|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left (2 x +1\right ) \left (y^{\prime }+y^{2}\right )-2 y-2 x -3 = 0
\] |
[_rational, _Riccati] |
✓ |
2.704 |
|
|
\[
{}\left (3 x -1\right ) \left (y^{\prime }+y^{2}\right )-\left (3 x +2\right ) y-6 x +8 = 0
\] |
[_rational, _Riccati] |
✓ |
3.010 |
|
|
\[
{}x^{2} \left (y^{\prime }+y^{2}\right )+x y+x^{2}-\frac {1}{4} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
1.668 |
|
|
\[
{}x^{2} \left (y^{\prime }+y^{2}\right )-7 x y+7 = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
2.608 |
|
|
\[
{}y^{\prime \prime }+9 y = \tan \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.243 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (2 x \right ) \sec \left (2 x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.410 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = \frac {4}{1+{\mathrm e}^{-x}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.150 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = 3 \,{\mathrm e}^{x} \sec \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.989 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 14 x^{{3}/{2}} {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.477 |
|
|
\[
{}y^{\prime \prime }-y = \frac {4 \,{\mathrm e}^{-x}}{1-{\mathrm e}^{-2 x}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.514 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = 2 x^{2}+2
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.854 |
|
|
\[
{}x y^{\prime \prime }+\left (2-2 x \right ) y^{\prime }+\left (x -2\right ) y = {\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.939 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 4 \sqrt {x}\, {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.983 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y = 4 \,{\mathrm e}^{-x \left (x +2\right )}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.879 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = x^{{5}/{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.832 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y = 2 x^{4} \sin \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
7.756 |
|
|
\[
{}\left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y = \left (2 x +1\right )^{2} {\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.249 |
|
|
\[
{}2 x y^{\prime \prime }+2 y^{\prime }+2 y = \sin \left (\sqrt {x}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.960 |
|
|
\[
{}x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y = 6 x^{3} {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.050 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (2 a -1\right ) x y^{\prime }+a^{2} y = x^{a +1}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.843 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y = x^{3} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.755 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }-4 x^{3} y = 8 x^{5}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
7.910 |
|
|
\[
{}\sin \left (x \right ) y^{\prime \prime }+\left (2 \sin \left (x \right )-\cos \left (x \right )\right ) y^{\prime }+\left (\sin \left (x \right )-\cos \left (x \right )\right ) y = {\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
2.491 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y = 8 x^{{5}/{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.835 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}+3\right ) y = x^{{7}/{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.933 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x -\left (x^{2}-2\right ) y = 3 x^{4}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.709 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x \left (x +1\right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y = x^{3} {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.034 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x -3 y = x^{{3}/{2}}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.683 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x +4\right ) y^{\prime }+2 \left (x +3\right ) y = x^{4} {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.611 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x \left (x +2\right ) y^{\prime }+\left (x^{2}+4 x +6\right ) y = 2 x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.855 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (x^{2}+6\right ) y = x^{4}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.719 |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 2 \left (x -1\right )^{2} {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.552 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 x \left (x +1\right ) y^{\prime }+\left (2 x +3\right ) y = x^{{5}/{2}} {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.597 |
|
|
\[
{}\left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y = \left (3 x -1\right )^{2} {\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.562 |
|
|
\[
{}\left (x -1\right )^{2} y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+2 y = \left (x -1\right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.819 |
|
|
\[
{}\left (x -1\right )^{2} y^{\prime \prime }-\left (x^{2}-1\right ) y^{\prime }+\left (x +1\right ) y = \left (x -1\right )^{3} {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.621 |
|
|
\[
{}\left (x -1\right )^{2} y^{\prime \prime }+4 y^{\prime } x +2 y = 2 x
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.755 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y = -2 x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.942 |
|
|
\[
{}\left (x +1\right ) \left (2 x +3\right ) y^{\prime \prime }+2 \left (x +2\right ) y^{\prime }-2 y = \left (2 x +3\right )^{2}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.121 |
|
|
\[
{}\left (x +2\right ) y^{\prime \prime }+y^{\prime } x +3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.626 |
|
|
\[
{}\left (3 x^{2}+1\right ) y^{\prime \prime }+3 x^{2} y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.663 |
|
|
\[
{}\left (2 x^{2}+1\right ) y^{\prime \prime }+\left (2-3 x \right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.671 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+\left (2-x \right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.665 |
|
|
\[
{}\left (3 x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.616 |
|
|
\[
{}x y^{\prime \prime }+\left (4+2 x \right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.710 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -3 x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.699 |
