Number of problems in this table is 574
Column notations: A is ODE degree. B is Program Number of solutions generated. C is CAS Number of solutions generated.
|
# |
ODE |
A |
B |
C |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}y^{\prime \prime } = y \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.494 |
|
|
\[ {}y^{\prime \prime } = 4 y \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.533 |
|
|
\[ {}y^{\prime \prime }+9 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.589 |
|
|
\[ {}y^{\prime \prime }+y = x \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.671 |
|
|
\[ {}y^{\prime \prime }+4 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
2.132 |
|
|
\[ {}y^{\prime \prime }-4 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.742 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.858 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.863 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.105 |
|
|
\[ {}\left (x^{2}+2\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.939 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.802 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+6 x y^{\prime }+4 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.922 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.594 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y = 0 \] |
1 |
2 |
1 |
[_Gegenbauer] |
✓ |
✓ |
1.015 |
|
|
\[ {}\left (x^{2}+3\right ) y^{\prime \prime }-7 x y^{\prime }+16 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.964 |
|
|
\[ {}\left (-x^{2}+2\right ) y^{\prime \prime }-x y^{\prime }+16 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
0.809 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+8 x y^{\prime }+12 y = 0 \] |
1 |
2 |
1 |
[_Gegenbauer] |
✓ |
✓ |
1.147 |
|
|
\[ {}3 y^{\prime \prime }+x y^{\prime }-4 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.676 |
|
|
\[ {}5 y^{\prime \prime }-2 x y^{\prime }+10 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.157 |
|
|
\[ {}y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.052 |
|
|
\[ {}y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.918 |
|
|
\[ {}y^{\prime \prime }+x y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.62 |
|
|
\[ {}y^{\prime \prime }+x^{2} y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.658 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.212 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }-2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.279 |
|
|
\[ {}y^{\prime \prime }+\left (-1+x \right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.931 |
|
|
\[ {}\left (-x^{2}+2 x \right ) y^{\prime \prime }-6 \left (-1+x \right ) y^{\prime }-4 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.664 |
|
|
\[ {}\left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.833 |
|
|
\[ {}\left (4 x^{2}+16 x +17\right ) y^{\prime \prime } = 8 y \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.982 |
|
|
\[ {}\left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.364 |
|
|
\[ {}y^{\prime \prime }+\left (1+x \right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.891 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }+2 x y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.466 |
|
|
\[ {}y^{\prime \prime }+x^{2} y^{\prime }+x^{2} y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.107 |
|
|
\[ {}\left (x^{3}+1\right ) y^{\prime \prime }+x^{4} y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.071 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}+1\right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.634 |
|
|
\[ {}y^{\prime \prime }+y \,{\mathrm e}^{-x} = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.036 |
|
|
\[ {}\cos \left (x \right ) y^{\prime \prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.58 |
|
|
\[ {}x y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+x y = 0 \] |
1 |
2 |
1 |
[_Lienard] |
✓ |
✓ |
5.636 |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+2 \alpha y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.105 |
|
|
\[ {}y^{\prime \prime } = x y \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.616 |
|
|
\[ {}y^{\prime \prime }-y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.523 |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.836 |
|
|
\[ {}y^{\prime \prime }+k^{2} x^{2} y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.906 |
|
|
\[ {}\left (1-x \right ) y^{\prime \prime }+y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.883 |
|
|
\[ {}\left (x^{2}+2\right ) y^{\prime \prime }-x y^{\prime }+4 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.98 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.959 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.736 |
|
|
\[ {}\left (-x^{2}+4\right ) y^{\prime \prime }+2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.764 |
|
|
\[ {}\left (-x^{2}+3\right ) y^{\prime \prime }-3 x y^{\prime }-y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.93 |
|
|
\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.961 |
|
|
\[ {}2 y^{\prime \prime }+x y^{\prime }+3 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.135 |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.22 |
|
|
\[ {}\left (x^{2}+2\right ) y^{\prime \prime }-x y^{\prime }+4 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.2 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.167 |
|
|
\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.384 |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+\lambda y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.231 |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.095 |
|
|
\[ {}\left (x^{2}+2\right ) y^{\prime \prime }-x y^{\prime }+4 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.167 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.152 |
|
|
\[ {}\left (-x^{2}+4\right ) y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.801 |
|
|
\[ {}y^{\prime \prime }+x^{2} y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.064 |
|
|
\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.602 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.16 |
|
|
\[ {}y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.104 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (1+x \right ) y^{\prime }+3 y \ln \left (x \right ) = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.661 |
|
|
\[ {}y^{\prime \prime }+x^{2} y^{\prime }+\sin \left (x \right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.214 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+6 x y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.216 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+6 x y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.325 |
|
|
\[ {}\left (x^{2}-2 x -3\right ) y^{\prime \prime }+x y^{\prime }+4 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.72 |
|
|
\[ {}\left (x^{2}-2 x -3\right ) y^{\prime \prime }+x y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.005 |
|
|
\[ {}\left (x^{2}-2 x -3\right ) y^{\prime \prime }+x y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.976 |
|
|
\[ {}\left (x^{3}+1\right ) y^{\prime \prime }+4 x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.957 |
|
|
\[ {}\left (x^{3}+1\right ) y^{\prime \prime }+4 x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.497 |
|
|
\[ {}x y^{\prime \prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.108 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+\alpha ^{2} y = 0 \] |
1 |
2 |
1 |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.509 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+\alpha \left (\alpha +1\right ) y = 0 \] |
1 |
2 |
1 |
[_Gegenbauer] |
✓ |
✓ |
1.694 |
|
|
\[ {}\left (2+x \right ) y^{\prime \prime }+x y^{\prime }+3 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.692 |
|
|
\[ {}\left (3 x^{2}+1\right ) y^{\prime \prime }+3 x^{2} y^{\prime }-2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.198 |
|
|
