Number of problems in this table is 322
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) |
|
\[ {}x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (2-x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.825 |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }-\left (4+6 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.872 |
|
|
\[ {}x^{2} \left (1+3 x \right ) y^{\prime \prime }+x \left (x^{2}+12 x +2\right ) y^{\prime }+2 x \left (x +3\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.703 |
|
|
\[ {}x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+4\right ) y^{\prime }+2 \left (-x^{2}+1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.086 |
|
|
\[ {}x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+2 x \left (x^{2}+5\right ) y^{\prime }+2 \left (-x^{2}+3\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.15 |
|
|
\[ {}2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+11 x \right ) y^{\prime }-\left (1-x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.006 |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-2 x \left (-x^{2}+2\right ) y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.863 |
|
|
\[ {}2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }-x \left (-7 x^{2}+12\right ) y^{\prime }+\left (3 x^{2}+7\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.335 |
|
|
\[ {}2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (7 x^{2}+4\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.399 |
|
|
\[ {}x \left (x^{2}+1\right ) y^{\prime \prime }+\left (7 x^{2}+4\right ) y^{\prime }+8 x y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.966 |
|
|
\[ {}4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.123 |
|
|
\[ {}4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }-4 x \left (-3 x^{2}-3 x +1\right ) y^{\prime }+3 \left (x^{2}-x +1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.202 |
|
|
\[ {}2 x^{2} \left (2+x \right ) y^{\prime \prime }-x \left (4-7 x \right ) y^{\prime }-\left (5-3 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.904 |
|
|
\[ {}x^{2} \left (1-2 x \right ) y^{\prime \prime }+x \left (8-9 x \right ) y^{\prime }+\left (-3 x +6\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.49 |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (10 x^{2}+3\right ) y^{\prime }-\left (-14 x^{2}+15\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.744 |
|
|
\[ {}x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-13 x^{2}+7\right ) y^{\prime }-14 x^{2} y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.445 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+\left (3+4 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.81 |
|
|
\[ {}x y^{\prime \prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
3.517 |
|
|
\[ {}4 x^{2} \left (1+x \right ) y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }-\left (1+3 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.544 |
|
|
\[ {}x \left (1+x \right ) y^{\prime \prime }+x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.295 |
|
|
\[ {}2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+21 x \right ) y^{\prime }-\left (1-9 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.757 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (2+x \right ) y^{\prime }-\left (2-3 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.216 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }-\left (9-x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.865 |
|
|
\[ {}x^{2} y^{\prime \prime }+10 x y^{\prime }+\left (14+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.977 |
|
|
\[ {}4 x^{2} \left (1+x \right ) y^{\prime \prime }+4 x \left (3+8 x \right ) y^{\prime }-\left (5-49 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.952 |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (3+10 x \right ) y^{\prime }+30 x y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.505 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-3 \left (x +3\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.24 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (1-2 x \right ) y^{\prime }-\left (x +4\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.227 |
|
|
\[ {}x \left (1+x \right ) y^{\prime \prime }-4 y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.062 |
|
|
\[ {}x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (9+13 x \right ) y^{\prime }+\left (7+5 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.611 |
|
|
\[ {}4 x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (4-x \right ) y^{\prime }-\left (7+5 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.32 |
|
|
\[ {}3 x^{2} \left (x +3\right ) y^{\prime \prime }-x \left (15+x \right ) y^{\prime }-20 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.538 |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (1-10 x \right ) y^{\prime }-\left (9-10 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.513 |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }+3 x^{2} y^{\prime }-\left (6-x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.335 |
|
|
\[ {}x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (3+14 x \right ) y^{\prime }+\left (6+100 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.242 |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (6+11 x \right ) y^{\prime }+\left (6+32 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.308 |
|
|
\[ {}4 x^{2} \left (1+x \right ) y^{\prime \prime }+4 x \left (1+4 x \right ) y^{\prime }-\left (49+27 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.602 |
|
|
