| # |
ODE |
CAS classification |
Solved |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
y \left (1\right ) &= 3 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.230 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y&=0 \\
y \left (2\right ) &= 10 \\
y^{\prime }\left (2\right ) &= 15 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.694 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
y \left (1\right ) &= 7 \\
y^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.013 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 3 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.046 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.088 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -12 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+8 y^{\prime } x -3 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.656 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.904 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +9 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.688 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+7 y^{\prime } x +25 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=72 x^{5} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.506 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.401 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x^{4} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.008 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }-4 y^{\prime } x +3 y&=8 x^{{4}/{3}} \\
\end{align*} | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✓ | 1.355 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +y&=\ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.311 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=x^{2}-1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.777 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
y \left (1\right ) &= 3 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.241 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y&=0 \\
y \left (2\right ) &= 10 \\
y^{\prime }\left (2\right ) &= 15 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.730 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
y \left (1\right ) &= 7 \\
y^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.069 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 3 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.046 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.096 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -12 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.536 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+8 y^{\prime } x -3 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.539 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +9 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+7 y^{\prime } x +25 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.894 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=72 x^{5} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.708 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.632 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x^{4} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.165 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }-4 y^{\prime } x +3 y&=8 x^{{4}/{3}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.427 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +y&=\ln \left (x \right ) \\
\end{align*} | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✓ | 1.500 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=x^{2}-1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.889 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.869 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+4 t y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.262 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+3 t y^{\prime }+\frac {5 y}{4}&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.029 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-4 t y^{\prime }-6 y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.865 |
|
| \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)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.999 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-t y^{\prime }+5 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.997 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+3 t y^{\prime }-3 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.721 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+7 t y^{\prime }+10 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.940 |
|
| \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)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.778 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+2 t y^{\prime }+\frac {y}{4}&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.745 |
|
| \begin{align*}
2 t^{2} y^{\prime \prime }-5 t y^{\prime }+5 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.097 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+3 t y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.980 |
|
| \begin{align*}
4 t^{2} y^{\prime \prime }-8 t y^{\prime }+9 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.774 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+5 t y^{\prime }+13 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.024 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=2 t^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.796 |
|
| \begin{align*}
\left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y&=2 \left (-1+t \right )^{2} {\mathrm e}^{-t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.010 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=\ln \left (x \right ) x^{2} \\
\end{align*} | [[_2nd_order, _linear, _nonhomogeneous]] | ✓ | ✓ | ✓ | ✓ | 1.497 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-2 t y^{\prime }+2 y&=4 t^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.717 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+7 t y^{\prime }+5 y&=t \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.598 |
|
| \begin{align*}
\left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y&=2 \left (-1+t \right ) {\mathrm e}^{-t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.038 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.193 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.871 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-\left (2 a -1\right ) x y^{\prime }+a^{2} y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.664 |
|
| \begin{align*}
4 x^{2} \sin \left (x \right ) y^{\prime \prime }-4 x \left (\sin \left (x \right )+\cos \left (x \right ) x \right ) y^{\prime }+\left (2 \cos \left (x \right ) x +3 \sin \left (x \right )\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.589 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.634 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=2 x^{2}+2 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.905 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x^{{5}/{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.691 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=2 x^{4} \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.138 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-\left (2 a -1\right ) x y^{\prime }+a^{2} y&=x^{a +1} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.405 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x -3 y&=x^{{3}/{2}} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.558 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x \left (x +4\right ) y^{\prime }+2 \left (x +3\right ) y&={\mathrm e}^{x} x^{4} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.810 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=2 \left (x -1\right )^{2} {\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.947 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }-4 x \left (x +1\right ) y^{\prime }+\left (2 x +3\right ) y&=x^{{5}/{2}} {\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.845 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y&=-2 x^{2} \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.411 |
|
| \begin{align*}
2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} | [[_2nd_order, _exact, _linear, _homogeneous]] | ✓ | ✓ | ✓ | ✓ | 1.174 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+\alpha t y^{\prime }+\beta y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.409 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+5 t y^{\prime }-5 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.766 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-t y^{\prime }-2 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.658 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.904 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+2 t y^{\prime }+2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.161 |
|
| \begin{align*}
\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
0.752 |
|
| \begin{align*}
\left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.714 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+3 t y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.023 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-t y^{\prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.908 |
|
| \begin{align*}
y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1}&=t^{2}+1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.104 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-5 t y^{\prime }+9 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.862 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+5 t y^{\prime }-5 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.737 |
|
| \begin{align*}
2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.845 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+3 t y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.016 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-t y^{\prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.908 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.854 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-t y^{\prime }+2 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.533 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-3 t y^{\prime }+4 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} | [[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] | ✓ | ✓ | ✓ | ✓ | 1.063 |
|
| \begin{align*}
2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.078 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+\alpha t y^{\prime }+\beta y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.230 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+5 t y^{\prime }-2 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.470 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.789 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+2 t y^{\prime }+2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.020 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+3 t y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.949 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-t y^{\prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| \begin{align*}
y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1}&=t^{2}+1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.115 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+5 t y^{\prime }-5 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| \begin{align*}
2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.772 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+3 t y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.894 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-t y^{\prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.744 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+3 t y^{\prime }+2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.885 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-t y^{\prime }-2 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.099 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-3 t y^{\prime }+4 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.929 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.639 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +16 y&=0 \\
