|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-2 x \left (2 x^{2}+1\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.876 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (5-x \right ) y^{\prime }+\left (9-4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.902 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+\left (-x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.954 |
|
|
\[
{}x^{2} \left (2 x^{2}+x +1\right ) y^{\prime \prime }+x \left (7 x^{2}+6 x +3\right ) y^{\prime }+\left (-3 x^{2}+6 x +1\right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.116 |
|
|
\[
{}x^{2} \left (x^{2}+2 x +1\right ) y^{\prime \prime }+x \left (4 x^{2}+3 x +1\right ) y^{\prime }-x \left (1-2 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.966 |
|
|
\[
{}4 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+12 x^{2} \left (x +1\right ) y^{\prime }+\left (3 x^{2}+3 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.123 |
|
|
\[
{}x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }-x \left (-2 x^{2}-4 x +1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.069 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+3 x \left (-2 x^{2}+3 x +5\right ) y^{\prime }+\left (-14 x^{2}+12 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.072 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x^{2}+x +1\right ) y^{\prime }+x \left (2-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.977 |
|
|
\[
{}x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+14 x +5\right ) y^{\prime }+\left (12 x^{2}+18 x +4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.001 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+2 x \left (x^{2}+x +4\right ) y^{\prime }+\left (3 x^{2}+5 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.130 |
|
|
\[
{}16 x^{2} y^{\prime \prime }+4 x \left (2 x^{2}+x +6\right ) y^{\prime }+\left (18 x^{2}+5 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.079 |
|
|
\[
{}9 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (-x^{2}+11 x +5\right ) y^{\prime }+\left (-7 x^{2}+16 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.070 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (1+4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.811 |
|
|
\[
{}36 x^{2} \left (1-2 x \right ) y^{\prime \prime }+24 x \left (1-9 x \right ) y^{\prime }+\left (1-70 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.974 |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (3-x \right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.856 |
|
|
\[
{}x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5-4 x \right ) y^{\prime }+\left (9-4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.828 |
|
|
\[
{}25 x^{2} y^{\prime \prime }+x \left (15+x \right ) y^{\prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.870 |
|
|
\[
{}2 x^{2} \left (x +2\right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (1-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.886 |
|
|
\[
{}x^{2} \left (9+4 x \right ) y^{\prime \prime }+3 y^{\prime } x +\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.980 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (3-2 x \right ) y^{\prime }+\left (4+3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.934 |
|
|
\[
{}x^{2} \left (1-4 x \right ) y^{\prime \prime }+3 x \left (1-6 x \right ) y^{\prime }+\left (1-12 x \right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.951 |
|
|
\[
{}x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (3+5 x \right ) y^{\prime }+\left (1-2 x \right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.891 |
|
|
\[
{}2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6-x \right ) y^{\prime }+\left (8-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.892 |
|
|
\[
{}x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (5+9 x \right ) y^{\prime }+\left (4+3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.064 |
|
|
\[
{}x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5+4 x \right ) y^{\prime }+\left (9+4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.037 |
|
|
\[
{}x^{2} \left (1+4 x \right ) y^{\prime \prime }-x \left (1-4 x \right ) y^{\prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.141 |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.027 |
|
|
\[
{}x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (7+x \right ) y^{\prime }+\left (9-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.993 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.823 |
|
|
\[
{}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-3 x \left (-x^{2}+1\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.833 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.763 |
|
|
\[
{}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.826 |
|
|
\[
{}2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+7 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.871 |
|
|
\[
{}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-4 x^{2}+1\right ) y^{\prime }+\left (2 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.834 |
|
|
\[
{}4 x^{2} \left (x^{2}+4\right ) y^{\prime \prime }+3 x \left (3 x^{2}+8\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.873 |
|
|
\[
{}3 x^{2} \left (x^{2}+3\right ) y^{\prime \prime }+x \left (11 x^{2}+3\right ) y^{\prime }+\left (5 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.891 |
|
|
\[
{}4 x^{2} \left (4 x^{2}+1\right ) y^{\prime \prime }+32 x^{3} y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.860 |
|
|
\[
{}9 x^{2} y^{\prime \prime }-3 x \left (-2 x^{2}+7\right ) y^{\prime }+\left (2 x^{2}+25\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.846 |
|
|
\[
{}x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (7 x^{2}+3\right ) y^{\prime }+\left (-3 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.885 |
|
|
\[
{}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }+\left (12 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.875 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.858 |
|
|
\[
{}x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-9 x^{2}+5\right ) y^{\prime }+\left (-3 x^{2}+4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.885 |
|
|
\[
{}x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (-x^{2}+14\right ) y^{\prime }+2 \left (x^{2}+9\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.898 |
|
|
\[
{}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (7 x^{2}+3\right ) y^{\prime }+\left (8 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.888 |
|
|
\[
{}x^{2} \left (1-2 x \right ) y^{\prime \prime }+3 y^{\prime } x +\left (1+4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.944 |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.768 |
|
|
\[
{}x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (2 x +1\right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.859 |
|
|
\[
{}4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x^{2} y^{\prime }+\left (1-5 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.995 |
|
|
\[
{}x^{2} \left (1-x \right ) y^{\prime \prime }-x \left (3-5 x \right ) y^{\prime }+\left (4-5 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.934 |
|
|
\[