\[ {}x^{2} \left (2 x +1\right ) y^{\prime \prime }-x \left (9+8 x \right ) y^{\prime }-12 x y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
3.184 |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+7\right ) y^{\prime }+12 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.235 |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (-x^{2}+7\right ) y^{\prime }+12 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.049 |
|
|
\[ {}x y^{\prime \prime }-5 y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
[_Lienard] |
✓ |
✓ |
3.675 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (2 x^{2}+1\right ) y^{\prime }-\left (-10 x^{2}+1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.537 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-\left (-x^{2}+3\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.819 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+2 x \left (x^{2}+8\right ) y^{\prime }+\left (3 x^{2}+5\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.649 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (x^{2}+1\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.996 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (-2 x^{2}+1\right ) y^{\prime }-4 \left (2 x^{2}+1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.185 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+8 x y^{\prime }-\left (-x^{2}+35\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.133 |
|
|
\[ {}9 x^{2} y^{\prime \prime }-3 x \left (2 x^{2}+11\right ) y^{\prime }+\left (10 x^{2}+13\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.015 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (-2 x^{2}+1\right ) y^{\prime }-4 \left (-x^{2}+1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
3.941 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (-3 x^{2}+1\right ) y^{\prime }-4 \left (-3 x^{2}+1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.589 |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (11 x^{2}+5\right ) y^{\prime }+24 x^{2} y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.002 |
|
|
\[ {}4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x y^{\prime }-\left (-x^{2}+35\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.145 |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-x^{2}+5\right ) y^{\prime }-\left (25 x^{2}+7\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.26 |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+5\right ) y^{\prime }-21 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.673 |
|
|
\[ {}x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }-x \left (x^{2}+3\right ) y^{\prime }-2 x y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.52 |
|
|
\[ {}4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (x^{2}+2\right ) y^{\prime }-\left (x^{2}+15\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.154 |
|
|
\[ {}t \left (t -2\right )^{2} y^{\prime \prime }+t y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.911 |
|
|
\[ {}t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.828 |
|
|
\[ {}t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+t y = 0 \] |
1 |
1 |
1 |
[_Lienard] |
✓ |
✓ |
2.205 |
|
|
\[ {}t^{2} y^{\prime \prime }+\left (-t^{2}+3 t \right ) y^{\prime }-t y = 0 \] |
1 |
1 |
1 |
[_Laguerre, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.906 |
|
|
\[ {}t^{2} y^{\prime \prime }+t \left (t +1\right ) y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.859 |
|
|
\[ {}t y^{\prime \prime }-\left (4+t \right ) y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[_Laguerre] |
✓ |
✓ |
2.333 |
|
|
\[ {}t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.273 |
|
|
\[ {}t^{2} y^{\prime \prime }+t y^{\prime }-\left (t +1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.022 |
|
|
\[ {}t y^{\prime \prime }+t y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.438 |
|
|
\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-1\right ) y = 0 \] |
1 |
1 |
1 |
[_Bessel] |
✓ |
✓ |
4.155 |
|
|
\[ {}t y^{\prime \prime }+3 y^{\prime }-3 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
4.17 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+x \left (x^{2}-4\right ) y^{\prime }+3 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.819 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (2 x -1\right ) y^{\prime }+x \left (-1+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.902 |
|
|
\[ {}x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.886 |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-\left (3 x^{2}+2\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.892 |
|
|
\[ {}x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-9 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.945 |
|
|
\[ {}\left (-x^{2}+x \right ) y^{\prime \prime }-3 y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.819 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (x -7\right ) y^{\prime }+\left (x +12\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.456 |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (x -4\right ) y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.497 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (-x^{2}+3\right ) y^{\prime }-3 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.385 |
|
|
\[ {}x y^{\prime \prime }+3 y^{\prime }-y = x \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.286 |
|
|
\[ {}x y^{\prime \prime }+3 y^{\prime }-y = x \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.216 |
|
|
\[ {}x y^{\prime \prime }-x y^{\prime }+y = x^{3} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.333 |
