|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.375 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } x +4 y = 0
\] |
[_erf] |
✓ |
0.500 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.405 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-2 y x = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
3.385 |
|
|
\[
{}y^{\prime \prime }+y x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.323 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.466 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-3 y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.454 |
|
|
\[
{}y^{\prime \prime }+2 x^{2} y^{\prime }+2 y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.461 |
|
|
\[
{}\left (x^{2}-3\right ) y^{\prime \prime }-3 y^{\prime } x -5 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.586 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.520 |
|
|
\[
{}\left (-4 x^{2}+1\right ) y^{\prime \prime }-20 y^{\prime } x -16 y = 0
\] |
[_Gegenbauer] |
✓ |
0.592 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y = 0
\] |
[_Gegenbauer] |
✓ |
0.395 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+4 y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.573 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.593 |
|
|
\[
{}y^{\prime \prime }-y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.681 |
|
|
\[
{}x y^{\prime \prime }-\left (x -1\right ) y^{\prime }-y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.792 |
|
|
\[
{}\left (2 x^{2}+1\right ) y^{\prime \prime }+7 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.513 |
|
|
\[
{}4 y^{\prime \prime }+y^{\prime } x +4 y = 0
\] |
[_Lienard] |
✓ |
0.360 |
|
|
\[
{}y^{\prime \prime }+2 x^{2} y^{\prime }+y x = 2 \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.523 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x -4 y = 6 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.479 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{1-x}+y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.602 |
|
|
\[
{}x^{2} y^{\prime \prime }+\frac {x y^{\prime }}{\left (-x^{2}+1\right )^{2}}+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.648 |
|
|
\[
{}\left (x -2\right )^{2} y^{\prime \prime }+\left (x -2\right ) {\mathrm e}^{x} y^{\prime }+\frac {4 y}{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.609 |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x \left (x -3\right )}-\frac {y}{x^{3} \left (x +3\right )} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.157 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-7 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.020 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+x \,{\mathrm e}^{x} y^{\prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.111 |
|
|
\[
{}4 x y^{\prime \prime }-y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
5.574 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+5 \,{\mathrm e}^{2 x} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.988 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+3 y^{\prime } x +y x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.852 |
|
|
\[
{}6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.850 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.971 |
|
|
\[
{}2 x y^{\prime \prime }+y^{\prime }-2 y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.598 |
|
|
\[
{}3 x^{2} y^{\prime \prime }-x \left (x +8\right ) y^{\prime }+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.845 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+2 \left (4 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.875 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-\left (5+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.027 |
|
|
\[
{}3 x^{2} y^{\prime \prime }+x \left (7+3 x \right ) y^{\prime }+\left (1+6 x \right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.823 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (1-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.658 |
|
|
\[
{}3 x^{2} y^{\prime \prime }+x \left (3 x^{2}+1\right ) y^{\prime }-2 y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.814 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (2 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.767 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (1-2 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.724 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.767 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (3-x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.701 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -\left (x +4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.604 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (-x^{2}+x \right ) y^{\prime }+\left (x^{3}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.306 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (2 \sqrt {5}-1\right ) x y^{\prime }+\left (\frac {19}{4}-3 x^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.164 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (-2 x^{5}+9 x \right ) y^{\prime }+\left (10 x^{4}+5 x^{2}+25\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.797 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (4 x +\frac {1}{2} x^{2}-\frac {1}{3} x^{3}\right ) y^{\prime }-\frac {7 y}{4} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
5.807 |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+y x = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.588 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+\left (4-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.668 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.728 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \cos \left (x \right ) y^{\prime }-2 y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.168 |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.792 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x -\frac {3}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.867 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (2 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.704 |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{3} y^{\prime }-\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
5.966 |
|
|
\[
{}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+7 x \,{\mathrm e}^{x} y^{\prime }+9 \left (1+\tan \left (x \right )\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.210 |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.283 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (1-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.818 |
|
|
\[
{}x y^{\prime \prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
3.047 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x^{2}+6\right ) y^{\prime }+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.873 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.846 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (1-4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
19.062 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.736 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.753 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.692 |
|
|
\[
{}x^{2} y^{\prime \prime }-x^{2} y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.865 |
|
|
\[
{}x^{2} y^{\prime \prime }-x^{2} y^{\prime }-\left (2+3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
6.937 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.740 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.902 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x \left (x +2\right ) y^{\prime }+2 \left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.974 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+\left (1-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.700 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }+\left (4 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.919 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-\left (3+4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.809 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[_Laguerre, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.757 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.866 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {9}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.834 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+y x = 0
\] |
[_Lienard] |
✓ |
2.739 |
|
|
\[
{}y^{\prime \prime }+y x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.306 |
|
|
\[
{}y^{\prime \prime }-x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.329 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-6 y^{\prime } x -4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.541 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.764 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+y x = 0
\] |
[_Lienard] |
✓ |
0.718 |
|
|
\[
{}2 x y^{\prime \prime }+5 \left (1-2 x \right ) y^{\prime }-5 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
5.096 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+y x = 0
\] |
[_Lienard] |
✓ |
0.563 |
|
|
\[
{}\left (4 x^{2}+1\right ) y^{\prime \prime }-8 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.447 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.766 |
|
|
\[
{}4 x y^{\prime \prime }+3 y^{\prime }+3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.895 |
|
|
\[
{}x^{2} y^{\prime \prime }+\frac {3 y^{\prime } x}{2}-\frac {\left (x +1\right ) y}{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.875 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (2-x \right ) y^{\prime }+\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
7.207 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 \left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.737 |
|
|
\[
{}y^{\prime \prime }+\left (1-\frac {3}{4 x^{2}}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.648 |
|
|
\[
{}5 y x +4 y^{2}+1+\left (x^{2}+2 y x \right ) y^{\prime } = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.471 |
|
|
\[
{}2 x \tan \left (y\right )+\left (x -x^{2} \tan \left (y\right )\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
7.567 |
|
|
\[
{}y^{2} \left (x^{2}+1\right )+y+\left (2 y x +1\right ) y^{\prime } = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.684 |
|
|
\[
{}4 x y^{2}+6 y+\left (5 x^{2} y+8 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
11.390 |
|
|
\[
{}5 x +2 y+1+\left (2 x +y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
6.603 |
|
|
\[
{}3 x -y+1-\left (6 x -2 y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
7.389 |
|
|
\[
{}x -2 y-3+\left (2 x +y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.012 |
|
|
\[
{}6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
15.507 |
|
|
\[
{}3 x -y-6+\left (x +y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
29.977 |
|