|
|
\[
{}\left (2-x \right ) y^{\prime \prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.582 |
|
|
\[
{}\left (x +1\right ) y^{\prime \prime }+2 \left (x -1\right )^{2} y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.666 |
|
|
\[
{}x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (2-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.376 |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }-\left (4+6 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.305 |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (-x^{2}-6 x +1\right ) y^{\prime }+\left (x^{2}+6 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.939 |
|
|
\[
{}x^{2} \left (1+3 x \right ) y^{\prime \prime }+x \left (x^{2}+12 x +2\right ) y^{\prime }+2 x \left (x +3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.890 |
|
|
\[
{}x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+4\right ) y^{\prime }+2 \left (-x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.948 |
|
|
\[
{}x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+2 x \left (x^{2}+5\right ) y^{\prime }+2 \left (-x^{2}+3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.401 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+6 y^{\prime } x +6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.618 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.581 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-8 y^{\prime } x +20 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.632 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-8 y^{\prime } x -12 y = 0
\] |
[_Gegenbauer] |
✓ |
0.612 |
|
|
\[
{}\left (2 x^{2}+1\right ) y^{\prime \prime }+7 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.615 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x +\frac {y}{4} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.611 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-5 y^{\prime } x -4 y = 0
\] |
[_Gegenbauer] |
✓ |
0.610 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-10 y^{\prime } x +28 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.610 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.516 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } x +3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.566 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.600 |
|
|
\[
{}\left (2 x^{2}+1\right ) y^{\prime \prime }-9 y^{\prime } x -6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.624 |
|
|
\[
{}\left (8 x^{2}+1\right ) y^{\prime \prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.599 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.606 |
|
|
\[
{}y^{\prime \prime }-\left (x -3\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.582 |
|
|
\[
{}\left (2 x^{2}-4 x +1\right ) y^{\prime \prime }+10 \left (x -1\right ) y^{\prime }+6 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.654 |
|
|
\[
{}\left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (x -2\right ) y^{\prime }+36 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.680 |
|
|
\[
{}\left (3 x^{2}+6 x +5\right ) y^{\prime \prime }+9 \left (x +1\right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.662 |
|
|
\[
{}\left (x^{2}-4\right ) y^{\prime \prime }-y^{\prime } x -3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.608 |
|
|
\[
{}y^{\prime \prime }+\left (x -3\right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.546 |
|
|
\[
{}\left (3 x^{2}-6 x +5\right ) y^{\prime \prime }+\left (x -1\right ) y^{\prime }+12 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.655 |
|
|
\[
{}\left (4 x^{2}-24 x +37\right ) y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.631 |
|
|
\[
{}\left (x^{2}-8 x +14\right ) y^{\prime \prime }-8 \left (x -4\right ) y^{\prime }+20 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.633 |
|
|
\[
{}\left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (x +1\right ) y^{\prime }+60 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.647 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.605 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +2 \alpha y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.594 |
|
|
\[
{}y^{\prime \prime }-x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.471 |
|
|
\[
{}\left (-2 x^{3}+1\right ) y^{\prime \prime }-10 x^{2} y^{\prime }-8 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.641 |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime \prime }+7 x^{2} y^{\prime }+9 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.614 |
|
|
\[
{}\left (-2 x^{3}+1\right ) y^{\prime \prime }+6 x^{2} y^{\prime }+24 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.622 |
|
|
\[
{}\left (-x^{3}+1\right ) y^{\prime \prime }+15 x^{2} y^{\prime }-36 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.637 |
|
|
\[
{}\left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.639 |
|
|
\[
{}y^{\prime \prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.465 |
|
|
\[
{}y^{\prime \prime }+x^{6} y^{\prime }+7 x^{5} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.554 |
|
|
\[
{}\left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.566 |
|
|
\[
{}\left (-x^{6}+1\right ) y^{\prime \prime }-12 x^{5} y^{\prime }-30 x^{4} y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.606 |
|
|
\[
{}y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.556 |
|
|
\[
{}\left (1+3 x \right ) y^{\prime \prime }+y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.631 |
|
|
\[
{}\left (2 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+8 x \right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.663 |
|
|
\[
{}\left (-2 x^{2}+1\right ) y^{\prime \prime }+\left (2-6 x \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.664 |
|
|
\[
{}\left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.684 |
|
|
\[
{}\left (x +2\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.633 |
|
|
\[
{}\left (x^{2}+3 x +3\right ) y^{\prime \prime }+\left (6+4 x \right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.685 |
|
|
\[
{}\left (x +4\right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.613 |
|
|
\[
{}\left (2 x^{2}-3 x +2\right ) y^{\prime \prime }-\left (4-6 x \right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.735 |
|
|
\[
{}\left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (x +1\right ) y^{\prime }+8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.698 |
|