 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }-3 y&=5 x^{4} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.322 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y&=\left (x -1\right )^{2} {\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.367 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y \,{\mathrm e}^{-2 x}&={\mathrm e}^{-3 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.451 |
|
| \begin{align*}
\left (x^{4}-x^{3}\right ) y^{\prime \prime }+\left (2 x^{3}-2 x^{2}-x \right ) y^{\prime }-y&=\frac {\left (x -1\right )^{2}}{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.387 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }+y \,{\mathrm e}^{2 x}&=x \,{\mathrm e}^{2 x}-1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.099 |
|
| \begin{align*}
x \left (x -1\right ) y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+2 y&=x^{2} \left (2 x -3\right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.379 |
|
| \begin{align*}
a y^{\prime \prime }+b y^{\prime }+\frac {b^{2} y}{4 a}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.306 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.207 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+2 t y^{\prime }-2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.212 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+3 t y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.209 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.226 |
|
| \begin{align*}
x y^{\prime \prime }-y^{\prime }+4 x^{3} y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.929 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.211 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-\left (x -\frac {3}{16}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.243 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.222 |
|
| \begin{align*}
x y^{\prime \prime }-\left (x +n \right ) y^{\prime }+n y&=0 \\
\end{align*} |
[_Laguerre] |
✓ |
✓ |
✓ |
✗ |
0.431 |
|
| \begin{align*}
y^{\prime \prime }+a \left (x y^{\prime }+y\right )&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.385 |
|
| \begin{align*}
t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y&={\mathrm e}^{2 t} t^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.385 |
|
| \begin{align*}
\left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y&=2 \left (t -1\right )^{2} {\mathrm e}^{-t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.401 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.127 |
|
| \begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.120 |
|
| \begin{align*}
x y^{\prime \prime }+3 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.107 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.115 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
0.132 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.123 |
|
| \begin{align*}
y^{\prime \prime }-\frac {x y^{\prime }}{x -1}+\frac {y}{x -1}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.121 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.114 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.125 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.125 |
|
| \begin{align*}
\left (x -3\right ) y^{\prime \prime }-\left (4 x -9\right ) y^{\prime }+3 \left (x -2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.122 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.099 |
|
| \begin{align*}
\left (x \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.132 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }-a^{2} y&=0 \\
\end{align*} |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.171 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-\left (x^{2}+2 x \right ) y^{\prime }+\left (x +2\right ) y&={\mathrm e}^{x} x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.290 |
|
| \begin{align*}
y^{\prime \prime }-a x y^{\prime }+a^{2} \left (x -1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.184 |
|
| \begin{align*}
\left (2 x^{3}-a \right ) y^{\prime \prime }-6 x^{2} y^{\prime }+6 y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.133 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-9 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.124 |
|
| \begin{align*}
x y^{\prime \prime } \left (x \cos \left (x \right )-2 \sin \left (x \right )\right )+\left (x^{2}+2\right ) y^{\prime } \sin \left (x \right )-2 y \left (x \sin \left (x \right )+\cos \left (x \right )\right )&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
✗ |
0.210 |
|
| \begin{align*}
y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*} |
[_Hermite] |
✓ |
✓ |
✓ |
✗ |
0.310 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
0.300 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
0.277 |
|
| \begin{align*}
y^{\prime \prime }+\cos \left (x \right ) y^{\prime }+\left (1+\sin \left (x \right )\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.761 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.119 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (2 x^{2}-x \right ) y^{\prime }-2 y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.126 |
|
| \begin{align*}
x^{3} y^{\prime \prime }+\left (5 x^{3}-x^{2}\right ) y^{\prime }+2 \left (3 x^{3}-x^{2}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.142 |
|
| \begin{align*}
x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }-y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.131 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (x +2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.131 |
|
| \begin{align*}
x y^{\prime \prime }+\left (x -1\right ) y^{\prime }+\left (3-12 x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.132 |
|
| \begin{align*}
x^{2} \left (1-\ln \left (x \right )\right ) y^{\prime \prime }+x y^{\prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.131 |
|
| \begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {9 y}{x^{4}}&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.264 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.247 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-7 x y^{\prime }+7 y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
0.135 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x^{{1}/{3}}}+\left (\frac {1}{4 x^{{2}/{3}}}-\frac {1}{6 x^{{4}/{3}}}-\frac {6}{x^{2}}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.151 |
|
| \begin{align*}
x \left (x -2\right ) y^{\prime \prime }-2 \left (x^{2}-3 x +3\right ) y^{\prime }+\left (x^{2}-4 x +6\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.150 |