\end{align*} | [[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] | ✓ | ✓ | ✓ | ✓ | 1.059 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }-16 y^{\prime } x +25 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.993 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +10 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.417 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-3 y^{\prime } x -18 y&=\ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.290 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-3 y^{\prime } x +2 y&=\ln \left (x^{2}\right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.073 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.451 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=1-x \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.772 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=4 x +\sin \left (\ln \left (x \right )\right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.921 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=\ln \left (x \right ) x^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.962 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x +3 y&=\left (x -1\right ) \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
57.925 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.036 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +3 y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.101 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.829 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +13 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.017 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=9 x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.957 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x^{4} \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.342 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.452 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.817 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x -8 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=\ln \left (x \right ) x^{2} \\
\end{align*} | [[_2nd_order, _linear, _nonhomogeneous]] | ✓ | ✓ | ✓ | ✓ | 1.129 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x -8 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.471 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.934 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=4 \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.705 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=\cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.754 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +9 y&=9 \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.458 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +5 y&=8 x \ln \left (x \right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.308 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x^{4} \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.586 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+6 y^{\prime } x +6 y&=4 \,{\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.503 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=\frac {x^{2}}{\ln \left (x \right )} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.240 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+m^{2} y&=x^{m} \ln \left (x \right )^{k} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.253 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +5 y&=0 \\
y \left (1\right ) &= \sqrt {2} \\
y^{\prime }\left (1\right ) &= 3 \sqrt {2} \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.329 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }+25 y&=0 \\
y \left (1\right ) &= \frac {3 \sqrt {3}}{2} \\
y^{\prime }\left (1\right ) &= {\frac {15}{2}} \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.121 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=x^{2}+2 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.687 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=\ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.362 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +5 y&=\frac {5 \ln \left (x \right )}{x^{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
23.016 |
|
| \begin{align*}
-y+y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.737 |
|
| \begin{align*}
y x -x^{2} y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.797 |
|
| \begin{align*}
y x -x^{2} y^{\prime }+y^{\prime \prime }&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.449 |
|
| \begin{align*}
-x^{3} y+x^{4} y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✗ | 1.173 |
|
| \begin{align*}
-a \,x^{-1+k} y+a \,x^{k} y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.563 |
|
| \begin{align*}
f \left (x \right ) y+\left (2+f \left (x \right ) x \right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.306 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.788 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=\left (1-x \right )^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.954 |
|
| \begin{align*}
y-y^{\prime } x +\left (-x \cot \left (x \right )+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.367 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.910 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.229 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.921 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=a \,x^{2} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.790 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=x^{2} \left (x +3\right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.414 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=3 x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.395 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +y&=\ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.598 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.047 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=x \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.259 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x -3 y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.838 |
|
| \begin{align*}
-a^{2} y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.033 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.237 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=4 x^{3} \\
\end{align*} | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✓ | 1.678 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=x^{3} \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.123 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=2 x \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.928 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=x^{5} \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.963 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.582 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y&=-x +2 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.904 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.017 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=x \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.408 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=a -x +x \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.876 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.814 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=5 x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.204 |
|
| \begin{align*}
-5 y-3 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.833 |
|
| \begin{align*}
-5 y-3 y^{\prime } x +x^{2} y^{\prime \prime }&=\ln \left (x \right ) x^{2} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.333 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.295 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&={\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.970 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=\ln \left (x +1\right ) \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.109 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.093 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x^{2} \left (x^{2}-1\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.684 |
|
| \begin{align*}
13 y+5 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\
\end{align*} | [[_Emden, _Fowler]] | ✓ | ✓ | ✓ | ✓ | 1.096 |
|
| \begin{align*}
16 y-7 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.826 |
|
| \begin{align*}
\operatorname {a2} y+\operatorname {a1} x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.398 |
|
| \begin{align*}
a \left (a +1\right ) y-2 a x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.937 |
|
| \begin{align*}
a \left (a +1\right ) y-2 a x y^{\prime }+x^{2} y^{\prime \prime }&={\mathrm e}^{x} x^{2+a} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.441 |
|
| \begin{align*}
-\left (1-x \right ) y+x \left (1-x \right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.595 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.487 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y&=x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.741 |
|
| \begin{align*}
2 \left (x +1\right ) y-2 x \left (x +1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.631 |
|
| \begin{align*}
-\left (-x^{2}+2\right ) y+x^{3} y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.694 |
|
| \begin{align*}
-\left (x^{2}+1\right ) y+x \left (-x^{2}+1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.845 |
|
| \begin{align*}
y-y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.700 |
|
| \begin{align*}
-y+y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
0.750 |
|
| \begin{align*}
y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.663 |
|
| \begin{align*}
-y+y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=x \left (-x^{2}+1\right )^{{3}/{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.821 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.689 |
|
| \begin{align*}
2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.691 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=\left (-x^{2}+1\right )^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.924 |
|
| \begin{align*}
6 y-2 y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✓ |
✗ |
0.507 |
|
| \begin{align*}
-2 y+2 y^{\prime } x +\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✗ | 0.654 |
|
| \begin{align*}
y+\left (3 x +2\right ) y^{\prime }+x \left (x +1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.705 |
|
| \begin{align*}
-6 y-2 \left (1-2 x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✓ |
✗ |
0.487 |
|
| \begin{align*}
2 \left (1-x \right ) y-\left (-x^{2}+2\right ) y^{\prime }+\left (-x +2\right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.757 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.604 |
|
| \begin{align*}
-3 y+y^{\prime } x +2 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.845 |
|
| \begin{align*}
-y+\left (x +1\right ) y^{\prime }+2 \left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✓ |
✗ |
0.678 |
|
| \begin{align*}
5 y-8 y^{\prime } x +4 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.009 |
|
| \begin{align*}
\left (x +3\right ) y-2 x \left (2+x \right ) y^{\prime }+4 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.697 |
|
| \begin{align*}
-\left (-2 x^{2}+3\right ) y+4 x^{3} y^{\prime }+4 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.832 |
|
| \begin{align*}
2 a^{2} y-2 a^{2} x y^{\prime }+\left (-a^{2} x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
0.851 |
|
| \begin{align*}
-2 b y+2 a y^{\prime }+x \left (b x +a \right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.829 |
|
| \begin{align*}
-y+y^{\prime } x +x^{3} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.633 |
|
| \begin{align*}
y x +3 x^{2} y^{\prime }+x^{3} y^{\prime \prime }&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.820 |
|
| \begin{align*}
y x +3 x^{2} y^{\prime }+x^{3} y^{\prime \prime }&=1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.361 |
|
| \begin{align*}
\left (a -1\right ) \left (a +b \right ) x y+\left (b \,x^{2}+a \right ) y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
3.428 |
|
| \begin{align*}
\left (2 x +1\right ) y-x \left (2 x +1\right ) y^{\prime }+x^{2} \left (x +1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.517 |
|
| \begin{align*}
2 \left (x +1\right ) y+2 x \left (-x +2\right ) y^{\prime }+\left (1-x \right ) x^{2} y^{\prime \prime }&=0 \\
\end{align*} | [[_2nd_order, _exact, _linear, _homogeneous]] | ✓ | ✓ | ✓ | ✗ | 0.776 |
|
| \begin{align*}
\left (6-9 x \right ) y-\left (4-5 x \right ) x y^{\prime }+\left (1-x \right ) x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.537 |