\[ {}\left (2 x^{2}+1\right ) y^{\prime \prime }+\left (2-3 x \right ) y^{\prime }+4 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.084 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+\left (2-x \right ) y^{\prime }+3 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.795 |
|
|
\[ {}\left (3 x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+4 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.325 |
|
|
\[ {}x y^{\prime \prime }+\left (2 x +4\right ) y^{\prime }+\left (2+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.193 |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-3 x y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.949 |
|
|
\[ {}\left (2-x \right ) y^{\prime \prime }+2 y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.926 |
|
|
\[ {}\left (1+x \right ) y^{\prime \prime }+2 \left (-1+x \right )^{2} y^{\prime }+3 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.762 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+6 x y^{\prime }+6 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.079 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.915 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }+20 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.989 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }-12 y = 0 \] |
1 |
2 |
1 |
[_Gegenbauer] |
✓ |
✓ |
1.35 |
|
|
\[ {}\left (2 x^{2}+1\right ) y^{\prime \prime }+7 x y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.413 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }+\frac {y}{4} = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.125 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-5 x y^{\prime }-4 y = 0 \] |
1 |
2 |
1 |
[_Gegenbauer] |
✓ |
✓ |
1.537 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-10 x y^{\prime }+28 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.098 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.941 |
|
|
\[ {}y^{\prime \prime }+2 x y^{\prime }+3 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.229 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.678 |
|
|
\[ {}\left (2 x^{2}+1\right ) y^{\prime \prime }-9 x y^{\prime }-6 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.303 |
|
|
\[ {}\left (8 x^{2}+1\right ) y^{\prime \prime }+2 y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.613 |
|
|
\[ {}y^{\prime \prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.678 |
|
|
\[ {}y^{\prime \prime }-\left (x -3\right ) y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.233 |
|
|
\[ {}\left (2 x^{2}-4 x +1\right ) y^{\prime \prime }+10 \left (-1+x \right ) y^{\prime }+6 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.867 |
|
|
\[ {}\left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (-2+x \right ) y^{\prime }+36 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.937 |
|
|
\[ {}\left (3 x^{2}+6 x +5\right ) y^{\prime \prime }+9 \left (1+x \right ) y^{\prime }+3 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.853 |
|
|
\[ {}\left (x^{2}-4\right ) y^{\prime \prime }-x y^{\prime }-3 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.126 |
|
|
\[ {}y^{\prime \prime }+\left (x -3\right ) y^{\prime }+3 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.271 |
|
|
\[ {}\left (3 x^{2}-6 x +5\right ) y^{\prime \prime }+\left (-1+x \right ) y^{\prime }+12 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.058 |
|
|
\[ {}\left (4 x^{2}-24 x +37\right ) y^{\prime \prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
3.811 |
|
|
\[ {}\left (x^{2}-8 x +14\right ) y^{\prime \prime }-8 \left (x -4\right ) y^{\prime }+20 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.535 |
|
|
\[ {}\left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (1+x \right ) y^{\prime }+60 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.551 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.031 |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+2 \alpha y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.162 |
|
|
\[ {}y^{\prime \prime }-x y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.676 |
|
|
\[ {}\left (-2 x^{3}+1\right ) y^{\prime \prime }-10 x^{2} y^{\prime }-8 x y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.298 |
|
|
\[ {}\left (x^{3}+1\right ) y^{\prime \prime }+7 x^{2} y^{\prime }+9 x y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.067 |
|
|
\[ {}\left (-2 x^{3}+1\right ) y^{\prime \prime }+6 x^{2} y^{\prime }+24 x y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.832 |
|
|
\[ {}\left (-x^{3}+1\right ) y^{\prime \prime }+15 x^{2} y^{\prime }-36 x y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
6.553 |
|
|
\[ {}\left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
68.069 |
|
|
\[ {}y^{\prime \prime }+x^{2} y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.76 |
|
|
\[ {}y^{\prime \prime }+x^{6} y^{\prime }+7 x^{5} y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.477 |
|
|
\[ {}\left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.901 |
|
|
\[ {}\left (-x^{6}+1\right ) y^{\prime \prime }-12 x^{5} y^{\prime }-30 x^{4} y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.833 |
|
|
\[ {}y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.617 |
|
|
\[ {}\left (1+3 x \right ) y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.715 |
|
|
\[ {}\left (2 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+8 x \right ) y^{\prime }+4 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.57 |
|
|
\[ {}\left (-2 x^{2}+1\right ) y^{\prime \prime }+\left (2-6 x \right ) y^{\prime }-2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
10.412 |
|
|
\[ {}\left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
6.886 |
|
|
\[ {}\left (2+x \right ) y^{\prime \prime }+\left (1+x \right ) y^{\prime }+3 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.241 |
|
|
\[ {}\left (x^{2}+3 x +3\right ) y^{\prime \prime }+\left (6+4 x \right ) y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.542 |
|
|
\[ {}\left (x +4\right ) y^{\prime \prime }+\left (2+x \right ) y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.271 |
|
|
\[ {}\left (2 x^{2}-3 x +2\right ) y^{\prime \prime }-\left (4-6 x \right ) y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
7.684 |
|
|
\[ {}\left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (1+x \right ) y^{\prime }+8 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.014 |
|
|
\[ {}\left (x^{2}-x +1\right ) y^{\prime \prime }-\left (1-4 x \right ) y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
6.842 |
|
|
\[ {}\left (2+x \right ) y^{\prime \prime }+\left (2+x \right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.301 |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.225 |
|
|
\[ {}\left (2 x^{2}+x +1\right ) y^{\prime \prime }+\left (1+7 x \right ) y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
8.727 |
|
|
\[ {}\left (x +3\right ) y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-\left (2-x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.668 |
|
|
\[ {}y^{\prime \prime }+3 x y^{\prime }+\left (2 x^{2}+4\right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.203 |
|
|
\[ {}\left (4 x +2\right ) y^{\prime \prime }-4 y^{\prime }-\left (6+4 x \right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.09 |
|
|
\[ {}\left (2 x +1\right ) y^{\prime \prime }-\left (1-2 x \right ) y^{\prime }-\left (3-2 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.756 |
|
|
\[ {}\left (5+2 x \right ) y^{\prime \prime }-y^{\prime }+\left (x +5\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.773 |
|
|
\[ {}\left (x +4\right ) y^{\prime \prime }-\left (2 x +4\right ) y^{\prime }+\left (x +6\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.638 |
|
|
\[ {}\left (3 x +2\right ) y^{\prime \prime }-x y^{\prime }+2 x y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.661 |
|
|
\[ {}\left (2 x +3\right ) y^{\prime \prime }+3 y^{\prime }-x y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.979 |
|
|
\[ {}\left (2 x +3\right ) y^{\prime \prime }-3 y^{\prime }-\left (2+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.889 |
|
|
\[ {}\left (10-2 x \right ) y^{\prime \prime }+\left (1+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.855 |
