Number of problems in this table is 208
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) |
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (-x^{2}-6 x +1\right ) y^{\prime }+\left (x^{2}+6 x +1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.104 |
|
|
\[ {}x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.125 |
|
|
\[ {}2 x^{2} \left (2+x \right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (1+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.281 |
|
|
\[ {}x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-2 x \left (2 x^{2}+1\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.961 |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (5-x \right ) y^{\prime }+\left (9-4 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.908 |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+\left (-x^{2}+1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
6.673 |
|
|
\[ {}x^{2} \left (2 x^{2}+x +1\right ) y^{\prime \prime }+x \left (7 x^{2}+6 x +3\right ) y^{\prime }+\left (-3 x^{2}+6 x +1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.783 |
|
|
\[ {}x^{2} \left (x^{2}+2 x +1\right ) y^{\prime \prime }+x \left (4 x^{2}+3 x +1\right ) y^{\prime }-x \left (1-2 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.627 |
|
|
\[ {}4 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+12 x^{2} \left (1+x \right ) y^{\prime }+\left (3 x^{2}+3 x +1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
11.103 |
|
|
\[ {}x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }-x \left (-2 x^{2}-4 x +1\right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
10.727 |
|
|
\[ {}9 x^{2} y^{\prime \prime }+3 x \left (-2 x^{2}+3 x +5\right ) y^{\prime }+\left (-14 x^{2}+12 x +1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.757 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (x^{2}+x +1\right ) y^{\prime }+x \left (2-x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.282 |
|
|
\[ {}x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+14 x +5\right ) y^{\prime }+\left (12 x^{2}+18 x +4\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.362 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+2 x \left (x^{2}+x +4\right ) y^{\prime }+\left (3 x^{2}+5 x +1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.482 |
|
|
\[ {}16 x^{2} y^{\prime \prime }+4 x \left (2 x^{2}+x +6\right ) y^{\prime }+\left (18 x^{2}+5 x +1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.434 |
|
|
\[ {}9 x^{2} \left (1+x \right ) y^{\prime \prime }+3 x \left (-x^{2}+11 x +5\right ) y^{\prime }+\left (-7 x^{2}+16 x +1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.66 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+\left (1+4 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.559 |
|
|
\[ {}36 x^{2} \left (1-2 x \right ) y^{\prime \prime }+24 x \left (1-9 x \right ) y^{\prime }+\left (1-70 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.61 |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (-x +3\right ) y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.954 |
|
|
\[ {}x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5-4 x \right ) y^{\prime }+\left (9-4 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.847 |
|
|
\[ {}25 x^{2} y^{\prime \prime }+x \left (15+x \right ) y^{\prime }+\left (1+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.423 |
|
|
\[ {}2 x^{2} \left (2+x \right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (1-x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.226 |
|
|
\[ {}x^{2} \left (9+4 x \right ) y^{\prime \prime }+3 x y^{\prime }+\left (1+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
7.327 |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (3-2 x \right ) y^{\prime }+\left (3 x +4\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.257 |
|
|
\[ {}x^{2} \left (1-4 x \right ) y^{\prime \prime }+3 x \left (1-6 x \right ) y^{\prime }+\left (1-12 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.175 |
|
|
\[ {}x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (3+5 x \right ) y^{\prime }+\left (1-2 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.047 |
|
|
\[ {}2 x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (6-x \right ) y^{\prime }+\left (8-x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.237 |
|
|
\[ {}x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (5+9 x \right ) y^{\prime }+\left (3 x +4\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.414 |
|
|
\[ {}x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5+4 x \right ) y^{\prime }+\left (9+4 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.19 |
|
|
\[ {}x^{2} \left (1+4 x \right ) y^{\prime \prime }-x \left (1-4 x \right ) y^{\prime }+\left (1+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.645 |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.734 |
|
|
\[ {}x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (7+x \right ) y^{\prime }+\left (9-x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.381 |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.831 |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-3 x \left (-x^{2}+1\right ) y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.59 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.886 |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+1\right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.666 |
|
|
\[ {}2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+7 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.486 |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-4 x^{2}+1\right ) y^{\prime }+\left (2 x^{2}+1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.882 |
|
|
\[ {}4 x^{2} \left (x^{2}+4\right ) y^{\prime \prime }+3 x \left (3 x^{2}+8\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.591 |
|
|
\[ {}3 x^{2} \left (x^{2}+3\right ) y^{\prime \prime }+x \left (11 x^{2}+3\right ) y^{\prime }+\left (5 x^{2}+1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.635 |
|
|
\[ {}4 x^{2} \left (4 x^{2}+1\right ) y^{\prime \prime }+32 x^{3} y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.06 |
|
|
\[ {}9 x^{2} y^{\prime \prime }-3 x \left (-2 x^{2}+7\right ) y^{\prime }+\left (2 x^{2}+25\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.053 |
|
|
\[ {}x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (7 x^{2}+3\right ) y^{\prime }+\left (-3 x^{2}+1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.106 |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }+\left (12 x^{2}+1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.846 |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.506 |
