# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
\[ {}\left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.381 |
|
\[ {}t y^{\prime \prime }+\left (t^{2}-1\right ) y^{\prime }+y t^{2} = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.844 |
|
\[ {}t^{2} y^{\prime \prime }-t \left (2+t \right ) y^{\prime }+\left (2+t \right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.886 |
|
\[ {}t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = 0 \] |
kovacic |
[_Laguerre] |
✓ |
✓ |
1.096 |
|
\[ {}\left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.308 |
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.7 |
|
\[ {}t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = 0 \] |
kovacic |
[_Laguerre] |
✓ |
✓ |
0.799 |
|
\[ {}\left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.897 |
|
\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.003 |
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.075 |
|
\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.171 |
|
\[ {}2 y^{\prime \prime }+x y^{\prime }+3 y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.338 |
|
\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.732 |
|
\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.928 |
|
\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.746 |
|
\[ {}\left (-x^{2}+4\right ) y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.282 |
|
\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.984 |
|
\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.933 |
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.819 |
|
\[ {}\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.815 |
|
\[ {}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.761 |
|
\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.763 |
|
\[ {}\left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.438 |
|
\[ {}x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (2+x \right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.756 |
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.677 |
|
\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.67 |
|
\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}+3\right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.876 |
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-\left (x^{2}-2\right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.85 |
|
\[ {}x^{2} y^{\prime \prime }-2 x \left (1+x \right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.971 |
|
\[ {}x^{2} y^{\prime \prime }-2 x \left (2+x \right ) y^{\prime }+\left (x^{2}+4 x +6\right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.032 |
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (x^{2}+6\right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.9 |
|
\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.918 |
|
\[ {}4 x^{2} y^{\prime \prime }-4 x \left (1+x \right ) y^{\prime }+\left (2 x +3\right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.901 |
|
\[ {}\left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.651 |
|
\[ {}\left (2+x \right ) y^{\prime \prime }+x y^{\prime }+3 y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.633 |
|
\[ {}x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (2-x \right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.134 |
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }-\left (4+6 x \right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.416 |
|
\[ {}x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+4\right ) y^{\prime }+2 \left (-x^{2}+1\right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.817 |
|
\[ {}x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+2 x \left (x^{2}+5\right ) y^{\prime }+2 \left (-x^{2}+3\right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.011 |
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+6 x y^{\prime }+6 y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.106 |
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.681 |
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }+20 y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.13 |
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }-12 y = 0 \] |
kovacic |
[_Gegenbauer] |
✓ |
✓ |
0.868 |
|
\[ {}\left (2 x^{2}+1\right ) y^{\prime \prime }+7 x y^{\prime }+2 y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.03 |
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-5 x y^{\prime }-4 y = 0 \] |
kovacic |
[_Gegenbauer] |
✓ |
✓ |
0.553 |
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-10 x y^{\prime }+28 y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.468 |
|
\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.367 |
|
\[ {}\left (2 x^{2}+1\right ) y^{\prime \prime }-9 x y^{\prime }-6 y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.878 |
|
\[ {}\left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (-2+x \right ) y^{\prime }+36 y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.151 |
|
\[ {}y^{\prime \prime }+\left (x -3\right ) y^{\prime }+3 y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.477 |
|
\[ {}\left (x^{2}-8 x +14\right ) y^{\prime \prime }-8 \left (x -4\right ) y^{\prime }+20 y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.839 |
|
\[ {}\left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (1+x \right ) y^{\prime }+60 y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.053 |
|
\[ {}\left (x^{3}+1\right ) y^{\prime \prime }+7 x^{2} y^{\prime }+9 x y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.331 |
|
\[ {}\left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
83.076 |
|
\[ {}y^{\prime \prime }+x^{6} y^{\prime }+7 x^{5} y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.924 |
|
\[ {}\left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
160.967 |
|
\[ {}y^{\prime \prime }+x^{5} y^{\prime }+6 y x^{4} = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.905 |
|
\[ {}\left (1+3 x \right ) y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
55.138 |
|