|
|
\[ {}\left (7+x \right ) y^{\prime \prime }+\left (8+2 x \right ) y^{\prime }+\left (x +5\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.452 |
|
|
\[ {}\left (6+4 x \right ) y^{\prime \prime }+\left (2 x +1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.432 |
|
|
\[ {}\left (\beta \,x^{2}+\alpha x +1\right ) y^{\prime \prime }+\left (\delta x +\gamma \right ) y^{\prime }+\epsilon y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
6.293 |
|
|
\[ {}\left (2 x^{2}+3 x +1\right ) y^{\prime \prime }+\left (6+8 x \right ) y^{\prime }+4 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.87 |
|
|
\[ {}\left (6 x^{2}-5 x +1\right ) y^{\prime \prime }-\left (10-24 x \right ) y^{\prime }+12 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.877 |
|
|
\[ {}\left (4 x^{2}-4 x +1\right ) y^{\prime \prime }-\left (8-16 x \right ) y^{\prime }+8 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.756 |
|
|
\[ {}\left (x^{2}+4 x +4\right ) y^{\prime \prime }+\left (8+4 x \right ) y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.683 |
|
|
\[ {}\left (3 x^{2}+8 x +4\right ) y^{\prime \prime }+\left (16+12 x \right ) y^{\prime }+6 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.912 |
|
|
\[ {}y^{\prime \prime }+2 x y^{\prime }+\left (2 x^{2}+3\right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.445 |
|
|
\[ {}y^{\prime \prime }-3 x y^{\prime }+\left (2 x^{2}+5\right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.171 |
|
|
\[ {}y^{\prime \prime }+5 x y^{\prime }-\left (-x^{2}+3\right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
12.941 |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }-\left (3 x^{2}+2\right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.189 |
|
|
\[ {}y^{\prime \prime }+3 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.48 |
|
|
\[ {}2 y^{\prime \prime }+5 x y^{\prime }+\left (2 x^{2}+4\right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.076 |
|
|
\[ {}3 y^{\prime \prime }+2 x y^{\prime }+\left (-x^{2}+4\right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.326 |
|
|
\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.84 |
|
|
\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.646 |
|
|
\[ {}\left (1+x \right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (2 x +1\right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.033 |
|
|
\[ {}y^{\prime \prime }+\left (x^{2}+2 x +1\right ) y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.675 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+\left (x^{2}+2\right ) y^{\prime }+x y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.793 |
|
|
\[ {}\left (1+x \right ) y^{\prime \prime }+\left (2 x^{2}-3 x +1\right ) y^{\prime }-\left (x -4\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.797 |
|
|
\[ {}y^{\prime \prime }+\left (3 x^{2}+12 x +13\right ) y^{\prime }+\left (5+2 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.101 |
|
|
\[ {}\left (3 x^{2}+2 x +1\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (1+x \right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
6.65 |
|
|
\[ {}\left (x^{2}+4 x +3\right ) y^{\prime \prime }-\left (-x^{2}+4 x +5\right ) y^{\prime }-\left (2+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.711 |
|
|
\[ {}\left (x^{2}+2 x +1\right ) y^{\prime \prime }+\left (1-x \right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.115 |
|
|
\[ {}\left (-2 x^{2}+x \right ) y^{\prime \prime }+\left (-x^{2}+3 x +1\right ) y^{\prime }+\left (2+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.659 |
|
|
\[ {}\left (2 x^{2}-11 x +16\right ) y^{\prime \prime }+\left (x^{2}-6 x +10\right ) y^{\prime }-\left (2-x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
8.518 |
|
|
\[ {}y^{\prime \prime }+t y^{\prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.953 |
|
|
\[ {}y^{\prime \prime }-t y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.784 |
|
|
\[ {}\left (t^{2}+2\right ) y^{\prime \prime }-t y^{\prime }-3 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.174 |
|
|
\[ {}y^{\prime \prime }-y t^{3} = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.09 |
|
|
\[ {}t \left (2-t \right ) y^{\prime \prime }-6 \left (-1+t \right ) y^{\prime }-4 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
4.537 |
|
|
\[ {}y^{\prime \prime }+t^{2} y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
3.493 |
|
|
\[ {}y^{\prime \prime }-y t^{3} = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.54 |
|
|
\[ {}y^{\prime \prime }+\left (t^{2}+2 t +1\right ) y^{\prime }-\left (4+4 t \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.217 |
|
|
\[ {}y^{\prime \prime }-2 t y^{\prime }+\lambda y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.348 |
|
|
\[ {}\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+\alpha \left (\alpha +1\right ) y = 0 \] |
1 |
2 |
1 |
[_Gegenbauer] |
✓ |
✓ |
1.877 |
|
|
\[ {}\left (-t^{2}+1\right ) y^{\prime \prime }-t y^{\prime }+\alpha ^{2} y = 0 \] |
1 |
2 |
1 |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.632 |
|
|
\[ {}y^{\prime \prime }+t^{3} y^{\prime }+3 t^{2} y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.387 |
|
|
\[ {}y^{\prime \prime }+t^{3} y^{\prime }+3 t^{2} y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.655 |
|
|
\[ {}\left (1-t \right ) y^{\prime \prime }+t y^{\prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.183 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+t y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.14 |
|
|
\[ {}y^{\prime \prime }+t y^{\prime }+{\mathrm e}^{t} y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.386 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+{\mathrm e}^{t} y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.13 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y \,{\mathrm e}^{-t} = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.431 |
|
|
\[ {}y^{\prime \prime }-y = \sin \left (x \right ) \] |
1 |
2 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.355 |
|
|
\[ {}y^{\prime \prime }-2 y = {\mathrm e}^{2 x} \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.317 |
|
|
\[ {}\left (1-2 x \right ) y^{\prime \prime }+4 x y^{\prime }-4 y = x^{2}-x \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.522 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 6 \left (-x^{2}+1\right )^{2} \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.392 |
|
|
\[ {}\left (-z^{2}+1\right ) y^{\prime \prime }-3 y^{\prime } z +\lambda y = 0 \] |
1 |
2 |
1 |
[_Gegenbauer] |
✓ |
✓ |
0.898 |
|
|
\[ {}f^{\prime \prime }+2 \left (z -1\right ) f^{\prime }+4 f = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.702 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } z -2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.505 |
|
|
\[ {}\left (z^{2}+5 z +6\right ) y^{\prime \prime }+2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.756 |
|
|
\[ {}\left (z^{2}+5 z +7\right ) y^{\prime \prime }+2 y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.793 |
|
|
\[ {}\left (-z^{2}+1\right ) y^{\prime \prime }-y^{\prime } z +m^{2} y = 0 \] |
1 |
2 |
1 |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
0.903 |
|
|
\[ {}y^{\prime \prime }-y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.402 |
|
|
\[ {}y^{\prime \prime }+2 x y^{\prime }+4 y = 0 \] |
1 |
2 |
1 |
[_erf] |
✓ |
✓ |
0.655 |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }-2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.526 |
|
|
\[ {}y^{\prime \prime }-x^{2} y^{\prime }-2 x y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.652 |
|
|
\[ {}y^{\prime \prime }+x y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.431 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+3 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.774 |
|
|
\[ {}y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.692 |
|
|
\[ {}y^{\prime \prime }+2 x^{2} y^{\prime }+2 x y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.713 |
|
|