|
| \begin{align*}
2 \left (1+3 x \right ) y+2 x \left (3 x +2\right ) y^{\prime }+x^{2} \left (x +1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.840 |
|
| \begin{align*}
-6 y x +6 x^{2} y^{\prime }+\left (-2 x^{3}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.754 |
|
| \begin{align*}
-\left (x +1\right ) y+x \left (3-5 x \right ) y^{\prime }+2 \left (1-x \right ) x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.588 |
|
| \begin{align*}
\left (-x +3\right ) y-x \left (4-x \right ) y^{\prime }+2 \left (-x +2\right ) x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.500 |
|
| \begin{align*}
-6 y x +2 y^{\prime }+x \left (3 x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✗ |
0.600 |
|
| \begin{align*}
\left (1+3 x \right ) y-4 x^{2} y^{\prime }+4 x^{2} \left (x +1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.497 |
|
| \begin{align*}
2 \left (b x +3 a \right ) y-2 x \left (b x +2 a \right ) y^{\prime }+x^{2} \left (b x +a \right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.645 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y-x \left (-x^{2}+1\right ) y^{\prime }+x^{4} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.569 |
|
| \begin{align*}
\left (-x^{2}+2\right ) y-x \left (-x^{2}+2\right ) y^{\prime }+x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.532 |
|
| \begin{align*}
-y+y^{\prime } x +x^{5} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.190 |
|
| \begin{align*}
\left (-2 x^{3}+1\right ) y-x \left (-2 x^{3}+1\right ) y^{\prime }+x^{5} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.668 |
|
| \begin{align*}
a^{2} x^{a -1} y+\left (-2 a +1\right ) x^{a} y^{\prime }+x^{a +1} y^{\prime \prime }&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✗ |
0.715 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.516 |
|
| \begin{align*}
y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\frac {2 y}{x^{2}}&=x \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.086 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.339 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=x^{2} {\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.355 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+3 y^{\prime } x -y&=\frac {1}{x} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.369 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
\end{align*} | [[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] | ✓ | ✓ | ✓ | ✓ | 1.112 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x -3 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.723 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.826 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+7 y^{\prime } x +9 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +6 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.108 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -16 y&=8 x^{4} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.747 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=x -\frac {1}{x} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.230 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=2 x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.431 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=6 \ln \left (x \right ) x^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.474 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +y&=2 x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.237 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.418 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.105 |
|
| \begin{align*}
\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.645 |
|
| \begin{align*}
2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.645 |
|
| \begin{align*}
\left (1-x \right ) x y^{\prime \prime }+2 \left (1-2 x \right ) y^{\prime }-2 y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.887 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -9 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.009 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.059 |
|
| \begin{align*}
t^{2} N^{\prime \prime }-2 t N^{\prime }+2 N&=t \ln \left (t \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.243 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}}&=\ln \left (x \right ) \\
\end{align*} | [[_2nd_order, _exact, _linear, _nonhomogeneous]] | ✓ | ✓ | ✓ | ✓ | 2.670 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.922 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.014 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x +\ln \left (x \right ) x^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.289 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=\ln \left (x \right )^{2}-\ln \left (x^{2}\right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.997 |
|
| \begin{align*}
2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=2 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.954 |
|
| \begin{align*}
\left (x^{2}+4\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=8 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.924 |
|
| \begin{align*}
\left (x \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+y \cos \left (x \right )&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.321 |
|
| \begin{align*}
y^{\prime \prime } x -3 y^{\prime }+\frac {3 y}{x}&=2+x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.456 |
|
| \begin{align*}
2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=\frac {-x^{2}+1}{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.931 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.033 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.790 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +y&=\sec \left (\ln \left (x \right )\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.020 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }+\left (1-x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.467 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}}&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.471 |
|
| \begin{align*}
y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.632 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x +4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.137 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime } x -y&=x^{2}+2 x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.213 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=x^{2}+2 x \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.007 |
|
| \begin{align*}
-y+y^{\prime } x +x^{3} y^{\prime \prime }&=\cos \left (\frac {1}{x}\right ) \\
\end{align*} | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✗ | 1.096 |
|
| \begin{align*}
x \left (x +1\right ) y^{\prime \prime }+\left (2+x \right ) y^{\prime }-y&=x +\frac {1}{x} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.624 |
|
| \begin{align*}
x^{2} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-y^{\prime } x +y&=x \left (1-\ln \left (x \right )\right )^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.852 |
|
| \begin{align*}
p \,x^{2} u^{\prime \prime }+q x u^{\prime }+r u&=f \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.026 |
|
| \begin{align*}
y^{\prime \prime }-\frac {x y^{\prime }}{-x^{2}+1}+\frac {y}{-x^{2}+1}&=0 \\
\end{align*} |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.516 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}}&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
18.359 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}}&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
18.138 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.511 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.613 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.700 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.084 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.257 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +5 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.892 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (-2-i\right ) x y^{\prime }+3 i y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.924 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -4 \pi y&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.497 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +10 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.113 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+10 y^{\prime } x +8 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.812 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -12 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.577 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\
\end{align*} | [[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] | ✓ | ✓ | ✓ | ✓ | 0.774 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.568 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x +3 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.104 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.916 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -16 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.822 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=\left (x^{2}-1\right )^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.871 |
|
| \begin{align*}
\left (x^{2}+x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-\left (2+x \right ) y&=x \left (x +1\right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.786 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=\left (1-x \right )^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.021 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=x \,{\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.251 |
|
| \begin{align*}
y^{\prime \prime }-x f \left (x \right ) y^{\prime }+f \left (x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.321 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {2}{x} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.609 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.953 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.870 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-3 y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.070 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+5 y^{\prime } x -2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.703 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -12 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -9 y&=0 \\
\end{align*} | [[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] | ✓ | ✓ | ✓ | ✓ | 1.030 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.938 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.932 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +5 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.260 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-3 t y^{\prime }+5 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.185 |
|
| \begin{align*}
x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y&=1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.704 |
|
| \begin{align*}
x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.638 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.212 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=2 x^{3}-x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.535 |
|
| \begin{align*}
y x -x^{2} y^{\prime }+y^{\prime \prime }&=x^{m +1} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.381 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.878 |
|
| \begin{align*}
-y+y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.552 |
|
| \begin{align*}
y x -x^{2} y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.958 |
|
| \begin{align*}
-x^{3} y+x^{4} y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
4.501 |
|
| \begin{align*}
y^{\prime \prime } x -\left (x^{2}-x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.753 |
|
| \begin{align*}
f \left (x \right ) y+\left (2+f \left (x \right ) x \right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.741 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y-a \,x^{2}&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.816 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +a y&=0 \\