|
|
\[ {}x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-9 x^{2}+5\right ) y^{\prime }+\left (-3 x^{2}+4\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.815 |
|
|
\[ {}x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (-x^{2}+14\right ) y^{\prime }+2 \left (x^{2}+9\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.304 |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (7 x^{2}+3\right ) y^{\prime }+\left (8 x^{2}+1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.913 |
|
|
\[ {}x^{2} \left (1-2 x \right ) y^{\prime \prime }+3 x y^{\prime }+\left (1+4 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.033 |
|
|
\[ {}x \left (1+x \right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.873 |
|
|
\[ {}x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (2 x +1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.907 |
|
|
\[ {}4 x^{2} \left (1+x \right ) y^{\prime \prime }+4 x^{2} y^{\prime }+\left (1-5 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.386 |
|
|
\[ {}x^{2} \left (1-x \right ) y^{\prime \prime }-x \left (3-5 x \right ) y^{\prime }+\left (4-5 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.865 |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (9 x^{2}+1\right ) y^{\prime }+\left (25 x^{2}+1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.878 |
|
|
\[ {}9 x^{2} y^{\prime \prime }+3 x \left (-x^{2}+1\right ) y^{\prime }+\left (7 x^{2}+1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.449 |
|
|
\[ {}x \left (x^{2}+1\right ) y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }-8 x y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.728 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+2 x \left (-x^{2}+4\right ) y^{\prime }+\left (7 x^{2}+1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.326 |
|
|
\[ {}4 x^{2} \left (1+x \right ) y^{\prime \prime }+8 x^{2} y^{\prime }+\left (1+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.868 |
|
|
\[ {}9 x^{2} \left (x +3\right ) y^{\prime \prime }+3 x \left (3+7 x \right ) y^{\prime }+\left (3+4 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.465 |
|
|
\[ {}x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (3 x^{2}+2\right ) y^{\prime }+\left (-x^{2}+2\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.637 |
|
|
\[ {}16 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x \left (9 x^{2}+1\right ) y^{\prime }+\left (49 x^{2}+1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.402 |
|
|
\[ {}x^{2} \left (3 x +4\right ) y^{\prime \prime }-x \left (4-3 x \right ) y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.661 |
|
|
\[ {}4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }+8 x^{2} \left (2 x +3\right ) y^{\prime }+\left (9 x^{2}+3 x +1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.943 |
|
|
\[ {}x^{2} \left (1-x \right )^{2} y^{\prime \prime }-x \left (-3 x^{2}+2 x +1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.954 |
|
|
\[ {}9 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+7 x +1\right ) y^{\prime }+\left (25 x^{2}+4 x +1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.076 |
|
|
\[ {}\left ({\mathrm e}^{t}-1\right ) y^{\prime \prime }+{\mathrm e}^{t} y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.695 |
|
|
\[ {}t y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 t y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.269 |
|
|
\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+t^{2} y = 0 \] |
1 |
1 |
1 |
[_Lienard] |
✓ |
✓ |
1.756 |
|
|
\[ {}t y^{\prime \prime }+\left (1-t \right ) y^{\prime }+\lambda y = 0 \] |
1 |
1 |
1 |
[_Laguerre] |
✓ |
✓ |
2.667 |
|
|
\[ {}t y^{\prime \prime }+y^{\prime }-4 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.659 |
|
|
\[ {}t^{2} y^{\prime \prime }-t \left (t +1\right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.703 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.703 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }+2 x y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.569 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 \left (1+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.678 |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (1+x \right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.668 |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (2 x +3\right ) y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.737 |
|
|
\[ {}x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }-5 x y^{\prime }+9 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.888 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (x^{2}-1\right ) y^{\prime }+\left (-x^{2}+1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.715 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }-2 x y = x^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.608 |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (x^{2}+3\right ) y^{\prime }+y = -2 x^{2}+x \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.102 |
|
|
\[ {}z \left (1-z \right ) y^{\prime \prime }+\left (1-z \right ) y^{\prime }+\lambda y = 0 \] |
1 |
1 |
1 |
[_Jacobi] |
✓ |
✓ |
1.181 |
|
|
\[ {}z y^{\prime \prime }+\left (2 z -3\right ) y^{\prime }+\frac {4 y}{z} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.787 |
|
|
\[ {}z y^{\prime \prime }+\left (1-z \right ) y^{\prime }+\lambda y = 0 \] |
1 |
1 |
1 |
[_Laguerre] |
✓ |
✓ |
1.276 |
|
|
\[ {}x y^{\prime \prime }-\left (-1+x \right ) y^{\prime }-x y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.005 |
|
|
\[ {}4 x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (2 x +1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.07 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (1-2 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.071 |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4-x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.055 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (-x +3\right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.967 |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (-x^{2}+x \right ) y^{\prime }+\left (x^{3}+1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.437 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+\left (4-x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.956 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.979 |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+7 x \,{\mathrm e}^{x} y^{\prime }+9 \left (1+\tan \left (x \right )\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
