|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.163 |
|
|
\[
{}\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.395 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.122 |
|
|
\[
{}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.090 |
|
|
\[
{}\left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.312 |
|
|
\[
{}x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.161 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.161 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.118 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}+3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.177 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }-\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.098 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x \left (x +1\right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.106 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x \left (x +2\right ) y^{\prime }+\left (x^{2}+4 x +6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.108 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (x^{2}+6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.167 |
|
|
\[
{}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.257 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 x \left (x +1\right ) y^{\prime }+\left (2 x +3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.130 |
|
|
\[
{}\left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.329 |
|
|
\[
{}\left (x +2\right ) y^{\prime \prime }+x y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.381 |
|
|
\[
{}x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (4+x \right ) y^{\prime }+\left (2-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.320 |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }-\left (4+6 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.323 |
|
|
\[
{}x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+4\right ) y^{\prime }+2 \left (-x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.451 |
|
|
\[
{}x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+2 x \left (x^{2}+5\right ) y^{\prime }+2 \left (-x^{2}+3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.495 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+6 x y^{\prime }+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.358 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.364 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }+20 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.367 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }-12 y = 0
\] |
[_Gegenbauer] |
✓ |
0.211 |
|
|
\[
{}\left (2 x^{2}+1\right ) y^{\prime \prime }+7 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.426 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-5 x y^{\prime }-4 y = 0
\] |
[_Gegenbauer] |
✓ |
0.329 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-10 x y^{\prime }+28 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.413 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.257 |
|
|
\[
{}\left (2 x^{2}+1\right ) y^{\prime \prime }-9 x y^{\prime }-6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.497 |
|
|
\[
{}\left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (-2+x \right ) y^{\prime }+36 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.675 |
|
|
\[
{}y^{\prime \prime }+\left (x -3\right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.385 |
|
|
\[
{}\left (x^{2}-8 x +14\right ) y^{\prime \prime }-8 \left (x -4\right ) y^{\prime }+20 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.342 |
|
|
\[
{}\left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (x +1\right ) y^{\prime }+60 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.691 |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime \prime }+7 x^{2} y^{\prime }+9 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.480 |
|
|
\[
{}\left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.252 |
|
|
\[
{}y^{\prime \prime }+x^{6} y^{\prime }+7 x^{5} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.500 |
|
|
\[
{}\left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
425.257 |
|
|
\[
{}y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.440 |
|
|
\[
{}\left (3 x +1\right ) y^{\prime \prime }+x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
30.487 |
|
|
\[
{}\left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.926 |
|
|
\[
{}\left (x +2\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.386 |
|
|
\[
{}\left (4+x \right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.379 |
|
|
\[
{}\left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (x +1\right ) y^{\prime }+8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.383 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.355 |
|
|
\[
{}\left (2 x^{2}+x +1\right ) y^{\prime \prime }+\left (1+7 x \right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.200 |
|
|
\[
{}\left (x +3\right ) y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-\left (2-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.197 |
|
|
\[
{}y^{\prime \prime }+3 x y^{\prime }+\left (2 x^{2}+4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.348 |
|
|
\[
{}\left (2+4 x \right ) y^{\prime \prime }-4 y^{\prime }-\left (6+4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.322 |
|
|
\[
{}y^{\prime \prime }-3 x y^{\prime }+\left (2 x^{2}+5\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.334 |
|
|
\[
{}2 y^{\prime \prime }+5 x y^{\prime }+\left (2 x^{2}+4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.214 |
|
|
\[
{}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.092 |
|
|
\[
{}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.089 |
|
|
\[
{}2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.210 |
|
|
\[
{}3 x^{2} y^{\prime \prime }+2 x \left (-2 x^{2}+x +1\right ) y^{\prime }+\left (-8 x^{2}+2 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.447 |
|
|
\[
{}12 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+35 x +11\right ) y^{\prime }-\left (-5 x^{2}-10 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.441 |
|
|
\[
{}x^{2} \left (10 x^{2}+x +5\right ) y^{\prime \prime }+x \left (48 x^{2}+3 x +4\right ) y^{\prime }+\left (36 x^{2}+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.154 |