\end{align*} | [[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] | ✓ | ✓ | ✓ | ✓ | 2.821 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y-3 x^{3}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.060 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y-x^{5} \ln \left (x \right )&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.075 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x -4 y-x \sin \left (x \right )-\left (a \,x^{2}+12 a +4\right ) \cos \left (x \right )&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.279 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y-5 x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.667 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x -5 y-\ln \left (x \right ) x^{2}&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.574 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y-x^{4}+x^{2}&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.671 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y-x^{3} \sin \left (x \right )&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.480 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+a x y^{\prime }+b y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.797 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x \left (x -1\right ) y^{\prime }+\left (x -1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.777 |
|
| \begin{align*}
2 \left (x +1\right ) y-2 x \left (x +1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.662 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x^{3} y^{\prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.292 |
|
| \begin{align*}
y-y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.671 |
|
| \begin{align*}
2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.475 |
|
| \begin{align*}
y+\left (3 x +2\right ) y^{\prime }+x \left (x +1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.548 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+5 y^{\prime } x -y-\ln \left (x \right )&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.355 |
|
| \begin{align*}
\left (a^{2} x^{2}-1\right ) y^{\prime \prime }+2 a^{2} x y^{\prime }-2 a^{2} y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
0.652 |
|
| \begin{align*}
\left (a \,x^{2}+b x \right ) y^{\prime \prime }+2 b y^{\prime }-2 a y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.664 |
|
| \begin{align*}
x^{3} y^{\prime \prime }-x^{2} y^{\prime }+y x -\ln \left (x \right )^{3}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.229 |
|
| \begin{align*}
x^{3} y^{\prime \prime }+3 x^{2} y^{\prime }+y x -1&=0 \\
\end{align*} | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✓ | 1.143 |
|
| \begin{align*}
\left (2 x +1\right ) y-x \left (2 x +1\right ) y^{\prime }+x^{2} \left (x +1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.386 |
|
| \begin{align*}
y^{\prime \prime }&=-\frac {2 \left (x -2\right ) y^{\prime }}{x \left (x -1\right )}+\frac {2 \left (x +1\right ) y}{x^{2} \left (x -1\right )} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.404 |
|
| \begin{align*}
y^{\prime \prime }&=\frac {\left (5 x -4\right ) y^{\prime }}{x \left (x -1\right )}-\frac {\left (9 x -6\right ) y}{x^{2} \left (x -1\right )} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.455 |
|
| \begin{align*}
y^{\prime \prime }&=\frac {\left (x -4\right ) y^{\prime }}{2 x \left (x -2\right )}-\frac {\left (x -3\right ) y}{2 x^{2} \left (x -2\right )} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.402 |
|
| \begin{align*}
y^{\prime \prime }&=\frac {y^{\prime }}{x +1}-\frac {\left (1+3 x \right ) y}{4 x^{2} \left (x +1\right )} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.388 |
|
| \begin{align*}
y^{\prime \prime }&=\frac {2 \left (a x +2 b \right ) y^{\prime }}{x \left (a x +b \right )}-\frac {\left (2 a x +6 b \right ) y}{\left (a x +b \right ) x^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.481 |
|
| \begin{align*}
y^{\prime \prime }&=\frac {\left (x^{2}-2\right ) y^{\prime }}{x \left (x^{2}-1\right )}-\frac {\left (x^{2}-2\right ) y}{x^{2} \left (x^{2}-1\right )} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.463 |
|
| \begin{align*}
y^{\prime \prime }&=\frac {2 x y^{\prime }}{x^{2}-1}-\frac {\left (a \left (a +1\right )-a \,x^{2} \left (a +3\right )\right ) y}{x^{2} \left (x^{2}-1\right )} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.711 |
|
| \begin{align*}
y^{\prime \prime }&=\frac {\left (7 a \,x^{2}+5\right ) y^{\prime }}{x \left (a \,x^{2}+1\right )}-\frac {\left (15 a \,x^{2}+5\right ) y}{x^{2} \left (a \,x^{2}+1\right )} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.508 |
|
| \begin{align*}
y^{\prime \prime }&=-\frac {y^{\prime }}{x^{4}}+\frac {y}{x^{5}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.562 |
|
| \begin{align*}
y^{\prime \prime }&=\frac {y^{\prime }}{x \left (\ln \left (x \right )-1\right )}-\frac {y}{x^{2} \left (\ln \left (x \right )-1\right )} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.282 |
|
| \begin{align*}
y^{\prime \prime }&=-\frac {x \sin \left (x \right ) y^{\prime }}{\cos \left (x \right ) x -\sin \left (x \right )}+\frac {\sin \left (x \right ) y}{\cos \left (x \right ) x -\sin \left (x \right )} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.412 |
|
| \begin{align*}
y^{\prime \prime }&=-\frac {\left (x^{2} \sin \left (x \right )-2 \cos \left (x \right ) x \right ) y^{\prime }}{x^{2} \cos \left (x \right )}-\frac {\left (2 \cos \left (x \right )-x \sin \left (x \right )\right ) y}{x^{2} \cos \left (x \right )} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
✗ |
0.748 |
|
| \begin{align*}
y^{\prime \prime }&=-\frac {x y^{\prime }}{f \left (x \right )}+\frac {y}{f \left (x \right )} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.417 |
|
| \begin{align*}
y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }-\left (a \,x^{n -1}+b \,x^{m -1}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.026 |
|
| \begin{align*}
y^{\prime \prime } x +\left (a \,x^{2}+b x +c \right ) y^{\prime }+\left (c -1\right ) \left (a x +b \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.991 |
|
| \begin{align*}
y^{\prime \prime } x +\left (a \,x^{3}+b \right ) y^{\prime }+a \left (b -1\right ) x^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.858 |
|
| \begin{align*}
y^{\prime \prime } x +\left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime }+\left (d -1\right ) \left (a \,x^{2}+b x +c \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.213 |
|
| \begin{align*}
y^{\prime \prime } x +\left (a \,x^{n}+2\right ) y^{\prime }+a \,x^{n -1} y&=0 \\
\end{align*} | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✗ | 0.606 |
|
| \begin{align*}
y^{\prime \prime } x +\left (a \,x^{n}+b \right ) y^{\prime }+a \left (b -1\right ) x^{n -1} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.587 |
|
| \begin{align*}
y^{\prime \prime } x +\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }+\left (c -1\right ) \left (a \,x^{n -1}+b \,x^{m -1}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
✗ |
1.037 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+a x y^{\prime }+b y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.546 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime } x +b \left (a \,x^{n}-1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.740 |
|
| \begin{align*}
x^{2} \left (a x +b \right ) y^{\prime \prime }-2 x \left (a x +2 b \right ) y^{\prime }+2 \left (a x +3 b \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.697 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {1}{\left (1-x \right )^{2}} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
4.430 |
|
| \begin{align*}
y x -x^{2} y^{\prime }+y^{\prime \prime }&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.109 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.580 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=\left (1-x \right )^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.870 |
|
| \begin{align*}
2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.546 |
|
| \begin{align*}
\left (2 x^{3}-1\right ) y^{\prime \prime }-6 x^{2} y^{\prime }+6 y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.607 |
|
| \begin{align*}
2 \left (x +1\right ) y-2 x \left (x +1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.754 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=x \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.214 |
|
| \begin{align*}
x^{5} y^{\prime \prime }+\left (2 x^{4}-x \right ) y^{\prime }-\left (2 x^{3}-1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.506 |
|
| \begin{align*}
t^{2} x^{\prime \prime }+3 t x^{\prime }+x&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.945 |
|
| \begin{align*}
t x^{\prime \prime }+4 x^{\prime }+\frac {2 x}{t}&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.961 |
|
| \begin{align*}
t^{2} x^{\prime \prime }-7 t x^{\prime }+16 x&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.722 |
|
| \begin{align*}
t^{2} x^{\prime \prime }+3 t x^{\prime }-8 x&=0 \\
x \left (1\right ) &= 0 \\
x^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.733 |
|
| \begin{align*}
t^{2} x^{\prime \prime }-t x^{\prime }+2 x&=0 \\
x \left (1\right ) &= 0 \\
x^{\prime }\left (1\right ) &= 1 \\
\end{align*} | [[_Emden, _Fowler]] | ✓ | ✓ | ✓ | ✓ | 1.312 |
|
| \begin{align*}
t^{2} x^{\prime \prime }-3 t x^{\prime }+3 x&=4 t^{7} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.708 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
y \left (1\right ) &= 3 \\
y^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.626 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=0 \\
y \left (2\right ) &= 3 \\
y^{\prime }\left (2\right ) &= -1 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.622 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-6 y^{\prime } x +10 y&=3 x^{4}+6 x^{3} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.555 |
|
| \begin{align*}
\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y&=\left (2+x \right )^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.151 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y&=x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.839 |
|
| \begin{align*}
x \left (x -2\right ) y^{\prime \prime }-\left (x^{2}-2\right ) y^{\prime }+2 \left (x -1\right ) y&=3 x^{2} \left (x -2\right )^{2} {\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.053 |
|
| \begin{align*}
\left (2 x +1\right ) \left (x +1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=\left (2 x +1\right )^{2} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.431 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.179 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.905 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }-4 y^{\prime } x +3 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.095 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.838 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.951 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +13 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.148 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }-4 y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.062 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +9 y&=0 \\
\end{align*} | [[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] | ✓ | ✓ | ✓ | ✓ | 0.921 |
|
| \begin{align*}
9 x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.859 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +10 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.136 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=4 x -6 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.666 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y&=2 x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.451 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=4 \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.301 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=2 x \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.936 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=4 \sin \left (\ln \left (x \right )\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.152 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x -10 y&=0 \\
y \left (1\right ) &= 5 \\
y^{\prime }\left (1\right ) &= 4 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.905 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
y \left (2\right ) &= 0 \\
y^{\prime }\left (2\right ) &= 4 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.559 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +3 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= -5 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.688 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y&=-6 x^{3}+4 x^{2} \\