244.654 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (1-x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.96 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+\left (1-4 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.892 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.918 |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.974 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.053 |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+\left (1-x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.027 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.875 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
[_Lienard] |
✓ |
✓ |
0.845 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 \left (1+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.93 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.833 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }+p x y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.644 |
|
|
\[ {}x \left (-x^{2}+1\right ) y^{\prime \prime }+\left (-3 x^{2}+1\right ) y^{\prime }-x y = 0 \] |
1 |
1 |
1 |
[[_elliptic, _class_I]] |
✓ |
✓ |
0.84 |
|
|
\[ {}x \left (-x^{2}+1\right ) y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
[[_elliptic, _class_II]] |
✓ |
✓ |
1.324 |
|
|
\[ {}\left (1+x \right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+x y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.496 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
[_Lienard] |
✓ |
✓ |
0.77 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.845 |
|
|
\[ {}x^{3} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.901 |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }-\left (2 x +1\right ) \left (-y+x y^{\prime }\right ) = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.035 |
|
|
\[ {}x y^{\prime \prime }+\left (4 x^{2}+1\right ) y^{\prime }+4 x \left (x^{2}+1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.019 |
|
|
\[ {}x y^{\prime \prime }+\left (x^{3}+1\right ) y^{\prime }+b x y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.65 |
|
|
\[ {}x \left (2+x \right ) y^{\prime \prime }+2 \left (1+x \right ) y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.984 |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x}-x y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.829 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.803 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }+10 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.833 |
|
|
\[ {}x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.846 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.875 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
[_Lienard] |
✓ |
✓ |
0.702 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+\left (16 x^{2}+1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.827 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }-7 x^{3} y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.873 |
|
|
\[ {}x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+\left (1+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.07 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
[_Lienard] |
✓ |
✓ |
0.717 |
|
|
\[ {}x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (-1+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.023 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }+\frac {y}{4} = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.823 |
|
|
\[ {}4 x y^{\prime \prime }+4 y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.855 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }+36 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.854 |
|
|
\[ {}x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (-1+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.902 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }-x y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.796 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[_Gegenbauer] |
✓ |
✓ |
1.394 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+x^{2} y = 0 \] |
1 |
1 |
1 |
[_Lienard] |
✓ |
✓ |
0.958 |
|
|
\[ {}x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+3 \left (x^{2}+x \right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.635 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (1+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.151 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+x^{2} y = 0 \] |
1 |
1 |
1 |
[_Lienard] |
✓ |
✓ |
2.013 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+\left (4 x +4\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.501 |
|
|
\[ {}4 x^{2} y^{\prime \prime }-8 x^{2} y^{\prime }+\left (4 x^{2}+1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.294 |
|
|
\[ {}x y^{\prime \prime }-\left (-1+x \right ) y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[_Laguerre] |
✓ |
✓ |
3.061 |
|
|
\[ {}x y^{\prime \prime }+\left (1+x \right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.652 |
|
|
\[ {}x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.698 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }+10 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
3.273 |
|
|
\[ {}x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.917 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.838 |
|
|
\[ {}2 x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.6 |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (1+x \right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.404 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+\left (1-2 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.422 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.481 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (4 x^{2}+1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.345 |
|
|
\[ {}x \left (1+x \right ) y^{\prime \prime }+\left (1+5 x \right ) y^{\prime }+3 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.598 |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (1+3 x \right ) y^{\prime }+\left (1-6 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.675 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (-1+x \right ) y^{\prime }+\left (1-x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.529 |
|
|
\[ {}x \left (-2+x \right ) y^{\prime \prime }+2 \left (-1+x \right ) y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.563 |
|
|
\[ {}x \left (-2+x \right ) y^{\prime \prime }+2 \left (-1+x \right ) y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.665 |
|
|
\[ {}4 \left (x -4\right )^{2} y^{\prime \prime }+\left (x -4\right ) \left (x -8\right ) y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.117 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }-x y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.156 |