|
| \begin{align*}
x \left (1-3 x \ln \left (x \right )\right ) y^{\prime \prime }+\left (1+9 x^{2} \ln \left (x \right )\right ) y^{\prime }-\left (3+9 x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
✗ |
0.245 |
|
| \begin{align*}
y^{\prime \prime }-\left (1+\frac {3}{2 x}\right ) y^{\prime }+\frac {3 y}{2 x^{2}}&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.158 |
|
| \begin{align*}
x \left (1-2 x \ln \left (x \right )\right ) y^{\prime \prime }+\left (1+4 x^{2} \ln \left (x \right )\right ) y^{\prime }-\left (4 x +2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
✗ |
0.243 |
|
| \begin{align*}
y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.148 |
|
| \begin{align*}
6 y-2 x y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.242 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
0.126 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+12 y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
0.146 |
|
| \begin{align*}
x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y&=0 \\
\end{align*} |
[_Laguerre] |
✓ |
✓ |
✓ |
✗ |
0.135 |
|
| \begin{align*}
x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+2 y&=0 \\
\end{align*} |
[_Laguerre] |
✓ |
✓ |
✓ |
✗ |
0.147 |
|
| \begin{align*}
x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+3 y&=0 \\
\end{align*} |
[_Laguerre] |
✓ |
✓ |
✓ |
✗ |
0.156 |
|
| \begin{align*}
y-x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.131 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+4 y&=0 \\
\end{align*} |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.128 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+9 y&=0 \\
\end{align*} |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.156 |
|
| \begin{align*}
2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.121 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.119 |
|
| \begin{align*}
x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\
y \left (1\right ) &= 2 \,{\mathrm e} \\
y^{\prime }\left (1\right ) &= -3 \,{\mathrm e} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.256 |
|
| \begin{align*}
2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=\left (x^{2}+1\right )^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.355 |
|
| \begin{align*}
x \left (1-2 x \ln \left (x \right )\right ) y^{\prime \prime }+\left (1+4 x^{2} \ln \left (x \right )\right ) y^{\prime }-\left (4 x +2\right ) y&={\mathrm e}^{2 x} \left (1-2 x \ln \left (x \right )\right )^{2} \\
y \left (\frac {1}{2}\right ) &= \frac {{\mathrm e}}{2} \\
y^{\prime }\left (\frac {1}{2}\right ) &= {\mathrm e} \left (2+\ln \left (2\right )\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
✗ |
1.261 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-y&=x^{2} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.248 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-y&=x^{2} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.243 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }+y&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.255 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }+y&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.249 |
|
| \begin{align*}
6 x^{2} y^{\prime \prime }-5 x y^{\prime }+4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.123 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.117 |
|
| \begin{align*}
x \left (x +1\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-\left (x +2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.137 |
|
| \begin{align*}
y^{\prime \prime }+x y^{\prime }+\left (3 x -9\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.160 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-3 t y^{\prime }+4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.177 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+2 t y^{\prime }-2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.159 |
|
| \begin{align*}
4 t^{2} y^{\prime \prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.160 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+2 t y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.151 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.172 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-4 t y^{\prime }+\left (t^{2}+6\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.171 |
|
| \begin{align*}
t y^{\prime \prime }-y^{\prime }+4 t^{3} y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.183 |
|
| \begin{align*}
t y^{\prime \prime }-2 \left (t +1\right ) y^{\prime }+4 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.178 |
|
| \begin{align*}
y^{\prime \prime }-2 \sec \left (t \right )^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.189 |
|
| \begin{align*}
t y^{\prime \prime }+\left (t -1\right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.164 |
|
| \begin{align*}
y^{\prime \prime }-\tan \left (t \right ) y^{\prime }-\sec \left (t \right )^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.188 |
|
| \begin{align*}
\left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.162 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-2 t y^{\prime }+\left (t^{2}+2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.166 |
|
| \begin{align*}
\left (-t^{2}+1\right ) y^{\prime \prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.178 |
|
| \begin{align*}
\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
0.176 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+5 t y^{\prime }+4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.182 |
|
| \begin{align*}
2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.108 |
|
| \begin{align*}
y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \sec \left (x \right )^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.148 |
|
| \begin{align*}
x^{3} y^{\prime \prime }+3 x^{2} y^{\prime }-3 y x&=1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.238 |
|
| \begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }-2 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.100 |
|
| \begin{align*}
x y^{\prime \prime }+2 y^{\prime }-y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.105 |
|
| \begin{align*}
y^{\prime \prime } \left (1+{\mathrm e}^{x}\right )-2 y^{\prime }-y \,{\mathrm e}^{x}&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.268 |
|
| \begin{align*}
y^{\prime \prime }-\tan \left (x \right ) y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.131 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+5 x y^{\prime }+4 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.165 |
|