\[ {}\left (x^{2}-3\right ) y^{\prime \prime }-3 x y^{\prime }-5 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.647 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.608 |
|
|
\[ {}\left (-4 x^{2}+1\right ) y^{\prime \prime }-20 x y^{\prime }-16 y = 0 \] |
1 |
2 |
1 |
[_Gegenbauer] |
✓ |
✓ |
0.921 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y = 0 \] |
1 |
2 |
1 |
[_Gegenbauer] |
✓ |
✓ |
0.691 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+4 x y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.723 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+\left (2+x \right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.855 |
|
|
\[ {}y^{\prime \prime }-{\mathrm e}^{x} y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.671 |
|
|
\[ {}\left (2 x^{2}+1\right ) y^{\prime \prime }+7 x y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.718 |
|
|
\[ {}4 y^{\prime \prime }+x y^{\prime }+4 y = 0 \] |
1 |
2 |
1 |
[_Lienard] |
✓ |
✓ |
1.668 |
|
|
\[ {}y^{\prime \prime }+2 x^{2} y^{\prime }+x y = 2 \cos \left (x \right ) \] |
1 |
2 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.144 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }-4 y = 6 \,{\mathrm e}^{x} \] |
1 |
2 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.201 |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{1-x}+x y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.216 |
|
|
\[ {}y^{\prime \prime }+x y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.419 |
|
|
\[ {}y^{\prime \prime }-x^{2} y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.498 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-6 x y^{\prime }-4 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.911 |
|
|
\[ {}\left (4 x^{2}+1\right ) y^{\prime \prime }-8 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.516 |
|
|
\[ {}y^{\prime \prime }+x y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.342 |
|
|
\[ {}y^{\prime \prime }+a \,x^{2} y = 1+x \] |
1 |
2 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.356 |
|
|
\[ {}\left (a^{2}+x^{2}\right ) y^{\prime \prime }+x y^{\prime }-n^{2} y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
0.938 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+a^{2} y = 0 \] |
1 |
2 |
1 |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
0.93 |
|
|
\[ {}4 y^{\prime \prime }+\frac {3 \left (-x^{2}+2\right ) y}{\left (-x^{2}+1\right )^{2}} = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.851 |
|
|
\[ {}y^{\prime \prime } = -4 y \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.408 |
|
|
\[ {}y^{\prime \prime } = y \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.356 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.475 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.326 |
|
|
\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.569 |
|
|
\[ {}\left (1+x \right ) y^{\prime \prime }-x^{2} y^{\prime }+3 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.993 |
|
|
\[ {}\left (x^{2}-2\right ) y^{\prime \prime }+2 y^{\prime }+\sin \left (x \right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
8.434 |
|
|
\[ {}\left (t^{2}-t -2\right ) x^{\prime \prime }+\left (t +1\right ) x^{\prime }-\left (t -2\right ) x = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.035 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+\left (x^{2}-2 x +1\right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.827 |
|
|
\[ {}{\mathrm e}^{x} y^{\prime \prime }-\left (x^{2}-1\right ) y^{\prime }+2 x y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.792 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.489 |
|
|
\[ {}y^{\prime \prime }+\left (-1+x \right ) y^{\prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.652 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.497 |
|
|
\[ {}w^{\prime \prime }-x^{2} w^{\prime }+w = 0 \] |
1 |
2 |
1 |
[_Lienard] |
✓ |
✓ |
0.769 |
|
|
\[ {}\left (2 x -3\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.852 |
|
|
\[ {}\left (1+x \right ) y^{\prime \prime }-3 x y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.993 |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-3 y = 0 \] |
1 |
1 |
1 |
[_Hermite] |
✓ |
✓ |
0.798 |
|
|
\[ {}\left (x^{2}+x +1\right ) y^{\prime \prime }-3 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.342 |
|
|
\[ {}\left (x^{2}-5 x +6\right ) y^{\prime \prime }-3 x y^{\prime }-y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.8 |
|
|
\[ {}y^{\prime \prime }-\tan \left (x \right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[_Lienard] |
✓ |
✓ |
2.783 |
|
|
\[ {}\left (x^{3}+1\right ) y^{\prime \prime }-x y^{\prime }+2 x^{2} y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.335 |
|
|
\[ {}\left (x^{2}-2 x \right ) y^{\prime \prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.675 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.786 |
|
|
\[ {}x^{2} y^{\prime \prime }-y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.814 |
|
|
\[ {}y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.793 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-{\mathrm e}^{x} y^{\prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.539 |
|
|
\[ {}y^{\prime \prime }+t y^{\prime }+{\mathrm e}^{t} y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.905 |
|
|
\[ {}y^{\prime \prime }-{\mathrm e}^{2 x} y^{\prime }+\cos \left (x \right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
7.862 |
|
|
\[ {}z^{\prime \prime }+x z^{\prime }+z = x^{2}+2 x +1 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.543 |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+3 y = x^{2} \] |
1 |
2 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.539 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = \cos \left (x \right ) \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.856 |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }+2 y = \cos \left (x \right ) \] |
1 |
2 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.188 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime }+y = \tan \left (x \right ) \] |
1 |
2 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.117 |
|
|
\[ {}y^{\prime \prime }-\sin \left (x \right ) y = \cos \left (x \right ) \] |
1 |
2 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.561 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+n \left (n +1\right ) y = 0 \] |
1 |
2 |
1 |
[_Gegenbauer] |
✓ |
✓ |
0.91 |
|
|
\[ {}y^{\prime \prime }+x y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.457 |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }-2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.516 |
|
|
\[ {}y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.593 |
|
|
\[ {}y^{\prime \prime }-x^{2} y^{\prime }-y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.794 |
|
|
\[ {}y^{\prime \prime }+2 x^{2} y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.48 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime }-y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.582 |
|
|
\[ {}y^{\prime \prime }-x y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.427 |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+x^{2} y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.901 |
|
|
\[ {}y^{\prime \prime }+x y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.401 |
|
|
\[ {}y^{\prime \prime }+2 x^{2} y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.416 |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }+x^{2} y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.938 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+p \left (p +1\right ) y = 0 \] |
1 |
2 |
1 |
[_Gegenbauer] |
✓ |
✓ |
0.976 |
|
|
\[ {}y^{\prime \prime }+x^{2} y = x^{2}+x +1 \] |
1 |
2 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.563 |
|
|
\[ {}z^{\prime \prime }+z^{\prime } t +\left (t^{2}-\frac {1}{9}\right ) z = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.991 |
|
|
\[ {}\left (-1+x \right ) \left (-2+x \right ) y^{\prime \prime }+\left (4 x -6\right ) y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.69 |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+8 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.019 |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+8 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.874 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+12 y = 0 \] |