y \left (2\right ) &= 4 \\
y^{\prime }\left (2\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.217 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y&=10 x^{2} \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= -6 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.287 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y&=2 x^{3} \\
y \left (2\right ) &= 0 \\
y^{\prime }\left (2\right ) &= -8 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.823 |
|
| \begin{align*}
\left (t^{3}-2 t^{2}\right ) x^{\prime \prime }-\left (t^{3}+2 t^{2}-6 t \right ) x^{\prime }+\left (3 t^{2}-6\right ) x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.762 |
|
| \begin{align*}
t^{2} x^{\prime \prime }+3 t x^{\prime }+3 x&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.267 |
|
| \begin{align*}
t^{2} x^{\prime \prime }+\left (2 t^{3}+7 t \right ) x^{\prime }+\left (8 t^{2}+8\right ) x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.758 |
|
| \begin{align*}
\frac {\left (t +1\right ) x^{\prime \prime }}{t}-\frac {x^{\prime }}{t^{2}}+\frac {x}{t^{3}}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.538 |
|
| \begin{align*}
t^{2} x^{\prime \prime }+t x^{\prime }+x&=0 \\
\end{align*} | [[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] | ✓ | ✓ | ✓ | ✓ | 0.922 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }+\frac {\lambda y}{x}&=0 \\
y \left (1\right ) &= 0 \\
y \left ({\mathrm e}^{\pi }\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.171 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }+\frac {\lambda y}{x}&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left ({\mathrm e}^{\pi }\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.053 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.411 |
|
| \begin{align*}
t^{2} x^{\prime \prime }-5 t x^{\prime }+10 x&=0 \\
x \left (1\right ) &= 2 \\
x^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.006 |
|
| \begin{align*}
t^{2} x^{\prime \prime }+t x^{\prime }-x&=0 \\
x \left (1\right ) &= 1 \\
x^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.102 |
|
| \begin{align*}
x^{2} z^{\prime \prime }+3 x z^{\prime }+4 z&=0 \\
z \left (1\right ) &= 0 \\
z^{\prime }\left (1\right ) &= 5 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.335 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x -3 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.446 |
|
| \begin{align*}
4 t^{2} x^{\prime \prime }+8 t x^{\prime }+5 x&=0 \\
x \left (1\right ) &= 2 \\
x^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.972 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +5 y&=0 \\
y \left (1\right ) &= -2 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.678 |
|
| \begin{align*}
3 x^{2} z^{\prime \prime }+5 x z^{\prime }-z&=0 \\
z \left (1\right ) &= 2 \\
z^{\prime }\left (1\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.468 |
|
| \begin{align*}
t^{2} x^{\prime \prime }+3 t x^{\prime }+13 x&=0 \\
x \left (1\right ) &= -1 \\
x^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.430 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=2 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.730 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.600 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x +1}-\frac {\left (2+x \right ) y}{x^{2} \left (x +1\right )}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.471 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+3 t y^{\prime }+y&=t^{7} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.559 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.227 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+3 y^{\prime } x -y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.865 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} | [[_Emden, _Fowler]] | ✓ | ✓ | ✓ | ✓ | 0.738 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+6 y^{\prime } x +4 y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.161 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
y \left (1\right ) &= 0 \\
y \left (2\right ) &= -4 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.278 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
y \left (2\right ) &= 4 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.336 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (2\right ) &= -12 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.392 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
y^{\prime }\left (1\right ) &= 3 \\
y^{\prime }\left (2\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.389 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
y \left (0\right ) &= 0 \\
y \left (2\right ) &= 4 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.108 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.811 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= -1 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.351 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=-3 x -\frac {3}{x} \\
y \left (1\right ) &= 3 \\
y^{\prime }\left (1\right ) &= -6 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
15.591 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 4 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.231 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+4 y^{\prime } x -y&=0 \\
y \left (1\right ) &= 8 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.294 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
y \left (1\right ) &= 5 \\
y^{\prime }\left (1\right ) &= 3 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.175 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.987 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.920 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} | [[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] | ✓ | ✓ | ✓ | ✓ | 1.079 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.771 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.777 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-19 y^{\prime } x +100 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.778 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +29 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.157 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +10 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.026 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +29 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.036 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.842 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.158 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -25 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.839 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+8 y^{\prime } x +5 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.014 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }-7 y^{\prime } x +3 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.873 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x -10 y&=0 \\
y \left (1\right ) &= 5 \\
y^{\prime }\left (1\right ) &= 4 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.851 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+4 y^{\prime } x -y&=0 \\
y \left (4\right ) &= 0 \\
y^{\prime }\left (4\right ) &= 2 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.470 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-11 y^{\prime } x +36 y&=0 \\
y \left (1\right ) &= {\frac {1}{2}} \\
y^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.064 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
y \left (1\right ) &= 3 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.266 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=0 \\
y \left (1\right ) &= 3 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.336 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +13 y&=0 \\
y \left (1\right ) &= 9 \\
y^{\prime }\left (1\right ) &= 3 \\
\end{align*} | [[_Emden, _Fowler]] | ✓ | ✓ | ✓ | ✓ | 1.269 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=10 x +12 \\
y \left (1\right ) &= 6 \\
y^{\prime }\left (1\right ) &= 8 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.608 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.314 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.322 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=22 x +24 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.369 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.238 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.200 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.165 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=4 x^{2}+2 x +3 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.244 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y&=\frac {5}{x^{3}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.477 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=\frac {50}{x^{3}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.638 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y&=85 \cos \left (2 \ln \left (x \right )\right ) \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.092 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }-7 y^{\prime } x +3 y&=4 x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.530 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y&=\frac {10}{x} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.797 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=6 x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.447 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=64 \ln \left (x \right ) x^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.420 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=3 \sqrt {x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.717 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=\sqrt {x} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.058 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -9 y&=12 x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.684 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x^{2} \\
\end{align*} | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✓ | 1.384 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=\ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.349 |
|
| \begin{align*}
y^{\prime \prime } x +\left (2 x +2\right ) y^{\prime }+2 y&=8 \,{\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.184 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime \prime }+y^{\prime } x -y&=\left (x +1\right )^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.913 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x -4 y&=\frac {10}{x} \\
y \left (1\right ) &= 3 \\
y^{\prime }\left (1\right ) &= -15 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.543 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -9 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.691 |
|
| \begin{align*}
16 y-7 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.742 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+7 y^{\prime } x +9 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.747 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +9 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.827 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -30 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.564 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+8 y^{\prime } x +y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-3 y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.839 |
|
| \begin{align*}
9 x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.747 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -9 y&=3 \sqrt {x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.707 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y&=18 \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.989 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x -2 y&=10 x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.069 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y&=6 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.468 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=\frac {1}{x^{2}+1} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.302 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {1}{\left (x +1\right )^{2}} \\