|
|
\[ {}\left (x^{2}+2 x \right ) y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+2 y = x^{2} \left (2+x \right )^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.933 |
|
|
\[ {}z y^{\prime \prime }-2 y^{\prime }+9 z^{5} y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
0.749 |
|
|
\[ {}z y^{\prime \prime }-2 y^{\prime }+y z = 0 \] |
1 |
1 |
1 |
[_Lienard] |
✓ |
✓ |
0.766 |
|
|
\[ {}\left (-2+x \right )^{2} y^{\prime \prime }+\left (-2+x \right ) {\mathrm e}^{x} y^{\prime }+\frac {4 y}{x} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.556 |
|
|
\[ {}4 x y^{\prime \prime }-x y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.968 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-\left (x +4\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.833 |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (-1+2 \sqrt {5}\right ) x y^{\prime }+\left (\frac {19}{4}-3 x^{2}\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.73 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (4 x +\frac {1}{2} x^{2}-\frac {1}{3} x^{3}\right ) y^{\prime }-\frac {7 y}{4} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.686 |
|
|
\[ {}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.934 |
|
|
\[ {}x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (2+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.025 |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x -\frac {3}{4}\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.122 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (2 x -1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.931 |
|
|
\[ {}x^{2} y^{\prime \prime }+x^{3} y^{\prime }-\left (2+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.369 |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.188 |
|
|
\[ {}x y^{\prime \prime }-y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.803 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (x^{2}+6\right ) y^{\prime }+6 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.296 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.032 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-\left (1+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.977 |
|
|
\[ {}x^{2} y^{\prime \prime }-x^{2} y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.04 |
|
|
\[ {}x^{2} y^{\prime \prime }-x^{2} y^{\prime }-\left (3 x +2\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.197 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.212 |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x \left (2+x \right ) y^{\prime }+2 \left (1+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.135 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }+\left (4 x -1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.223 |
|
|
\[ {}4 x^{2} y^{\prime \prime }-\left (3+4 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.931 |
|
|
\[ {}x y^{\prime \prime }-x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[_Laguerre, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.821 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (2+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.071 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {9}{4}\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.127 |
|
|
\[ {}x y^{\prime \prime }-y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
[_Lienard] |
✓ |
✓ |
1.889 |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
[_Lienard] |
✓ |
✓ |
0.98 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.024 |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (2-x \right ) y^{\prime }+\left (x^{2}+2\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.198 |
|
|
\[ {}y^{\prime \prime }+\left (1-\frac {3}{4 x^{2}}\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.905 |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }+a^{3} x^{2} y = 2 \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.596 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (2 x^{2}+x \right ) y^{\prime }-4 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.881 |
|
|
\[ {}\left (-x^{2}+x \right ) y^{\prime \prime }+3 y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.914 |
|
|
\[ {}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (-2+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.833 |
|
|
\[ {}x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (-2+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.793 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.021 |
|
|
\[ {}x y^{\prime \prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.99 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }+\left (3 x -1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.419 |
|
|
\[ {}\left (-x^{2}+x \right ) y^{\prime \prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.274 |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (x^{2}+4 x \right ) y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.307 |
|
|
\[ {}4 x \left (1-x \right ) y^{\prime \prime }-4 y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[_Jacobi] |
✓ |
✓ |
1.45 |
|
|
\[ {}\left (-x^{2}+x \right ) y^{\prime \prime }+3 y^{\prime }+2 y = 3 x^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.829 |
|
|
\[ {}2 x \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.099 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.815 |
|
|
\[ {}\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.043 |
|
|
\[ {}\left (x^{2}+x \right ) y^{\prime \prime }+3 y^{\prime }-6 x y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.754 |
|
|
