|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x^{2} y^{\prime \prime }+2 x f \left (x \right ) y^{\prime }+\left (f^{\prime }\left (x \right ) x +f \left (x \right )^{2}-f \left (x \right )+a \,x^{2}+b x +c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.039 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x^{2} f \left (x \right ) y^{\prime }+\left (x^{2} \left (f^{\prime }\left (x \right )+f \left (x \right )^{2}+a \right )-v \left (v -1\right )\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.077 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x -2 f \left (x \right ) x^{2}\right ) y^{\prime }+\left (x^{2} \left (1+f \left (x \right )^{2}-f^{\prime }\left (x \right )\right )-f \left (x \right ) x -v^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.050 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.652 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-9 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.594 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+a y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.157 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.834 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-v \left (v -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.007 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.209 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+3 x y^{\prime }+a y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.286 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y-2 \cos \left (x \right )+2 x = 0
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.616 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+a x y^{\prime }+\left (a -2\right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.697 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-v \left (v +1\right ) y = 0
\] |
[_Gegenbauer] |
✗ |
0.563 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-n \left (n +1\right ) y+\frac {d}{d x}\operatorname {LegendreP}\left (n , x\right ) = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.649 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime }+2 = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.408 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime }+a y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.416 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime }+f \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.451 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.099 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }-a = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.059 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }-l y = 0
\] |
[_Gegenbauer] |
✗ |
0.899 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }-v \left (v +1\right ) y = 0
\] |
[_Gegenbauer] |
✗ |
0.969 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }-\left (v +2\right ) \left (v -1\right ) y = 0
\] |
[_Gegenbauer] |
✗ |
586.521 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-\left (3 x +1\right ) y^{\prime }-\left (x^{2}-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.780 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.808 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+2 \left (n +1\right ) x y^{\prime }-\left (v +n +1\right ) \left (v -n \right ) y = 0
\] |
[_Gegenbauer] |
✗ |
1.349 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-2 \left (n -1\right ) x y^{\prime }-\left (v -n +1\right ) \left (v +n \right ) y = 0
\] |
[_Gegenbauer] |
✗ |
1.344 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-2 \left (v -1\right ) x y^{\prime }-2 v y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.726 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+2 a x y^{\prime }+a \left (a -1\right ) y = 0
\] |
[_Gegenbauer] |
✓ |
2.801 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+a x y^{\prime }+\left (b \,x^{2}+c x +d \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.260 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.268 |
|
|
\[
{}\left (-a^{2}+x^{2}\right ) y^{\prime \prime }+8 x y^{\prime }+12 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.207 |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }-\left (x -1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.236 |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.237 |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+\left (2+3 x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.362 |
|
|
\[
{}\left (x^{2}+x -2\right ) y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }-\left (6 x^{2}+7 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.552 |
|
|
\[
{}x \left (x -1\right ) y^{\prime \prime }+a y^{\prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.399 |
|
|
\[
{}x \left (x -1\right ) y^{\prime \prime }+\left (2 x -1\right ) y^{\prime }-v \left (v +1\right ) y = 0