1 |
2 |
1 |
[_Gegenbauer] |
✓ |
✓ |
1.562 |
|
|
\[ {}y^{\prime \prime } = \left (-1+x \right ) y \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.369 |
|
|
\[ {}y^{\prime \prime }+\left ({\mathrm e}^{x}-1\right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.612 |
|
|
\[ {}y^{\prime \prime }-x^{2} y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.468 |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.622 |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.432 |
|
|
\[ {}y^{\prime \prime }+4 x y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.502 |
|
|
\[ {}y^{\prime \prime }-x y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.546 |
|
|
\[ {}y^{\prime \prime }+x^{2} y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.434 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+p^{2} y = 0 \] |
1 |
2 |
1 |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
0.91 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.447 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.502 |
|
|
\[ {}x y^{\prime \prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.648 |
|
|
\[ {}y^{\prime \prime }+2 x^{3} y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.522 |
|
|
\[ {}y^{\prime \prime }-x y = \frac {1}{1-x} \] |
1 |
2 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.446 |
|
|
\[ {}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+x^{2} y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.484 |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.389 |
|
|
\[ {}\cos \left (x \right ) y^{\prime \prime }-\sin \left (x \right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.514 |
|
|
\[ {}\left (x^{2}-25\right ) y^{\prime \prime }+2 x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.944 |
|
|
\[ {}\left (x^{2}-25\right ) y^{\prime \prime }+2 x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.046 |
|
|
\[ {}\left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.242 |
|
|
\[ {}\left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.914 |
|
|
\[ {}y^{\prime \prime }-x y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.388 |
|
|
\[ {}y^{\prime \prime }+x^{2} y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.417 |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
[_Lienard] |
✓ |
✓ |
0.623 |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
[_Hermite] |
✓ |
✓ |
0.487 |
|
|
\[ {}y^{\prime \prime }+x^{2} y^{\prime }+x y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.594 |
|
|
\[ {}y^{\prime \prime }+2 x y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.529 |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }+y^{\prime } = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.513 |
|
|
\[ {}\left (2+x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.757 |
|
|
\[ {}y^{\prime \prime }-\left (1+x \right ) y^{\prime }-y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.653 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-6 y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.441 |
|
|
\[ {}\left (x^{2}+2\right ) y^{\prime \prime }+3 x y^{\prime }-y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.774 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime }-y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.58 |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.497 |
|
|
\[ {}\left (1+x \right ) y^{\prime \prime }-\left (2-x \right ) y^{\prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.58 |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+8 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.85 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.231 |
|
|
\[ {}y^{\prime \prime }+\sin \left (x \right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.974 |
|
|
\[ {}y^{\prime \prime }+{\mathrm e}^{x} y^{\prime }-y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.783 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.514 |
|
|
\[ {}\left (x^{2}-9\right )^{2} y^{\prime \prime }+\left (x +3\right ) y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.428 |
|
|
\[ {}\left (x^{2}+x -6\right ) y^{\prime \prime }+\left (x +3\right ) y^{\prime }+\left (-2+x \right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.285 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+5 \left (1+x \right ) y^{\prime }+\left (x^{2}-x \right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.198 |
|
|
\[ {}y^{\prime \prime }-x^{2} y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.407 |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.378 |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.541 |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }+3 y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.632 |
|
|
\[ {}y^{\prime \prime }-x^{2} y^{\prime }+x y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.708 |
|
|
\[ {}\cos \left (x \right ) y^{\prime \prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.364 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.58 |
|
|
\[ {}\left (2+x \right ) y^{\prime \prime }+3 y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.421 |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.371 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }+x y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.673 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }+x^{2} y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.868 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
[_Gegenbauer] |
✓ |
✓ |
0.648 |
|
|
\[ {}y^{\prime \prime }+\left (x^{2}+1\right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.763 |
|
|
\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.582 |
|
|
\[ {}y^{\prime \prime }+3 x y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.577 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+30 y = 0 \] |
1 |
2 |
1 |
[_Gegenbauer] |
✓ |
✓ |
1.666 |
|
|
\[ {}\left (-2+x \right )^{2} y^{\prime \prime }+\left (2+x \right ) y^{\prime }-y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.76 |
|
|
\[ {}y^{\prime \prime }+\left (-1+x \right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.667 |
|
|
\[ {}4 \left (t^{2}-3 t +2\right ) y^{\prime \prime }-2 y^{\prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.032 |
|
|
\[ {}2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.016 |
|
|
\[ {}y^{\prime \prime }+\left ({\mathrm e}^{-2 x}-\frac {1}{9}\right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.844 |
|
|
\[ {}\left (2 x +1\right )^{2} y^{\prime \prime }+2 \left (2 x +1\right ) y^{\prime }+16 x \left (1+x \right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.085 |
|
|
\[ {}y^{\prime \prime }+x y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.415 |
|
|
\[ {}y^{\prime \prime }+k^{2} x^{2} y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.596 |
|
|
\[ {}y^{\prime \prime }+k^{2} x^{4} y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.563 |
|
|
\[ {}y^{\prime \prime }+4 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.38 |
|
|
\[ {}\left (-1+x \right )^{2} y^{\prime \prime }-\left (-1+x \right ) y^{\prime }-35 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.861 |
|
|
\[ {}16 \left (1+x \right )^{2} y^{\prime \prime }+3 y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.674 |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
[_Hermite] |
✓ |
✓ |
0.684 |
|
|
\[ {}y^{\prime \prime }+3 x^{2} y^{\prime }-x y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.015 |
|
|
\[ {}y^{\prime \prime }-x^{2} y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.46 |
|
|
\[ {}y^{\prime \prime }+x^{3} y^{\prime }+x^{2} y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.029 |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.444 |
|
|
\[ {}y^{\prime \prime }+\left (-1+x \right )^{2} y^{\prime }-\left (-1+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.578 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.714 |