\[ {}\sin \left (x \right ) y^{\prime \prime }+\cos \left (x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.543 |
|
|
\[ {}x y^{\prime \prime }-2 y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.696 |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
[_Lienard] |
✓ |
✓ |
0.826 |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.016 |
|
|
\[ {}x \left (-x^{2}+2\right ) y^{\prime \prime }-\left (x^{2}+4 x +2\right ) \left (\left (1-x \right ) y^{\prime }+y\right ) = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.262 |
|
|
\[ {}2 x^{2} \left (2-x \right ) y^{\prime \prime }-x \left (4-x \right ) y^{\prime }+\left (-x +3\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.068 |
|
|
\[ {}x^{2} \left (1-x \right ) y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.832 |
|
|
\[ {}x y^{\prime \prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.671 |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }-3 x y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.03 |
|
|
\[ {}\sin \left (x \right ) y^{\prime \prime }-2 \cos \left (x \right ) y^{\prime }-\sin \left (x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.325 |
|
|
\[ {}x y^{\prime \prime }-2 y^{\prime }+y = \cos \left (x \right ) \] |
1 |
0 |
0 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
3.997 |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.357 |
|
|
\[ {}x y^{\prime \prime }+x^{3} y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.458 |
|
|
\[ {}x y^{\prime \prime }+x y^{\prime }-{\mathrm e}^{x} y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.292 |
|
|
\[ {}x y^{\prime \prime }+x^{5} y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.616 |
|
|
\[ {}\sin \left (x \right ) y^{\prime \prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.315 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (x -\frac {3}{4}\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.823 |
|
|
\[ {}x \left (x +3\right )^{2} y^{\prime \prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.356 |
|
|
\[ {}y^{\prime \prime }-\frac {y^{\prime }}{x}+\frac {y}{\left (-1+x \right )^{3}} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.741 |
|
|
\[ {}\left (x^{3}+4 x \right ) y^{\prime \prime }-2 x y^{\prime }+6 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.747 |
|
|
\[ {}x \left (x^{2}+1\right )^{2} y^{\prime \prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.371 |
|
|
\[ {}x y^{\prime \prime }+\left (x +3\right ) y^{\prime }+7 x^{2} y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.582 |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }-x y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.832 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.994 |
|
|
\[ {}x y^{\prime \prime }-x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[_Laguerre, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.98 |
|
|
\[ {}y^{\prime \prime }+\frac {3 y^{\prime }}{x}-2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.066 |
|
|
\[ {}x y^{\prime \prime }+\left (x -6\right ) y^{\prime }-3 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.284 |
|
|
\[ {}x \left (-1+x \right ) y^{\prime \prime }+3 y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.985 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y = 0 \] |
1 |
1 |
1 |
[_Bessel] |
✓ |
✓ |
2.938 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-25\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.084 |
|
|
\[ {}y^{\prime }+x y^{\prime \prime }+\left (x -\frac {4}{x}\right ) y = 0 \] |
1 |
1 |
1 |
[_Bessel] |
✓ |
✓ |
2.836 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (9 x^{2}-4\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.777 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.009 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}-64\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.53 |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
3.089 |
|
|
\[ {}x y^{\prime \prime }+3 y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
[_Lienard] |
✓ |
✓ |
2.964 |
|
|
\[ {}x y^{\prime \prime }-y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
[_Lienard] |
✓ |
✓ |
2.952 |
|
|
\[ {}x y^{\prime \prime }-5 y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
[_Lienard] |
✓ |
✓ |
2.888 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.863 |
|
|
\[ {}x y^{\prime \prime }+3 y^{\prime }+x^{3} y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.922 |
|
|
\[ {}9 x^{2} y^{\prime \prime }+9 x y^{\prime }+\left (x^{6}-36\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.916 |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.931 |
|
|
\[ {}16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.993 |
|
|
\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (16 x^{4}+3\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.965 |
|
|
\[ {}x y^{\prime \prime }-\left (2+x \right ) y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[_Laguerre] |
✓ |
✓ |
0.957 |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
[_Lienard] |
✓ |
✓ |
0.807 |
|
|
\[ {}x y^{\prime \prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.934 |
|
|
\[ {}x y^{\prime \prime }+2 x^{3} y^{\prime }+\left (x^{2}-2\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.98 |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }+4 x y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.793 |
|
|
\[ {}x y^{\prime \prime }+\left (2-2 x \right ) y^{\prime }+\left (-2+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.082 |
|
|
\[ {}x^{2} y^{\prime \prime }+6 x y^{\prime }+\left (4 x^{2}+6\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.957 |