|
|
\[
{}18 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (x^{2}+11 x +5\right ) y^{\prime }-\left (-5 x^{2}-2 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.428 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x \left (2 x +3\right ) y^{\prime }-\left (1-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.334 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x \left (x +5\right ) y^{\prime }-\left (2-3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.361 |
|
|
\[
{}3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.462 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (1-2 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.185 |
|
|
\[
{}3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (3 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.642 |
|
|
\[
{}2 x^{2} \left (x +3\right ) y^{\prime \prime }+x \left (1+5 x \right ) y^{\prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.374 |
|
|
\[
{}x^{2} \left (4+x \right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.696 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.315 |
|
|
\[
{}6 x^{2} y^{\prime \prime }+x \left (10-x \right ) y^{\prime }-\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.418 |
|
|
\[
{}x^{2} \left (4 x +3\right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }-\left (4 x +3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.404 |
|
|
\[
{}2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+11 x \right ) y^{\prime }-\left (1-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.203 |
|
|
\[
{}x^{2} \left (x +2\right ) y^{\prime \prime }+5 x \left (1-x \right ) y^{\prime }-\left (2-8 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.864 |
|
|
\[
{}8 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-13 x^{2}+1\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.434 |
|
|
\[
{}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-2 x \left (-x^{2}+2\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.398 |
|
|
\[
{}x \left (x^{2}+3\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-8 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.367 |
|
|
\[
{}4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+x \left (-19 x^{2}+7\right ) y^{\prime }-\left (14 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.428 |
|
|
\[
{}3 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+x \left (-11 x^{2}+1\right ) y^{\prime }+\left (-5 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.466 |
|
|
\[
{}2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }-x \left (-7 x^{2}+12\right ) y^{\prime }+\left (3 x^{2}+7\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.438 |
|
|
\[
{}2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (7 x^{2}+4\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.416 |
|
|
\[
{}2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+5 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-40 x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.542 |
|
|
\[
{}x \left (x^{2}+1\right ) y^{\prime \prime }+\left (7 x^{2}+4\right ) y^{\prime }+8 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.370 |
|
|
\[
{}2 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }-\left (-4 x^{2}+3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.420 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+3 x \left (x^{2}+3\right ) y^{\prime }-\left (-5 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.391 |
|
|
\[
{}6 x^{2} y^{\prime \prime }+x \left (6 x^{2}+1\right ) y^{\prime }+\left (9 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.444 |
|
|
\[
{}9 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+3\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.414 |
|
|
\[
{}4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.373 |
|
|
\[
{}8 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+2 x \left (34 x^{2}+5\right ) y^{\prime }-\left (-30 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.513 |
|
|
\[
{}2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.182 |
|
|
\[
{}6 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (50 x^{2}+1\right ) y^{\prime }+\left (30 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.198 |
|
|
\[
{}28 x^{2} \left (1-3 x \right ) y^{\prime \prime }-7 x \left (5+9 x \right ) y^{\prime }+7 \left (2+9 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.196 |
|
|
\[
{}8 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+2 x \left (-21 x^{2}+10\right ) y^{\prime }-\left (35 x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.197 |
|
|
\[
{}4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }-4 x \left (-3 x^{2}-3 x +1\right ) y^{\prime }+3 \left (x^{2}-x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.145 |
|
|
\[
{}3 x^{2} \left (x +1\right )^{2} y^{\prime \prime }-x \left (-11 x^{2}-10 x +1\right ) y^{\prime }+\left (5 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.191 |
|
|
\[
{}4 x^{2} \left (x^{2}+2 x +3\right ) y^{\prime \prime }-x \left (-15 x^{2}-14 x +3\right ) y^{\prime }+\left (7 x^{2}+3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.210 |
|
|
\[
{}x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.402 |
|
|
\[
{}2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.292 |
|
|
\[
{}x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-2 x \left (2 x^{2}+1\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.438 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (5-x \right ) y^{\prime }+\left (9-4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.507 |
|
|
\[
{}4 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+12 x^{2} \left (x +1\right ) y^{\prime }+\left (3 x^{2}+3 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.888 |
|
|
\[
{}x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }-x \left (-2 x^{2}-4 x +1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.970 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+3 x \left (-2 x^{2}+3 x +5\right ) y^{\prime }+\left (-14 x^{2}+12 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.599 |
|
|
\[
{}x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+14 x +5\right ) y^{\prime }+\left (12 x^{2}+18 x +4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.629 |
|