|
|
\[ {}y^{\prime \prime }+{\mathrm e}^{x} y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.763 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+\alpha \left (\alpha +1\right ) y = 0 \] |
1 |
2 |
1 |
[_Gegenbauer] |
✓ |
✓ |
1.148 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
[_Gegenbauer] |
✓ |
✓ |
0.834 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.6 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }+x y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.859 |
|
|
\[ {}y^{\prime \prime }+2 x y^{\prime }-y = x \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.941 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-x^{2} y = 1 \] |
1 |
2 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.894 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.693 |
|
|
\[ {}y^{\prime \prime }+\left (1+x \right ) y^{\prime }-y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.433 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.546 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.254 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-x y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.583 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-x y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.191 |
|
|
\[ {}y^{\prime \prime }+\left (p +\frac {1}{2}-\frac {x^{2}}{4}\right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.589 |
|
|
\[ {}y^{\prime \prime }+x y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.131 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+p^{2} y = 0 \] |
1 |
2 |
1 |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.573 |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+2 p y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.516 |
|
|
\[ {}y^{\prime \prime }+\sin \left (x \right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
9.463 |
|
|
\[ {}x y^{\prime \prime }+\sin \left (x \right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
6.506 |
|
|
\[ {}y^{\prime \prime }+2 x y = x^{2} \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.428 |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }+y = x \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.408 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = x^{3}-x \] |
1 |
2 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.9 |
|
|
\[ {}2 y^{\prime \prime }+x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.777 |
|
|
\[ {}\left (x^{2}+4\right ) y^{\prime \prime }-y^{\prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.219 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.671 |
|
|
\[ {}y^{\prime \prime }-\left (1+x \right ) y^{\prime }-x y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.997 |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }+\left (1+x \right ) y^{\prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.751 |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.683 |
|
|
\[ {}y^{\prime \prime }-y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.633 |
|
|
\[ {}y^{\prime \prime }-y^{\prime } = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.651 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.764 |
|
|
\[ {}y^{\prime \prime }-x y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.735 |
|
|
\[ {}y^{\prime \prime }+x^{2} y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.128 |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
[_Lienard] |
✓ |
✓ |
1.317 |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
[_Hermite] |
✓ |
✓ |
1.102 |
|
|
\[ {}y^{\prime \prime }+x^{2} y^{\prime }+x y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.14 |
|
|
\[ {}y^{\prime \prime }+2 x y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.138 |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }+y^{\prime } = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.951 |
|
|
\[ {}\left (2+x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.309 |
|
|
|
||||||||
|
\[ {}y^{\prime \prime }-\left (1+x \right ) y^{\prime }-y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.353 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-6 y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.9 |
|
|
\[ {}\left (x^{2}+2\right ) y^{\prime \prime }+3 x y^{\prime }-y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.374 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime }-y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.204 |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.3 |
|
|
\[ {}\left (1+x \right ) y^{\prime \prime }-\left (2-x \right ) y^{\prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.518 |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+8 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.01 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.915 |
|
|
\[ {}y^{\prime \prime }+\sin \left (x \right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.837 |
|
|
\[ {}y^{\prime \prime }+{\mathrm e}^{x} y^{\prime }-y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.603 |
|
|
\[ {}\cos \left (x \right ) y^{\prime \prime }+y^{\prime }+5 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
8.135 |
|
|
\[ {}\cos \left (x \right ) y^{\prime \prime }+y^{\prime }+5 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
15.289 |
|
|
\[ {}y^{\prime \prime }-x y = 1 \] |
1 |
2 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.869 |
|
|
\[ {}y^{\prime \prime }-4 x y^{\prime }-4 y = {\mathrm e}^{x} \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.461 |
|
|
\[ {}x y^{\prime \prime }+\sin \left (x \right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.773 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.865 |
|
|
\[ {}y^{\prime \prime }+\cos \left (x \right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.819 |
|
|
\[ {}\left (x^{2}-9\right )^{2} y^{\prime \prime }+\left (x +3\right ) y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.377 |
|
|
\[ {}\left (x^{2}+x -6\right ) y^{\prime \prime }+\left (x +3\right ) y^{\prime }+\left (-2+x \right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.799 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+5 \left (1+x \right ) y^{\prime }+\left (x^{2}-x \right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.187 |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.452 |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }+3 y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.828 |
|
|
\[ {}y^{\prime \prime }-x^{2} y^{\prime }+x y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.98 |
|
|
\[ {}\cos \left (x \right ) y^{\prime \prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.129 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.398 |
|
|
\[ {}\left (2+x \right ) y^{\prime \prime }+3 y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.838 |
|
|
\[ {}\left (1-2 \sin \left (x \right )\right ) y^{\prime \prime }+x y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
12.342 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.143 |
|
|
\[ {}x y^{\prime \prime }+\left (1-\cos \left (x \right )\right ) y^{\prime }+x^{2} y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
8.286 |
|
|
\[ {}y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 10 x^{3}-2 x +5 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.0 |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.938 |
|
|
\[ {}y^{\prime \prime }-9 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.974 |
|
|
\[ {}y^{\prime \prime }+3 x y^{\prime }+3 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.813 |
|
|
\[ {}\left (4 x^{2}+1\right ) y^{\prime \prime }-8 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.494 |
|
|
\[ {}\left (-4 x^{2}+1\right ) y^{\prime \prime }+8 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.385 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.154 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+10 x y^{\prime }+20 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.828 |
|
|
\[ {}\left (x^{2}+4\right ) y^{\prime \prime }+2 x y^{\prime }-12 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.882 |