\[ {}\left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.248 |
|
\[ {}\left (2+x \right ) y^{\prime \prime }+\left (1+x \right ) y^{\prime }+3 y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.903 |
|
\[ {}\left (x +4\right ) y^{\prime \prime }+\left (2+x \right ) y^{\prime }+2 y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.878 |
|
\[ {}\left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (1+x \right ) y^{\prime }+8 y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.053 |
|
\[ {}x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.573 |
|
\[ {}\left (2 x^{2}+x +1\right ) y^{\prime \prime }+\left (1+7 x \right ) y^{\prime }+2 y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.07 |
|
\[ {}\left (x +3\right ) y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-\left (2-x \right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.766 |
|
\[ {}y^{\prime \prime }+3 x y^{\prime }+\left (2 x^{2}+4\right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.786 |
|
\[ {}\left (2+4 x \right ) y^{\prime \prime }-4 y^{\prime }-\left (6+4 x \right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.802 |
|
\[ {}y^{\prime \prime }-3 x y^{\prime }+\left (2 x^{2}+5\right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.749 |
|
\[ {}2 y^{\prime \prime }+5 x y^{\prime }+\left (2 x^{2}+4\right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.62 |
|
\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.428 |
|
\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.333 |
|
\[ {}2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.671 |
|
\[ {}3 x^{2} y^{\prime \prime }+2 x \left (-2 x^{2}+x +1\right ) y^{\prime }+\left (-8 x^{2}+2 x \right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.122 |
|
\[ {}12 x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (3 x^{2}+35 x +11\right ) y^{\prime }-\left (-5 x^{2}-10 x +1\right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.388 |
|
\[ {}x^{2} \left (10 x^{2}+x +5\right ) y^{\prime \prime }+x \left (48 x^{2}+3 x +4\right ) y^{\prime }+\left (36 x^{2}+x \right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
3.028 |
|
\[ {}18 x^{2} \left (1+x \right ) y^{\prime \prime }+3 x \left (x^{2}+11 x +5\right ) y^{\prime }-\left (-5 x^{2}-2 x +1\right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.391 |
|
\[ {}2 x^{2} y^{\prime \prime }+x \left (2 x +3\right ) y^{\prime }-\left (1-x \right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.907 |
|
\[ {}2 x^{2} y^{\prime \prime }+x \left (x +5\right ) y^{\prime }-\left (2-3 x \right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.968 |
|
\[ {}3 x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.091 |
|
\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (1-2 x \right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.727 |
|
\[ {}3 x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-\left (1+3 x \right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.275 |
|
\[ {}2 x^{2} \left (x +3\right ) y^{\prime \prime }+x \left (1+5 x \right ) y^{\prime }+y \left (1+x \right ) = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.286 |
|
\[ {}x^{2} \left (x +4\right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.541 |
|
\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y \left (1+x \right ) = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.772 |
|
\[ {}6 x^{2} y^{\prime \prime }+x \left (10-x \right ) y^{\prime }-\left (2+x \right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.209 |
|
\[ {}x^{2} \left (3+4 x \right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }-\left (3+4 x \right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.213 |
|
\[ {}2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+11 x \right ) y^{\prime }-\left (1-x \right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.952 |
|
\[ {}x^{2} \left (2+x \right ) y^{\prime \prime }+5 x \left (1-x \right ) y^{\prime }-\left (2-8 x \right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.171 |
|
\[ {}8 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-13 x^{2}+1\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.553 |
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-2 x \left (-x^{2}+2\right ) y^{\prime }+4 y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.059 |
|
\[ {}x \left (x^{2}+3\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-8 x y = 0 \] |
kovacic |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.099 |
|
\[ {}4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+x \left (-19 x^{2}+7\right ) y^{\prime }-\left (14 x^{2}+1\right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.785 |
|
\[ {}3 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+x \left (-11 x^{2}+1\right ) y^{\prime }+\left (-5 x^{2}+1\right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.487 |
|
\[ {}2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }-x \left (-7 x^{2}+12\right ) y^{\prime }+\left (3 x^{2}+7\right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.221 |
|
\[ {}2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (7 x^{2}+4\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.164 |
|
\[ {}2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+5 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-40 x^{2}+2\right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.838 |
|
\[ {}x \left (x^{2}+1\right ) y^{\prime \prime }+\left (7 x^{2}+4\right ) y^{\prime }+8 x y = 0 \] |
kovacic |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.987 |
|
\[ {}2 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }-\left (-4 x^{2}+3\right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.195 |
|
\[ {}9 x^{2} y^{\prime \prime }+3 x \left (x^{2}+3\right ) y^{\prime }-\left (-5 x^{2}+1\right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.014 |
|
\[ {}6 x^{2} y^{\prime \prime }+x \left (6 x^{2}+1\right ) y^{\prime }+\left (9 x^{2}+1\right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.312 |
|
|
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