\end{align*} | [[_2nd_order, _exact, _linear, _nonhomogeneous]] | ✓ | ✓ | ✓ | ✗ | 1.642 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {1}{x} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.585 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }+2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.993 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-12 y^{\prime } x +42 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.999 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+3 t y^{\prime }+5 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.026 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-12 t y^{\prime }+42 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= -1 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.231 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +5 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.449 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x -16 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.881 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.012 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.997 |
|
| \begin{align*}
y^{\prime \prime }-\frac {y^{\prime }}{t}+\frac {y}{t^{2}}&=\frac {1}{t} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.850 |
|
| \begin{align*}
2 t^{2} y^{\prime \prime }-3 t y^{\prime }-3 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.736 |
|
| \begin{align*}
3 t^{2} y^{\prime \prime }-5 t y^{\prime }-3 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= {\frac {17}{3}} \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.191 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+7 t y^{\prime }-7 y&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= -22 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.383 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.562 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+a t y^{\prime }+b y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.713 |
|
| \begin{align*}
3 t^{2} y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.543 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-t y^{\prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.176 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+3 t y^{\prime }+y&=\ln \left (t \right ) \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.287 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }+4 y&=t \\
\end{align*} | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✓ | 1.978 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-4 t y^{\prime }-6 y&=2 \ln \left (t \right ) \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.614 |
|
| \begin{align*}
t^{2} \left (\ln \left (t \right )-1\right ) y^{\prime \prime }-t y^{\prime }+y&=-\frac {3 \left (1+\ln \left (t \right )\right )}{4 \sqrt {t}} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.748 |
|
| \begin{align*}
\left (\sin \left (t \right )-t \cos \left (t \right )\right ) y^{\prime \prime }-t \sin \left (t \right ) y^{\prime }+\sin \left (t \right ) y&=t \\
y \left (\frac {\pi }{4}\right ) &= 0 \\
y^{\prime }\left (\frac {\pi }{4}\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.017 |
|
| \begin{align*}
5 y-8 y^{\prime } x +4 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.328 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }-4 y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.353 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-8 y^{\prime } x +8 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.414 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-7 y^{\prime } x +7 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.548 |
|
| \begin{align*}
9 x^{2} y^{\prime \prime }-9 y^{\prime } x +10 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.355 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-2 y^{\prime } x +20 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.413 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +10 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.345 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+8 y^{\prime } x +y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.024 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.010 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+7 y^{\prime } x +9 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.001 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=\frac {1}{x^{5}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.684 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.879 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +y&=\frac {1}{x^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.938 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=\frac {1}{x^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.033 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y&=2 x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.082 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -16 y&=\ln \left (x \right ) \\
\end{align*} | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✓ | 2.125 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=8 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.582 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +36 y&=x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.740 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }-4 y^{\prime } x +2 y&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.769 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-7 y^{\prime } x +7 y&=0 \\
y \left (1\right ) &= -1 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.969 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=0 \\
y \left (1\right ) &= -1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.451 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.635 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+3 y^{\prime } x -y&=\frac {1}{x^{2}} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.859 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=\ln \left (x \right ) \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.300 |
|
| \begin{align*}
9 x^{2} y^{\prime \prime }+27 y^{\prime } x +10 y&=\frac {1}{x} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.823 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.332 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.733 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.077 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.717 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +y&=x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.779 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=0 \\
y \left (-1\right ) &= 0 \\
y^{\prime }\left (-1\right ) &= 2 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
7.443 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
y \left (-1\right ) &= 0 \\
y^{\prime }\left (-1\right ) &= 1 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.500 |
|
| \begin{align*}
6 x^{2} y^{\prime \prime }+5 y^{\prime } x -y&=0 \\
y \left (1\right ) &= a \\
y^{\prime }\left (1\right ) &= b \\
\end{align*} | [[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] | ✓ | ✓ | ✓ | ✓ | 0.950 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-5 t y^{\prime }+5 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.540 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+7 y^{\prime } x +8 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.326 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.454 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.092 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.217 |
|
| \begin{align*}
5 x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.433 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-7 y^{\prime } x +25 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.375 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=8 x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.742 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.221 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.967 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x +6 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.118 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +y&=x \left (6-\ln \left (x \right )\right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.820 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x -3 y&=-\frac {16 \ln \left (x \right )}{x} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.497 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x -2 y&=x^{2}-2 x +2 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.326 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=x^{m} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.244 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=2 \ln \left (x \right )^{2}+12 x \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.187 |
|
| \begin{align*}
\left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x -3\right ) y^{\prime }-2 y&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✓ |
✗ |
0.670 |
|
| \begin{align*}
\left (2 x^{2}+3 x \right ) y^{\prime \prime }-6 \left (x +1\right ) y^{\prime }+6 y&=6 \\
\end{align*} | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✗ | 0.992 |
|
| \begin{align*}
a \,x^{2} y^{\prime \prime }+b x y^{\prime }+c y&=d \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.928 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.404 |
|
| \begin{align*}
y-y^{\prime } x +\left (-x \cot \left (x \right )+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.912 |
|
| \begin{align*}
a \,x^{2} y^{\prime \prime }+b x y^{\prime }+c y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.162 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.753 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.989 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +\frac {5 y}{4}&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.871 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x -6 y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.726 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x +4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.925 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.917 |
|
| \begin{align*}
-3 y+y^{\prime } x +2 x^{2} y^{\prime \prime }&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.003 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+8 y^{\prime } x +17 y&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= -3 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.310 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=0 \\
y \left (-1\right ) &= 2 \\
y^{\prime }\left (-1\right ) &= 3 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +5 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= -1 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.279 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=\ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.205 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+7 y^{\prime } x +5 y&=x \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.327 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=3 x^{2}+2 \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.687 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=\sin \left (\ln \left (x \right )\right ) \\
\end{align*} | [[_2nd_order, _linear, _nonhomogeneous]] | ✓ | ✓ | ✓ | ✓ | 1.838 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=2 t^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.694 |
|
| \begin{align*}
\left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y&=2 \left (-1+t \right )^{2} {\mathrm e}^{-t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.888 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=g \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.004 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=\ln \left (x \right ) x^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.181 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-2 t y^{\prime }+2 y&=4 t^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.405 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+7 t y^{\prime }+5 y&=t \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.287 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=2 x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.245 |
|
| \begin{align*}
y^{\prime \prime }+\frac {x y^{\prime }}{1-x}-\frac {y}{1-x}&=x -1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.534 |
|