|
|
\[ {}\left (x^{2}-9\right ) y^{\prime \prime }+3 x y^{\prime }-3 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.393 |
|
|
\[ {}y^{\prime \prime }+2 x y^{\prime }+5 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.072 |
|
|
\[ {}\left (x^{2}+4\right ) y^{\prime \prime }+6 x y^{\prime }+4 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.947 |
|
|
\[ {}\left (2 x^{2}+1\right ) y^{\prime \prime }-5 x y^{\prime }+3 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.461 |
|
|
\[ {}y^{\prime \prime }+x^{2} y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.352 |
|
|
\[ {}\left (-4 x^{2}+1\right ) y^{\prime \prime }+6 x y^{\prime }-4 y = 0 \] |
1 |
2 |
1 |
[_Gegenbauer] |
✓ |
✓ |
2.733 |
|
|
\[ {}\left (2 x^{2}+1\right ) y^{\prime \prime }+3 x y^{\prime }-3 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.287 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+3 y = x^{2} \] |
1 |
2 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.608 |
|
|
\[ {}y^{\prime \prime }+2 x y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.465 |
|
|
\[ {}y^{\prime \prime }+3 x y^{\prime }+7 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.521 |
|
|
\[ {}2 y^{\prime \prime }+9 x y^{\prime }-36 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.346 |
|
|
\[ {}\left (x^{2}+4\right ) y^{\prime \prime }+x y^{\prime }-9 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
0.402 |
|
|
\[ {}\left (x^{2}+4\right ) y^{\prime \prime }+3 x y^{\prime }-8 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.399 |
|
|
\[ {}\left (9 x^{2}+1\right ) y^{\prime \prime }-18 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.351 |
|
|
\[ {}\left (3 x^{2}+1\right ) y^{\prime \prime }+13 x y^{\prime }+7 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.476 |
|
|
\[ {}\left (2 x^{2}+1\right ) y^{\prime \prime }+11 x y^{\prime }+9 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.76 |
|
|
\[ {}y^{\prime \prime }-2 \left (x +3\right ) y^{\prime }-3 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.688 |
|
|
\[ {}y^{\prime \prime }+\left (-2+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.365 |
|
|
\[ {}\left (x^{2}-2 x +2\right ) y^{\prime \prime }-4 \left (-1+x \right ) y^{\prime }+6 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.389 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-10 x y^{\prime }-18 y = 0 \] |
1 |
2 |
1 |
[_Gegenbauer] |
✓ |
✓ |
1.44 |
|
|
\[ {}y^{\prime \prime }+2 x y^{\prime }-8 y = 0 \] |
1 |
2 |
1 |
[_erf] |
✓ |
✓ |
0.324 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.628 |
|
|
\[ {}\left (1+x \right ) \left (3 x -1\right ) y^{\prime \prime }+\cos \left (x \right ) y^{\prime }-3 x y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
17.183 |
|
|
\[ {}y^{\prime \prime }+\left (x -6\right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.036 |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = \ln \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.628 |
|
|
\[ {}\cos \left (x \right ) y^{\prime \prime }+2 x y^{\prime }-x y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
63.965 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime }+y = x \,{\mathrm e}^{x} \] |
1 |
2 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
11.66 |
|
|
\[ {}y^{\prime \prime }+\left (-1+x \right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.198 |
|
|
\[ {}y^{\prime \prime }+y = {\mathrm e}^{a \cos \left (x \right )} \] |
1 |
2 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.888 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.904 |
|
|
\[ {}y^{\prime \prime }+8 x y^{\prime }-4 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.03 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}+1\right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.504 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+\left (x^{2}-4\right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.453 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+\left (3 x +2\right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.218 |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }+\left (-2+3 x \right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.304 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+x y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.793 |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }-\left (-2+3 x \right ) y^{\prime }+2 x y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.398 |
|
|
\[ {}\left (x^{3}-1\right ) y^{\prime \prime }+x^{2} y^{\prime }+x y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.626 |
|
|
\[ {}\left (x +3\right ) y^{\prime \prime }+\left (2+x \right ) y^{\prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.268 |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.427 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }-2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.961 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+2 x y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.406 |
|
|
\[ {}\left (2 x^{2}-3\right ) y^{\prime \prime }-2 x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.647 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.33 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.447 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
4.06 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+n \left (n +1\right ) y = 0 \] |
1 |
2 |
1 |
[_Gegenbauer] |
✓ |
✓ |
1.48 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+n \left (n +1\right ) y = 0 \] |
1 |
2 |
1 |
[_Gegenbauer] |
✓ |
✓ |
1.398 |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
[_Hermite] |
✓ |
✓ |
0.776 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.93 |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }-4 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.044 |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+4 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.38 |
|
|
\[ {}y^{\prime \prime }+4 x y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.817 |
|
|
\[ {}\left (x^{2}-1\right )^{2} y^{\prime \prime }+\left (1+x \right ) y^{\prime }-y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.297 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.634 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.757 |
|
|
\[ {}\left (x^{2}+4\right ) y^{\prime \prime }+2 x y^{\prime } = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.624 |
|
|
\[ {}y^{\prime \prime }-3 x^{2} y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.682 |
|
|
\[ {}\left (-x^{2}+4\right ) y^{\prime \prime }-5 x y^{\prime }-3 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.056 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+4 y = 0 \] |
1 |
2 |
1 |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
0.883 |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+6 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.042 |
|
|
\[ {}y^{\prime \prime }+\left (2+x \right ) y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.145 |
|
|
\[ {}\left (x^{2}-2 x +2\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }-3 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.981 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-x y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.984 |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-2 x y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.004 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+\lambda y = 0 \] |
1 |
2 |
1 |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.175 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+\lambda y = 0 \] |
1 |
2 |
1 |
[_Gegenbauer] |
✓ |
✓ |
1.141 |
|
|
\[ {}y^{\prime \prime }+4 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.535 |
|
|
\[ {}y^{\prime \prime }-x^{2} y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.559 |
|
|
\[ {}y^{\prime \prime }+{\mathrm e}^{2 x} y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.727 |
|
|
\[ {}\sin \left (x \right ) y^{\prime \prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.102 |
|
|