\] |
[_Jacobi] |
✗ |
0.888 |
|
|
\[
{}x \left (x -1\right ) y^{\prime \prime }+\left (\left (a +1\right ) x +b \right ) y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.341 |
|
|
\[
{}x \left (x -1\right ) y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c y = 0
\] |
[_Jacobi] |
✗ |
1.344 |
|
|
\[
{}x \left (x -1\right ) y^{\prime \prime }+\left (\left (a +1\right ) x +b \right ) y^{\prime }-l y = 0
\] |
[_Jacobi] |
✗ |
1.388 |
|
|
\[
{}x \left (x -1\right ) y^{\prime \prime }+\left (\left (\operatorname {a1} +\operatorname {b1} +1\right ) x -\operatorname {d1} \right ) y^{\prime }+\operatorname {a1} \operatorname {b1} \operatorname {d1} = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.443 |
|
|
\[
{}x \left (x +2\right ) y^{\prime \prime }+2 \left (n +1+\left (n +1-2 l \right ) x -l \,x^{2}\right ) y^{\prime }+\left (2 l \left (p -n -1\right ) x +2 p l +m \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.554 |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime \prime }+\left (x^{2}+x -1\right ) y^{\prime }-\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.716 |
|
|
\[
{}x \left (x +3\right ) y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y-\left (20 x +30\right ) \left (x^{2}+3 x \right )^{{7}/{3}} = 0
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
3.136 |
|
|
\[
{}\left (x^{2}+3 x +4\right ) y^{\prime \prime }+\left (x^{2}+x +1\right ) y^{\prime }-\left (2 x +3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.730 |
|
|
\[
{}\left (x -1\right ) \left (-2+x \right ) y^{\prime \prime }-\left (2 x -3\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
256.680 |
|
|
\[
{}\left (-2+x \right )^{2} y^{\prime \prime }-\left (-2+x \right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.088 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-\left (2 x^{2}+l -5 x \right ) y^{\prime }-\left (4 x -1\right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.881 |
|
|
\[
{}2 x \left (x -1\right ) y^{\prime \prime }+\left (2 x -1\right ) y^{\prime }+\left (a x +b \right ) y = 0
\] |
[_Jacobi] |
✗ |
0.711 |
|
|
\[
{}2 x \left (x -1\right ) y^{\prime \prime }+\left (\left (2 v +5\right ) x -2 v -3\right ) y^{\prime }+\left (v +1\right ) y = 0
\] |
[_Jacobi] |
✗ |
1.073 |
|
|
\[
{}\left (2 x^{2}+6 x +4\right ) y^{\prime \prime }+\left (10 x^{2}+21 x +8\right ) y^{\prime }+\left (12 x^{2}+17 x +8\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.490 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.785 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (4 a^{2} x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.966 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-\left (-4 k x +4 m^{2}+x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.680 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (-v^{2}+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.990 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (-x^{2}+2 \left (1-m +2 l \right ) x -m^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.908 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 x y^{\prime }-\left (4 x^{2}+1\right ) y-4 \sqrt {x^{3}}\, {\mathrm e}^{x} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.436 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 x y^{\prime }-\left (a \,x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.439 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 x y^{\prime }+f \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.138 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+5 x y^{\prime }-y-\ln \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.971 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+8 x y^{\prime }-\left (4 x^{2}+12 x +3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.443 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 x \left (2 x -1\right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.989 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 x^{3} y^{\prime }+\left (x^{2}+6\right ) \left (x^{2}-4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.905 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 x^{2} \ln \left (x \right ) y^{\prime }+\left (x^{2} \ln \left (x \right )^{2}+2 x -8\right ) y-4 x^{2} \sqrt {{\mathrm e}^{x} x^{-x}} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.546 |
|
|
\[
{}\left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }-12 y-3 x -1 = 0
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.463 |
|
|
\[
{}x \left (4 x -1\right ) y^{\prime \prime }+\left (\left (4 a +2\right ) x -a \right ) y^{\prime }+a \left (a -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.229 |
|
|
\[
{}\left (3 x -1\right )^{2} y^{\prime \prime }+3 \left (3 x -1\right ) y^{\prime }-9 y-\ln \left (3 x -1\right )^{2} = 0
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.995 |