|
|
\[ {}3 t \left (t +1\right ) y^{\prime \prime }+t y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.411 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (x^{2}-1\right ) y}{4} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.963 |
|
|
\[ {}x y^{\prime \prime }+5 y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
[_Lienard] |
✓ |
✓ |
2.921 |
|
|
\[ {}x y^{\prime \prime }-5 y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
[_Lienard] |
✓ |
✓ |
2.754 |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (x^{2}-2\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.975 |
|
|
\[ {}x y^{\prime \prime }-\left (1+x \right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[_Laguerre] |
✓ |
✓ |
0.92 |
|
|
\[ {}x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.921 |
|
|
\[ {}y^{\prime \prime }+\frac {y}{4 x} = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.878 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.196 |
|
|
\[ {}3 x^{2} y^{\prime \prime }+x^{6} y^{\prime }+2 x y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.418 |
|
|
\[ {}x y^{\prime \prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
4.078 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.151 |
|
|
\[ {}4 x^{2} y^{\prime \prime }-4 x \,{\mathrm e}^{x} y^{\prime }+3 \cos \left (x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
56.942 |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.217 |
|
|
\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (-x^{3}+3\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.227 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x \left (1+x \right ) y^{\prime }+2 \left (1+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.293 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y = 0 \] |
1 |
1 |
1 |
[_Bessel] |
✓ |
✓ |
4.095 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x^{2} y^{\prime }+\left (-2+4 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
4.155 |
|
|
\[ {}\left (1+3 x \right ) x y^{\prime \prime }-\left (1+x \right ) y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
9.423 |
|
|
\[ {}x^{2} y^{\prime \prime }+\sin \left (x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
8.851 |
|
|
\[ {}x^{3} y^{\prime \prime }+\left (-1+\cos \left (2 x \right )\right ) y^{\prime }+2 x y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
39.095 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+4 x y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
7.579 |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
[_Lienard] |
✓ |
✓ |
2.411 |
|
|
\[ {}x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.453 |
|
|
\[ {}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.519 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y = 0 \] |
1 |
1 |
1 |
[_Bessel] |
✓ |
✓ |
6.876 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.597 |
|
|
\[ {}x y^{\prime \prime }-4 y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
[_Lienard] |
✓ |
✓ |
3.286 |
|
|
\[ {}x \left (x +3\right )^{2} y^{\prime \prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.531 |
|
|
\[ {}y^{\prime \prime }-\frac {y^{\prime }}{x}+\frac {y}{\left (-1+x \right )^{3}} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
9.521 |
|
|
\[ {}\left (x^{3}+4 x \right ) y^{\prime \prime }-2 x y^{\prime }+6 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
11.376 |
|
|
\[ {}x \left (x^{2}+1\right )^{2} y^{\prime \prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
9.225 |
|
|
\[ {}x y^{\prime \prime }+\left (x +3\right ) y^{\prime }+7 x^{2} y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
11.715 |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }-x y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.204 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.059 |
|
|
\[ {}x y^{\prime \prime }-x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[_Laguerre, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
9.587 |
|
|
\[ {}y^{\prime \prime }+\frac {3 y^{\prime }}{x}-2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
8.763 |
|
|
\[ {}x y^{\prime \prime }+\left (x -6\right ) y^{\prime }-3 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.729 |
|
|
\[ {}x \left (-1+x \right ) y^{\prime \prime }+3 y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.42 |
|
|
\[ {}y^{\prime \prime }+\frac {2 y^{\prime }}{t}+\lambda y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.193 |
|
|
\[ {}x y^{\prime \prime }-\left (2+x \right ) y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[_Laguerre] |
✓ |
✓ |
1.625 |
|
|
\[ {}\left ({\mathrm e}^{x}-1-x \right ) y^{\prime \prime }+x y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.122 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.935 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }-\left (4 x^{2}+1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.307 |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x \left (-2+x \right ) y^{\prime }+2 \left (2-3 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.983 |
|
|
\[ {}x^{2} \left (2 x +1\right ) y^{\prime \prime }+2 x \left (6 x +1\right ) y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.066 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (3 x +2\right ) y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.859 |
|
|
\[ {}x y^{\prime \prime }-\left (x +3\right ) y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[_Laguerre] |
✓ |
✓ |
1.937 |
|
|
\[ {}x \left (1+x \right ) y^{\prime \prime }+\left (x +5\right ) y^{\prime }-4 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.132 |