{}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (9 x^{2}+1\right ) y^{\prime }+\left (25 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.878 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+3 x \left (-x^{2}+1\right ) y^{\prime }+\left (7 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.882 |
|
|
\[
{}x \left (x^{2}+1\right ) y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }-8 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.724 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+2 x \left (-x^{2}+4\right ) y^{\prime }+\left (7 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.805 |
|
|
\[
{}4 x^{2} \left (x +1\right ) y^{\prime \prime }+8 x^{2} y^{\prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.834 |
|
|
\[
{}9 x^{2} \left (x +3\right ) y^{\prime \prime }+3 x \left (3+7 x \right ) y^{\prime }+\left (3+4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.863 |
|
|
\[
{}x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (3 x^{2}+2\right ) y^{\prime }+\left (-x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.757 |
|
|
\[
{}16 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x \left (9 x^{2}+1\right ) y^{\prime }+\left (49 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.786 |
|
|
\[
{}x^{2} \left (4+3 x \right ) y^{\prime \prime }-x \left (4-3 x \right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.824 |
|
|
\[
{}4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }+8 x^{2} \left (2 x +3\right ) y^{\prime }+\left (9 x^{2}+3 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.895 |
|
|
\[
{}x^{2} \left (1-x \right )^{2} y^{\prime \prime }-x \left (-3 x^{2}+2 x +1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.857 |
|
|
\[
{}9 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+7 x +1\right ) y^{\prime }+\left (25 x^{2}+4 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.892 |
|
|
\[
{}2 x^{2} \left (x +2\right ) y^{\prime \prime }-x \left (4-7 x \right ) y^{\prime }-\left (5-3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.529 |
|
|
\[
{}x^{2} \left (1-2 x \right ) y^{\prime \prime }+x \left (8-9 x \right ) y^{\prime }+\left (6-3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.055 |
|
|
\[
{}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (10 x^{2}+3\right ) y^{\prime }-\left (-14 x^{2}+15\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.489 |
|
|
\[
{}x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-13 x^{2}+7\right ) y^{\prime }-14 x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.928 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +\left (3+4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.256 |
|
|
\[
{}x y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.109 |
|
|
\[
{}4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }-\left (1+3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.369 |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.248 |
|
|
\[
{}2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+21 x \right ) y^{\prime }-\left (1-9 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.502 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x +2\right ) y^{\prime }-\left (2-3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.276 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 y^{\prime } x -\left (9-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.264 |
|
|
\[
{}x^{2} y^{\prime \prime }+10 y^{\prime } x +\left (14+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.241 |
|
|
\[
{}4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (3+8 x \right ) y^{\prime }-\left (5-49 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.513 |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (3+10 x \right ) y^{\prime }+30 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.322 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-3 \left (x +3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.306 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (1-2 x \right ) y^{\prime }-\left (x +4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.389 |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }-4 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.861 |
|
|
\[
{}x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (9+13 x \right ) y^{\prime }+\left (7+5 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.264 |
|
|
\[
{}4 x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (4-x \right ) y^{\prime }-\left (7+5 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.082 |
|
|
\[
{}3 x^{2} \left (x +3\right ) y^{\prime \prime }-x \left (15+x \right ) y^{\prime }-20 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.050 |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (1-10 x \right ) y^{\prime }-\left (9-10 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.141 |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }+3 x^{2} y^{\prime }-\left (6-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.032 |
|
|
\[
{}x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (3+14 x \right ) y^{\prime }+\left (6+100 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.033 |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6+11 x \right ) y^{\prime }+\left (6+32 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.044 |
|
|
\[
{}4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (1+4 x \right ) y^{\prime }-\left (49+27 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.127 |
|
|
\[
{}x^{2} \left (2 x +1\right ) y^{\prime \prime }-x \left (9+8 x \right ) y^{\prime }-12 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.444 |
|
|
\[
{}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+7\right ) y^{\prime }+12 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.381 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (-x^{2}+7\right ) y^{\prime }+12 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.239 |
|
|
\[
{}x y^{\prime \prime }-5 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
1.143 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (2 x^{2}+1\right ) y^{\prime }-\left (-10 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.367 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x -\left (-x^{2}+3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.197 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+2 x \left (x^{2}+8\right ) y^{\prime }+\left (3 x^{2}+5\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.319 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x^{2}+1\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.207 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (-2 x^{2}+1\right ) y^{\prime }-4 \left (2 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.252 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+8 y^{\prime } x -\left (-x^{2}+35\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.266 |
|
|
\[
{}9 x^{2} y^{\prime \prime }-3 x \left (2 x^{2}+11\right ) y^{\prime }+\left (10 x^{2}+13\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.435 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (-2 x^{2}+1\right ) y^{\prime }-4 \left (-x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.322 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (-3 x^{2}+1\right ) y^{\prime }-4 \left (-3 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.295 |
|