|
|
\[
{}9 x \left (x -1\right ) y^{\prime \prime }+3 \left (2 x -1\right ) y^{\prime }-20 y = 0
\] |
[_Jacobi] |
✓ |
1.445 |
|
|
\[
{}16 x^{2} y^{\prime \prime }+\left (4 x +3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.342 |
|
|
\[
{}16 x^{2} y^{\prime \prime }+32 x y^{\prime }-\left (4 x +5\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
6.083 |
|
|
\[
{}\left (27 x^{2}+4\right ) y^{\prime \prime }+27 x y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.205 |
|
|
\[
{}48 x \left (x -1\right ) y^{\prime \prime }+\left (152 x -40\right ) y^{\prime }+53 y = 0
\] |
[_Jacobi] |
✗ |
1.348 |
|
|
\[
{}50 x \left (x -1\right ) y^{\prime \prime }+25 \left (2 x -1\right ) y^{\prime }-2 y = 0
\] |
[_Jacobi, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
3.143 |
|
|
\[
{}144 x \left (x -1\right ) y^{\prime \prime }+\left (120 x -48\right ) y^{\prime }+y = 0
\] |
[_Jacobi] |
✗ |
1.194 |
|
|
\[
{}144 x \left (x -1\right ) y^{\prime \prime }+\left (168 x -96\right ) y^{\prime }+y = 0
\] |
[_Jacobi] |
✗ |
0.998 |
|
|
\[
{}a \,x^{2} y^{\prime \prime }+b x y^{\prime }+\left (c \,x^{2}+d x +f \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.962 |
|
|
\[
{}\operatorname {a2} \,x^{2} y^{\prime \prime }+\left (\operatorname {a1} \,x^{2}+\operatorname {b1} x \right ) y^{\prime }+\left (\operatorname {a0} \,x^{2}+\operatorname {b0} x +\operatorname {c0} \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
2.445 |
|
|
\[
{}\left (a \,x^{2}+1\right ) y^{\prime \prime }+a x y^{\prime }+b y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
292.637 |
|
|
\[
{}\left (a^{2} x^{2}-1\right ) y^{\prime \prime }+2 a^{2} x y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.330 |
|
|
\[
{}\left (a^{2} x^{2}-1\right ) y^{\prime \prime }+2 a^{2} x y^{\prime }-2 a^{2} y = 0
\] |
[_Gegenbauer] |
✓ |
1.694 |
|
|
\[
{}\left (a \,x^{2}+b x \right ) y^{\prime \prime }+2 b y^{\prime }-2 a y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.510 |
|
|
\[
{}\operatorname {A2} \left (a x +b \right )^{2} y^{\prime \prime }+\operatorname {A1} \left (a x +b \right ) y^{\prime }+\operatorname {A0} \left (a x +b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.717 |
|
|
\[
{}\left (a \,x^{2}+b x +c \right ) y^{\prime \prime }+\left (d x +f \right ) y^{\prime }+g y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
3.797 |
|
|
\[
{}x^{3} y^{\prime \prime }+x y^{\prime }-\left (2 x +3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.454 |
|
|
\[
{}x^{3} y^{\prime \prime }+2 x y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.541 |
|
|
\[
{}x^{3} y^{\prime \prime }+x^{2} y^{\prime }+\left (a \,x^{2}+b x +a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.504 |
|
|
\[
{}x^{3} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.487 |
|
|
\[
{}x^{3} y^{\prime \prime }-x^{2} y^{\prime }+x y-\ln \left (x \right )^{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.705 |
|
|
\[
{}x^{3} y^{\prime \prime }-\left (x^{2}-1\right ) y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.678 |
|
|
\[
{}x^{3} y^{\prime \prime }+3 x^{2} y^{\prime }+x y-1 = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.596 |
|
|
\[
{}x \left (x^{2}+1\right ) y^{\prime \prime }+\left (2 x^{2}+1\right ) y^{\prime }-v \left (v +1\right ) x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.122 |
|
|
\[
{}x \left (x^{2}+1\right ) y^{\prime \prime }+2 \left (x^{2}-1\right ) y^{\prime }-2 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.308 |
|
|
\[
{}x \left (x^{2}+1\right ) y^{\prime \prime }+\left (2 \left (n +1\right ) x^{2}+2 n +1\right ) y^{\prime }-\left (v -n \right ) \left (v +n +1\right ) x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.398 |
|
|
\[
{}x \left (x^{2}+1\right ) y^{\prime \prime }-\left (2 \left (n -1\right ) x^{2}+2 n -1\right ) y^{\prime }+\left (v +n \right ) \left (-v +n -1\right ) x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.368 |
|
|
\[
{}x \left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime }+y a \,x^{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.529 |
|
|
\[
{}x \left (x^{2}-1\right ) y^{\prime \prime }+\left (x^{2}-1\right ) y^{\prime }-x y = 0
\] |
[[_elliptic, _class_II]] |
✗ |
107.424 |
|
|
\[
{}x \left (x^{2}-1\right ) y^{\prime \prime }+\left (3 x^{2}-1\right ) y^{\prime }+x y = 0
\] |
[[_elliptic, _class_I]] |
✗ |
0.976 |
|
|
\[
{}x \left (x^{2}-1\right ) y^{\prime \prime }+\left (a \,x^{2}+b \right ) y^{\prime }+c x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.562 |
|
|
\[
{}x \left (x^{2}+2\right ) y^{\prime \prime }-y^{\prime }-6 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.959 |
|
|
\[
{}x \left (x^{2}-2\right ) y^{\prime \prime }-\left (x^{3}+3 x^{2}-2 x -2\right ) y^{\prime }+\left (x^{2}+4 x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.633 |
|