|
|
\[ {}x \left (1+x \right ) y^{\prime \prime }+\left (x +5\right ) y^{\prime }-4 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.178 |
|
|
\[ {}x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.834 |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }-3 y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.644 |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }-3 y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.109 |
|
|
\[ {}x y^{\prime \prime }+\left (3 x +4\right ) y^{\prime }+3 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.885 |
|
|
\[ {}x y^{\prime \prime }-2 \left (2+x \right ) y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.036 |
|
|
\[ {}x y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.912 |
|
|
\[ {}x \left (x +3\right ) y^{\prime \prime }-9 y^{\prime }-6 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.949 |
|
|
\[ {}x \left (1-2 x \right ) y^{\prime \prime }-2 \left (2+x \right ) y^{\prime }+8 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.108 |
|
|
\[ {}x y^{\prime \prime }+\left (x^{3}-1\right ) y^{\prime }+x^{2} y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.567 |
|
|
\[ {}x^{2} \left (4 x -1\right ) y^{\prime \prime }+x \left (1+5 x \right ) y^{\prime }+3 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.217 |
|
|
\[ {}x y^{\prime \prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.102 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+\left (3+4 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.342 |
|
|
\[ {}2 x y^{\prime \prime }+6 y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.357 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+2 x \left (2-x \right ) y^{\prime }-\left (1+3 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.632 |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (6+x \right ) y^{\prime }+10 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.472 |
|
|
\[ {}x y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }+8 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.535 |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[_Jacobi] |
✓ |
✓ |
2.27 |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[_Jacobi] |
✓ |
✓ |
2.376 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y = 0 \] |
1 |
1 |
1 |
[_Bessel] |
✓ |
✓ |
2.136 |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+\left (8+5 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.368 |
|
|
\[ {}x y^{\prime \prime }+\left (-x +3\right ) y^{\prime }-5 y = 0 \] |
1 |
1 |
1 |
[_Laguerre] |
✓ |
✓ |
2.562 |
|
|
\[ {}9 x^{2} y^{\prime \prime }-15 x y^{\prime }+7 \left (1+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.523 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (1-2 x \right ) y^{\prime }-\left (1+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.598 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-\left (6 x^{2}-3 x +1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.129 |
|
|
\[ {}x y^{\prime \prime }+x y^{\prime }+\left (x^{4}+1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.507 |
|
|
\[ {}x y^{\prime \prime }-\left (2+x \right ) y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.366 |
|
|
\[ {}x y^{\prime \prime }-\left (2+x \right ) y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
[_Laguerre] |
✓ |
✓ |
2.484 |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.95 |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (x^{2}+3\right ) y^{\prime }+6 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.961 |
|
|
\[ {}x \left (-x^{2}+1\right ) y^{\prime \prime }-\left (x^{2}+7\right ) y^{\prime }+4 x y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.112 |
|
|
\[ {}4 x^{2} y^{\prime \prime }-2 x \left (2+x \right ) y^{\prime }+\left (x +3\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.056 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-\left (x +3\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.02 |
|
|
\[ {}x \left (-x^{2}+1\right ) y^{\prime \prime }+5 \left (-x^{2}+1\right ) y^{\prime }-4 x y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.937 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-\left (x^{2}+4\right ) y = 0 \] |
1 |
1 |
1 |
[[_Bessel, _modified]] |
✓ |
✓ |
2.235 |
|
|
\[ {}x \left (1-2 x \right ) y^{\prime \prime }-2 \left (2+x \right ) y^{\prime }+18 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.143 |
|
|
\[ {}x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.898 |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
[_Lienard] |
✓ |
✓ |
1.501 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.627 |
|
|
\[ {}x \left (-1+x \right ) y^{\prime \prime }+3 x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.53 |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.919 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.74 |
|
|
\[ {}\left (x^{2}-x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.196 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (x^{2}+6 x \right ) y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.009 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}-8\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.206 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-\left (x^{2}+\frac {5}{4}\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.864 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.55 |
|
|