|
|
\[ {}x y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }-x y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.358 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (2 x +3\right ) y^{\prime }+\left (1+3 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.818 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+8 x \left (1+x \right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.729 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x \left (1+x \right ) y^{\prime }+\left (1-3 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.703 |
|
|
\[ {}x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.408 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (x^{3}+x +1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.152 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }+x \left (1+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.639 |
|
|
\[ {}x \left (-2+x \right )^{2} y^{\prime \prime }-2 \left (-2+x \right ) y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.171 |
|
|
\[ {}x \left (-2+x \right )^{2} y^{\prime \prime }-2 \left (-2+x \right ) y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.595 |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.429 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (x^{2}-3\right ) y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.306 |
|
|
\[ {}4 x^{2} y^{\prime \prime }-x^{2} y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.582 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+3 x^{2} y^{\prime }+\left (1+3 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.023 |
|
|
\[ {}x y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+2 x y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.531 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (x +3\right ) y^{\prime }+\left (2 x +1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.567 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 \left (1+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.473 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+2 x y^{\prime }-x y = 1 \] |
1 |
0 |
0 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
1.352 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.472 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.36 |
|
|
\[ {}x y^{\prime \prime }+\left (1+x \right ) y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.688 |
|
|
\[ {}x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.018 |
|
|
\[ {}2 x^{2} \left (2+x \right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (1+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.253 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+2 x y^{\prime }-x y = \sin \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.121 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+2 x y^{\prime }-x y = x \sin \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.728 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+2 x y^{\prime }-x y = \sin \left (x \right ) \cos \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.309 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+2 x y^{\prime }-x y = x^{3}+x \sin \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.411 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-x y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.385 |
|
|
\[ {}x^{2} y^{\prime \prime }-9 x y^{\prime }+25 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.118 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.232 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.334 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-x^{2} y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.259 |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }+\left (1-5 x \right ) y^{\prime }-4 y = 0 \] |
1 |
1 |
1 |
[_Jacobi] |
✓ |
✓ |
1.351 |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x -3}+\frac {y}{x -4} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.136 |
|
|
\[ {}y^{\prime \prime }+\left (\frac {1}{x}-\frac {1}{3}\right ) y^{\prime }+\left (\frac {1}{x}-\frac {1}{4}\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
6.148 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+\left (1-4 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.11 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+\frac {y}{1-x} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.257 |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x}+y = 0 \] |
1 |
1 |
1 |
[_Lienard] |
✓ |
✓ |
1.086 |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (2 x^{2}+5 x \right ) y^{\prime }+\left (9+4 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.265 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+8 x^{2} y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.282 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (-x^{4}+x \right ) y^{\prime }+3 x^{3} y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.655 |
|
|
\[ {}4 y^{\prime \prime }+\frac {\left (4 x -3\right ) y}{\left (-1+x \right )^{2}} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.477 |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x}+y = 0 \] |
1 |
1 |
1 |
[_Lienard] |
✓ |
✓ |
0.997 |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (2 x^{2}+5 x \right ) y^{\prime }+9 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.208 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+8 x y^{\prime }+\left (1-4 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.211 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+\left (1-4 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.082 |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x}+y = 0 \] |
1 |
1 |
1 |
[_Lienard] |
✓ |
✓ |
1.54 |
|
|
\[ {}y^{\prime \prime }-\left (\frac {1}{x}+2\right ) y^{\prime }+\left (x +\frac {1}{x^{2}}\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.827 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.137 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.024 |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }+y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.405 |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[_Jacobi] |
✓ |
✓ |
1.47 |
|
|
\[ {}x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+k y = 0 \] |
1 |
1 |
1 |
[_Laguerre] |
✓ |
✓ |
1.949 |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+10 y = 0 \] |
1 |
1 |
1 |
[_Jacobi] |
✓ |
✓ |
1.582 |
|
|
\[ {}x \left (1+x \right ) y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }-10 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.648 |
|
|
|
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