| \begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {n \left (n +1\right ) y}{x^{2}}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.471 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.770 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=x \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.002 |
|
| \begin{align*}
x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y x&=1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.979 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.790 |
|
| \begin{align*}
-5 y-3 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.539 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
y \left (1\right ) &= 3 \\
y^{\prime }\left (1\right ) &= 5 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.432 |
|
| \begin{align*}
y^{\prime \prime }-x f \left (x \right ) y^{\prime }+f \left (x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.800 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +10 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.466 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+10 y^{\prime } x +8 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.844 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -12 y&=0 \\
\end{align*} | [[_Emden, _Fowler]] | ✓ | ✓ | ✓ | ✓ | 1.150 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.843 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.142 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x +3 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.596 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.262 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -16 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.985 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=\left (x^{2}-1\right )^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.691 |
|
| \begin{align*}
\left (x^{2}+x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-\left (2+x \right ) y&=x \left (x +1\right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.835 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=\left (1-x \right )^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.130 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=x \,{\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.647 |
|
| \begin{align*}
t^{2} x^{\prime \prime }-6 t x^{\prime }+12 x&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.866 |
|
| \begin{align*}
t^{2} x^{\prime \prime }-2 t x^{\prime }+2 x&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.109 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {1}{x} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.701 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +5 y&=\frac {1}{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.653 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.184 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x -8 y&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.727 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=\ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.654 |
|
| \begin{align*}
\left (x^{2}-x \right ) y^{\prime \prime }+\left (3 x -2\right ) y^{\prime }+y&=0 \\
\end{align*} | [[_2nd_order, _exact, _linear, _homogeneous]] | ✓ | ✓ | ✓ | ✗ | 1.498 |
|
| \begin{align*}
\left (3 x^{2}+x \right ) y^{\prime \prime }+2 \left (1+6 x \right ) y^{\prime }+6 y&=\sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.227 |
|
| \begin{align*}
y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\frac {2 y}{x^{2}}&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.728 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=2 \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.339 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x -4 y&=x^{4} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.124 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=x^{4} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.008 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -20 y&=\left (x +1\right )^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.820 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+7 y^{\prime } x +5 y&=x^{5} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.344 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&={\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.648 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=x^{m} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.902 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x^{m} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.205 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {1}{\left (1-x \right )^{2}} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.388 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+\left (m^{2}+n^{2}\right ) y&=n^{2} x^{m} \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.886 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +y&=\frac {\ln \left (x \right ) \sin \left (\ln \left (x \right )\right )+1}{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.301 |
|
| \begin{align*}
y x -x^{2} y^{\prime }+y^{\prime \prime }&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.097 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.984 |
|
| \begin{align*}
-y+y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=x \left (-x^{2}+1\right )^{{3}/{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.512 |
|
| \begin{align*}
-y+y^{\prime } x +y^{\prime \prime }&=f \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.140 |
|
| \begin{align*}
2 \left (x +1\right ) y-2 x \left (x +1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.753 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +5 y&=\frac {1}{x} \\
\end{align*} | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✓ | 1.429 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.709 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=2 \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.548 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +5 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.039 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+7 y^{\prime } x +5 y&=x^{5} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.601 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=x^{4} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.154 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x^{4} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.440 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x -4 y&=x^{4} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.179 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=x^{m} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.143 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x^{m} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.339 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&={\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.880 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x -3 y&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.128 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -20 y&=\left (x +1\right )^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.866 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=x \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.229 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +5 y&=x^{2} \sin \left (\ln \left (x \right )\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
56.003 |
|
| \begin{align*}
y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=2 x \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
3.581 |
|
| \begin{align*}
\left (-b \,x^{2}+a x \right ) y^{\prime \prime }+2 a y^{\prime }+2 b y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.905 |
|
| \begin{align*}
y x -x^{2} y^{\prime }+y^{\prime \prime }&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.776 |
|
| \begin{align*}
-y+y^{\prime } x +y^{\prime \prime }&=X \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.347 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=\left (1-x \right )^{2} \\
\end{align*} | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✗ | 1.170 |
|
| \begin{align*}
2 \left (x +1\right ) y-2 x \left (x +1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=-4 x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.020 |
|
| \begin{align*}
-y+y^{\prime } x&=\left (x -1\right ) \left (y^{\prime \prime }-x +1\right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.112 |
|
| \begin{align*}
2 \left (x +1\right ) y-2 x \left (x +1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.949 |
|
| \begin{align*}
\left (x^{2}+a \right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.870 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=8 x^{3} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.885 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.331 |
|
| \begin{align*}
-y+y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=x \left (-x^{2}+1\right )^{{3}/{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.701 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-\left (x^{2}+2 x \right ) y^{\prime }+\left (2+x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.582 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=2 x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.791 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {1}{\left (1-x \right )^{2}} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.989 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+\left (m^{2}+n^{2}\right ) y&=n^{2} x^{m} \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.508 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +y&=\frac {\ln \left (x \right ) \sin \left (\ln \left (x \right )\right )+1}{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.900 |
|
| \begin{align*}
-y+y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=x \left (-x^{2}+1\right )^{{3}/{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.862 |
|
| \begin{align*}
\left (x \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+y \cos \left (x \right )&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.120 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&={\mathrm e}^{x} x^{2} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.855 |
|
| \begin{align*}
2 \left (x +1\right ) y-2 x \left (x +1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.126 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x -4 y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.088 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
0.973 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✗ | 1.248 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.540 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.004 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.118 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +3 y&=0 \\
y \left (1\right ) &= 3 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.339 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x -3 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.962 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x -3 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.897 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.637 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x -3 y&=3 x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.301 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y&=x^{2}+x \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.957 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=2 x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.546 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +3 y&=5 x^{2} \\
y \left (1\right ) &= 3 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
27.446 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=3 x^{2}-x \\
y \left (1\right ) &= \pi \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.999 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x -15 y&={\mathrm e}^{x} x^{4} \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.712 |
|
| \begin{align*}
t^{2} x^{\prime \prime }+a t x^{\prime }+x&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.637 |
|
| \begin{align*}
t^{2} x^{\prime \prime }-t x^{\prime }-3 x&=0 \\
x \left (1\right ) &= 0 \\
x^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.835 |
|
| \begin{align*}
t^{2} x^{\prime \prime }+t x^{\prime }+x&=t \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.123 |
|
| \begin{align*}