\[ {}x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.73 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+4 x^{4} y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.769 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.93 |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (6+x \right ) y^{\prime }+10 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.208 |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
[_Lienard] |
✓ |
✓ |
1.28 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.358 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (x^{4}+x \right ) y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.565 |
|
|
\[ {}x y^{\prime \prime }-\left (x^{2}+2\right ) y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
[_Lienard] |
✓ |
✓ |
1.503 |
|
|
\[ {}x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.303 |
|
|
\[ {}\left (2 x^{2}-x \right ) y^{\prime \prime }+\left (2 x -2\right ) y^{\prime }+\left (-2 x^{2}+3 x -2\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.867 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+\frac {3 y}{4} = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.119 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (-1+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.758 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }-3 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.982 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+8 \left (x^{2}-1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.838 |
|
|
\[ {}x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\frac {3 y}{4} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.026 |
|
|
\[ {}2 x y^{\prime \prime }+6 y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
3.831 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}-3\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.7 |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }-3 x y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
4.221 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y = 0 \] |
1 |
1 |
1 |
[_Bessel] |
✓ |
✓ |
3.886 |
|
|
\[ {}x y^{\prime \prime }+4 y^{\prime }-x y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.228 |
|
|
\[ {}x \left (-1+x \right ) y^{\prime \prime }+3 x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.608 |
|
|
\[ {}\left (x^{2}-6 x \right ) y^{\prime \prime }+4 \left (x -3\right ) y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.237 |
|
|
\[ {}\left (-x^{4}+x^{3}\right ) y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+827 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.955 |
|
|
\[ {}\left (4 x^{2}-1\right ) y^{\prime \prime }+\left (4-\frac {2}{x}\right ) y^{\prime }+\frac {\left (-x^{2}+1\right ) y}{x^{2}+1} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.801 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.18 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (-4+4 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.79 |
|
|
\[ {}\left (-9 x^{4}+x^{2}\right ) y^{\prime \prime }-6 x y^{\prime }+10 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.319 |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (1-\frac {1}{x^{2}}\right ) y = 0 \] |
1 |
1 |
1 |
[_Bessel] |
✓ |
✓ |
2.846 |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+4 x y = 0 \] |
1 |
1 |
1 |
[_Laguerre] |
✓ |
✓ |
3.245 |
|
|
\[ {}\left (x -3\right ) y^{\prime \prime }+\left (x -3\right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.125 |
|
|
\[ {}y^{\prime \prime }+\frac {2 y^{\prime }}{2+x}+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.444 |
|
|
\[ {}\left (x -3\right )^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }-3 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.636 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (-x^{2}+2\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.257 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x^{2} y^{\prime }+\left (x^{2}-2\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.482 |
|
|
\[ {}x^{2} \left (2 x +1\right ) y^{\prime \prime }+x y^{\prime }+\left (4 x^{3}-4\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.866 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-\left (2 x +1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.799 |
|
|
\[ {}x y^{\prime \prime }+4 y^{\prime }+\frac {12 y}{\left (2+x \right )^{2}} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.595 |
|
|
\[ {}x y^{\prime \prime }+4 y^{\prime }+\frac {12 y}{\left (2+x \right )^{2}} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.553 |
|
|
\[ {}\left (x -3\right ) y^{\prime \prime }+\left (x -3\right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.032 |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+4 x y = 0 \] |
1 |
1 |
1 |
[_Laguerre] |
✓ |
✓ |
4.856 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (-4+4 x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.403 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (-1+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.704 |
|
|
\[ {}x y^{\prime \prime }+2 x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.007 |
|
|
\[ {}y^{\prime \prime }+\left (\frac {1}{2 x}-2\right ) y^{\prime }-\frac {35 y}{16 x^{2}} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.348 |
|
|
\[ {}x^{2} y^{\prime \prime }+7 x y^{\prime }-7 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.222 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.449 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (16 x^{2}-25\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.785 |
|
|
\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+\left (-2 x^{2}+7\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.89 |
|
|
|
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