\[ {}y^{\prime \prime }+x y = \sin \left (x \right ) \] |
1 |
2 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.025 |
|
|
\[ {}y^{\prime \prime }-\sin \left (x \right ) y^{\prime }-x y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.483 |
|
|
\[ {}\sin \left (x \right ) y^{\prime \prime }+x^{2} y^{\prime }-{\mathrm e}^{x} y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
87.506 |
|
|
\[ {}\sinh \left (x \right ) y^{\prime \prime }+x^{2} y^{\prime }-{\mathrm e}^{x} y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
16.42 |
|
|
\[ {}\sinh \left (x \right ) y^{\prime \prime }+x^{2} y^{\prime }-\sin \left (x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
172.314 |
|
|
\[ {}{\mathrm e}^{3 x} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+\frac {2 y}{x^{2}+4} = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
28.862 |
|
|
\[ {}y^{\prime \prime }+\frac {\left (1+{\mathrm e}^{x}\right ) y}{-{\mathrm e}^{x}+1} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.645 |
|
|
\[ {}\left (x^{2}-4\right ) y^{\prime \prime }+\left (x^{2}+x -6\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.214 |
|
|
\[ {}x y^{\prime \prime }+\left (-{\mathrm e}^{x}+1\right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.217 |
|
|
\[ {}\sin \left (\pi \,x^{2}\right ) y^{\prime \prime }+x^{2} y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.764 |
|
|
\[ {}y^{\prime \prime }-{\mathrm e}^{x} y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.3 |
|
|
\[ {}y^{\prime \prime }+3 x y^{\prime }-{\mathrm e}^{x} y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.239 |
|
|
\[ {}x y^{\prime \prime }-3 x y^{\prime }+\sin \left (x \right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.786 |
|
|
\[ {}y^{\prime \prime }+y \ln \left (x \right ) = 0 \] |
1 |
1 |
1 |
[_Titchmarsh] |
✓ |
✓ |
1.066 |
|
|
\[ {}\sqrt {x}\, y^{\prime \prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.191 |
|
|
\[ {}y^{\prime \prime }+\left (6 x^{2}+2 x +1\right ) y^{\prime }+\left (2+12 x \right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.326 |
|
|
\[ {}y^{\prime \prime }-{\mathrm e}^{x} y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.108 |
|
|
\[ {}y^{\prime \prime }+\cos \left (x \right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.992 |
|
|
\[ {}y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.44 |
|
|
\[ {}\sqrt {x}\, y^{\prime \prime }+y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
6.071 |
|
|
\[ {}\left (x -3\right )^{2} y^{\prime \prime }-2 \left (x -3\right ) y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.005 |
|
|
\[ {}\left (-1+x \right )^{2} y^{\prime \prime }-5 \left (-1+x \right ) y^{\prime }+9 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.19 |
|
|
\[ {}\left (2+x \right )^{2} y^{\prime \prime }+\left (2+x \right ) y^{\prime } = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.795 |
|
|
\[ {}3 \left (-2+x \right )^{2} y^{\prime \prime }-4 \left (x -5\right ) y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.511 |
|
|
\[ {}\left (x -5\right )^{2} y^{\prime \prime }+\left (x -5\right ) y^{\prime }+4 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.296 |
|
|
\[ {}x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.245 |
|
|
\[ {}\left (x^{2}+4\right )^{2} y^{\prime \prime }+y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.651 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+7 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.577 |
|
|
\[ {}\left (-2+x \right ) y^{\prime \prime }+y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.383 |
|
|
\[ {}\left (x^{2}-4\right ) y^{\prime \prime }+16 \left (2+x \right ) y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
15.529 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }-18 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.031 |
|
|
\[ {}y^{\prime \prime }-11 y^{\prime }+30 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.037 |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.655 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{-x} \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.111 |
|
|
\[ {}\left (-2 x -2\right ) y^{\prime \prime }+2 y^{\prime }+4 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.113 |
|
|
\[ {}\left (3 x +2\right ) y^{\prime \prime }+3 x y^{\prime } = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.095 |
|
|
\[ {}\left (1+3 x \right ) y^{\prime \prime }-3 y^{\prime }-2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.133 |
|
|
\[ {}\left (-x^{2}+2\right ) y^{\prime \prime }+2 \left (-1+x \right ) y^{\prime }+4 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.313 |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }+4 y = 0 \] |
1 |
2 |
1 |
[_Hermite] |
✓ |
✓ |
0.263 |
|
|
\[ {}\left (2 x^{2}+2\right ) y^{\prime \prime }+2 x y^{\prime }-3 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
0.904 |
|
|
\[ {}\left (3-2 x \right ) y^{\prime \prime }+2 y^{\prime }-2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.09 |
|
|
\[ {}y^{\prime \prime }-4 x^{2} y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.684 |
|
|
\[ {}\left (2 x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }-3 y = 0 \] |
1 |
2 |
1 |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.914 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime } = \sin \left (x \right ) \] |
1 |
2 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
3.002 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+x y = \cos \left (x \right ) \] |
1 |
2 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.41 |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.977 |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+6 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.855 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.996 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+9 y = 0 \] |
1 |
2 |
1 |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
0.999 |
|
|
\[ {}y^{\prime \prime }-\cos \left (x \right ) y = \sin \left (x \right ) \] |
1 |
2 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.432 |
|
|
\[ {}\left (x^{2}-3 x -4\right ) y^{\prime \prime }-\left (1+x \right ) y^{\prime }+\left (x^{2}-1\right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.627 |
|
|
\[ {}\left (x^{2}-25\right )^{2} y^{\prime \prime }-\left (x +5\right ) y^{\prime }+10 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
9.745 |
|
|
\[ {}y^{\prime \prime }+x y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.681 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+k \left (k +1\right ) y = 0 \] |
1 |
2 |
1 |
[_Gegenbauer] |
✓ |
✓ |
1.566 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.025 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }-3 y = x \,{\mathrm e}^{x} \] |
1 |
2 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.16 |
|
|
\[ {}\left (2 x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }-3 y = 0 \] |
1 |
2 |
1 |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.023 |
|
|
\[ {}y^{\prime \prime }+x y = 0 \] |
1 |
2 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.148 |
|
|
\[ {}y^{\prime \prime }-\sin \left (x \right ) y^{\prime } = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.501 |
|
|
\[ {}x y^{\prime \prime }+\sin \left (x \right ) y = x \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.568 |
|
|
\[ {}\ln \left (x \right ) y^{\prime \prime }-\sin \left (x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
40.846 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.511 |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }+y = 1 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.207 |
|
|
\[ {}y^{\prime \prime }-\left (x^{2}+1\right ) y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.238 |
|
|
\[ {}y^{\prime \prime } = x^{2} y-y^{\prime } \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.415 |
|
|
\[ {}y^{\prime \prime }-{\mathrm e}^{x} y = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.629 |
|
|
|
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|
|
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|
|