t^{2} x^{\prime \prime }+3 t x^{\prime }-3 x&=t^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.619 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }-\frac {4 y}{x}&=x^{3}+x \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
3.368 |
|
| \begin{align*}
2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=6 \left (x^{2}+1\right )^{2} \\
\end{align*} | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✗ | 1.560 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=x^{3} \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.547 |
|
| \begin{align*}
x^{2} u^{\prime \prime }-3 x u^{\prime }+13 u&=0 \\
u \left (1\right ) &= -1 \\
u^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.480 |
|
| \begin{align*}
x^{2} u^{\prime \prime }-3 x u^{\prime }+13 u&=0 \\
u \left (1\right ) &= -1 \\
u^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.656 |
|
| \begin{align*}
x^{2} \cos \left (x \right ) y^{\prime \prime }+\left (x \sin \left (x \right )-2 \cos \left (x \right )\right ) \left (-y+y^{\prime } x \right )&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.342 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
1.476 |
|
| \begin{align*}
y^{\prime \prime } x +\left (x +3\right ) y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.297 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+7 y^{\prime } x +8 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.165 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.620 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -12 y&=2 x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.752 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.778 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x -y&=1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
✓ |
1.045 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.141 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} |
[_Hermite] |
✓ |
✓ |
✓ |
✗ |
0.526 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=x \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
1.091 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
0.533 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=x \,{\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.864 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.830 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=\ln \left (x \right ) \\
\end{align*} | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✓ | 1.950 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=x^{2}+16 \ln \left (x \right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.564 |
|
| \begin{align*}
t^{2} i^{\prime \prime }+2 i^{\prime } t +i&=t \ln \left (t \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.096 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -9 y&=\sqrt {x}+\frac {1}{\sqrt {x}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.470 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x -3 y&=x^{2}-4 x +2 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.179 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.730 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.859 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=3 x -2 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.718 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y&=24 x +24 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.491 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y&=0 \\
y \left (\frac {1}{2}\right ) &= 2 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.524 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.750 |
|
| \begin{align*}
y-y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.695 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.132 |
|
| \begin{align*}
5 x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.185 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.868 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }+4 y^{\prime } x +y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.115 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.961 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x -4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.691 |
|
| \begin{align*}
-3 y+y^{\prime } x +2 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.836 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +5 y&=0 \\
\end{align*} | [[_Emden, _Fowler]] | ✓ | ✓ | ✓ | ✓ | 1.012 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\frac {7 y^{\prime } x}{2}-\frac {3 y}{2}&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.176 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
y \left (-1\right ) &= 1 \\
y^{\prime }\left (-1\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.079 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.476 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\frac {7 y^{\prime } x}{2}-\frac {3 y}{2}&=0 \\
y \left (-4\right ) &= 1 \\
y^{\prime }\left (-4\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.153 |
|
| \begin{align*}
y^{\prime \prime }-\frac {5 y^{\prime }}{x}+\frac {5 y}{x^{2}}&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.171 |
|
| \begin{align*}
3 y^{\prime \prime } x -4 y^{\prime }+\frac {5 y}{x}&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✗ |
1.076 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=\tan \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.531 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x -10 y&=x \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.084 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }-2 y^{\prime } x -8 y&=3 x +5 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.316 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x -4 y&=x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.963 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x -8 y&={\mathrm e}^{x} \left (x^{2}+2\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.946 |
|
| \begin{align*}
5 x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=\sqrt {x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.651 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x -4 y&=x^{{1}/{4}} \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.284 |
|
| \begin{align*}
-3 y+y^{\prime } x +2 x^{2} y^{\prime \prime }&=\frac {1}{x^{3}} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.292 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+7 y^{\prime } x -3 y&=\frac {\ln \left (x \right )}{x^{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.173 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=\ln \left (x \right ) \left (\frac {1}{x^{3}}+\frac {1}{x^{5}}\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.550 |
|
| \begin{align*}
-3 y+y^{\prime } x +2 x^{2} y^{\prime \prime }&=\frac {1}{x^{3}} \\
y \left (\frac {1}{4}\right ) &= 0 \\
y^{\prime }\left (\frac {1}{4}\right ) &= {\frac {14}{9}} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.664 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=\ln \left (x \right ) \\
y \left (1\right ) &= A \\
y \left (2\right ) &= B \\
\end{align*} | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✓ | 2.458 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.954 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }-y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.393 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.505 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=6 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.692 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }-y x&=2 x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.568 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=\ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.559 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+a x y^{\prime }+b y&=f \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
5.029 |
|
| \begin{align*}
3 t^{2} y^{\prime \prime }+2 t y^{\prime }+y&={\mathrm e}^{2 t} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
7.269 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }-y&=\sqrt {t} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.264 |
|
| \begin{align*}
\left (-1+t \right ) y^{\prime \prime }-t y^{\prime }+y&=2 t \,{\mathrm e}^{-t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.041 |
|
| \begin{align*}
\left (-1+t \right ) y^{\prime \prime }-t y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.634 |
|
| \begin{align*}
\left (-1+t \right ) y^{\prime \prime }-t y^{\prime }+y&=2 t \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.108 |
|
| \begin{align*}
\left (-1+t \right ) y^{\prime \prime }-t y^{\prime }+y&=2 t \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.080 |
|
| \begin{align*}
\left (-1+t \right ) y^{\prime \prime }-t y^{\prime }+y&=2 t \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.102 |
|
| \begin{align*}
\left (-1+t \right ) y^{\prime \prime }-t y^{\prime }+y&=2 t \,{\mathrm e}^{-t} \\
y \left (0\right ) &= a \\
y^{\prime }\left (0\right ) &= b \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.065 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y&=t^{5} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.541 |
|
| \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)]‘]] | ✓ | ✓ | ✓ | ✓ | 1.087 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y&=t^{5} \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.868 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y&=t^{5} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.854 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y&=t^{5} \\
y \left (1\right ) &= -1 \\
y^{\prime }\left (1\right ) &= 3 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.841 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y&=t^{5} \\
y \left (1\right ) &= a \\
y^{\prime }\left (1\right ) &= b \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.829 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+3 t y^{\prime }-4 y&=t^{4} \\
y \left (-1\right ) &= y_{1} \\
y^{\prime }\left (-1\right ) &= y_{1} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.988 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.169 |
|
| \begin{align*}
\left (-1+t \right ) y^{\prime \prime }-t y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.662 |
|
| \begin{align*}
\left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.665 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }+4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.869 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+2 t y^{\prime }-2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.712 |
|
| \begin{align*}
2 t^{2} y^{\prime \prime }-5 t y^{\prime }+3 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.985 |
|
| \begin{align*}
9 t^{2} y^{\prime \prime }+3 t y^{\prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.823 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }-2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.964 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-3 t y^{\prime }-21 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.605 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+7 t y^{\prime }+9 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.800 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }-4 y&=0 \\
\end{align*} | [[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] | ✓ | ✓ | ✓ | ✓ | 0.867 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }+4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.828 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-3 t y^{\prime }+13 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.063 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+2 t y^{\prime }-2 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.959 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }+4 y&=0 \\
y \left (1\right ) &= -3 \\
y^{\prime }\left (1\right ) &= 4 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.217 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-2 t y^{\prime }+2 y&=t^{4} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.728 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-t y^{\prime }+y&=t \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.628 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.911 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.173 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +y&=\sec \left (\ln \left (x \right )\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.148 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }+\left (1-x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.471 |
|