|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}4 x -2 y y^{\prime }+{y^{\prime }}^{2} x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.488 |
|
|
\[
{}2 x^{2} y+{y^{\prime }}^{2} = x^{3} y^{\prime }
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.029 |
|
|
\[
{}y {y^{\prime }}^{2} = 3 x y^{\prime }+y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.950 |
|
|
\[
{}8 x +1 = y {y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
0.972 |
|
|
\[
{}y {y^{\prime }}^{2}+2 y^{\prime }+1 = 0
\] |
[_quadrature] |
✓ |
3.004 |
|
|
\[
{}\left (1+{y^{\prime }}^{2}\right ) x = \left (x +y\right ) y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
3.398 |
|
|
\[
{}x^{2}-3 y y^{\prime }+{y^{\prime }}^{2} x = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
3.790 |
|
|
\[
{}y+2 x y^{\prime } = {y^{\prime }}^{2} x
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.174 |
|
|
\[
{}x = {y^{\prime }}^{2}+y^{\prime }
\] |
[_quadrature] |
✓ |
0.190 |
|
|
\[
{}x = y-{y^{\prime }}^{3}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
0.497 |
|
|
\[
{}x +2 y y^{\prime } = {y^{\prime }}^{2} x
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
0.967 |
|
|
\[
{}4 x -2 y y^{\prime }+{y^{\prime }}^{2} x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.448 |
|
|
\[
{}x {y^{\prime }}^{3} = y y^{\prime }+1
\] |
[_dAlembert] |
✓ |
0.316 |
|
|
\[
{}y \left (1+{y^{\prime }}^{2}\right ) = 2 x y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.918 |
|
|
\[
{}2 x +{y^{\prime }}^{2} x = 2 y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.439 |
|
|
\[
{}x = y y^{\prime }+{y^{\prime }}^{2}
\] |
[_dAlembert] |
✓ |
1.538 |
|
|
\[
{}4 {y^{\prime }}^{2} x +2 x y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
12.705 |
|
|
\[
{}y = y^{\prime } x \left (y^{\prime }+1\right )
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.871 |
|
|
\[
{}2 x {y^{\prime }}^{3}+1 = y {y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.607 |
|
|
\[
{}{y^{\prime }}^{3}+x y y^{\prime } = 2 y^{2}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
8.911 |
|
|
\[
{}3 {y^{\prime }}^{4} x = {y^{\prime }}^{3} y+1
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
3.502 |
|
|
\[
{}2 {y^{\prime }}^{5}+2 x y^{\prime } = y
\] |
[_dAlembert] |
✓ |
1.131 |
|
|
\[
{}\frac {1}{{y^{\prime }}^{2}}+x y^{\prime } = 2 y
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
24.663 |
|
|
\[
{}2 y = 3 x y^{\prime }+4+2 \ln \left (y^{\prime }\right )
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
35.917 |
|
|
\[
{}y = x y^{\prime }+{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.412 |
|
|
\[
{}y = x y^{\prime }+\frac {1}{y^{\prime }}
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.489 |
|
|
\[
{}y = x y^{\prime }-\sqrt {y^{\prime }}
\] |
[[_homogeneous, ‘class G‘], _Clairaut] |
✓ |
0.892 |
|
|
\[
{}y = x y^{\prime }+\ln \left (y^{\prime }\right )
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
1.923 |
|
|
\[
{}y = x y^{\prime }+\frac {3}{{y^{\prime }}^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.582 |
|
|
\[
{}y = x y^{\prime }-{y^{\prime }}^{{2}/{3}}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
1.531 |
|
|
\[
{}y = x y^{\prime }+{\mathrm e}^{y^{\prime }}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
1.878 |
|
|
\[
{}\left (y-x y^{\prime }\right )^{2} = 1+{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.634 |
|
|
\[
{}{y^{\prime }}^{2} x -y y^{\prime }-2 = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.437 |
|
|
\[
{}y^{2}-2 x y y^{\prime }+{y^{\prime }}^{2} \left (x^{2}-1\right ) = 0
\] |
[_separable] |
✓ |
0.783 |
|
|
\[
{}y^{\prime } = \sqrt {1-y}
\] |
[_quadrature] |
✓ |
0.257 |
|
|
\[
{}y^{\prime } = x y-x^{2}
\] |
[_linear] |
✓ |
0.480 |
|
|
\[
{}y^{\prime } = y^{2} x^{2}
\] |
[_separable] |
✓ |
0.323 |
|
|
\[
{}y^{\prime } = 3 x +\frac {y}{x}
\] |
[_linear] |
✓ |
0.449 |
|
|
\[
{}y^{\prime } = \ln \left (x y\right )
\] |
[‘y=_G(x,y’)‘] |
✓ |
0.412 |
|
|
\[
{}y^{\prime } = 1+y^{2}
\] |
[_quadrature] |
✓ |
0.304 |
|
|
\[
{}y^{\prime } = x^{2}+y^{2}
\] |
[[_Riccati, _special]] |
✓ |
0.427 |
|
|
\[
{}y^{\prime } = \sqrt {1+x y}
\] |
[‘y=_G(x,y’)‘] |
✓ |
0.178 |
|
|
\[
{}y^{\prime } = \cos \left (x \right )+\sin \left (y\right )
\] |
[‘y=_G(x,y’)‘] |
✓ |
0.424 |
|
|
\[
{}y^{\prime \prime }-y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.531 |
|
|
\[
{}y^{\prime \prime }-2 y = {\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.436 |
|
|
\[
{}y^{\prime \prime }+2 y y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.170 |
|
|
\[
{}y^{\prime \prime } = \sin \left (y\right )
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
0.476 |
|
|
\[
{}y^{\prime \prime }+\frac {{y^{\prime }}^{2}}{2}-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.207 |
|
|
\[
{}y^{\prime \prime } = \sin \left (x y\right )
\] |
[NONE] |
✓ |
0.840 |
|
|
\[
{}y^{\prime \prime } = \cos \left (x y\right )
\] |
[NONE] |
✓ |
0.823 |
|
|
\[
{}2 x y^{\prime \prime }+5 y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.560 |
|
|
\[
{}3 x \left (3 x +2\right ) y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.781 |
|
|
\[
{}x^{2} \left (x +4\right ) y^{\prime \prime }+7 x y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.738 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.685 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.735 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+\left (3 x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.719 |
|
|
\[
{}\left (x^{3}+2 x^{2}\right ) y^{\prime \prime }-x y^{\prime }+\left (1-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.787 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-3 \left (x^{2}+x \right ) y^{\prime }+\left (3 x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.742 |
|
|
\[
{}3 x^{2} y^{\prime \prime }+\left (-x^{2}+5 x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.763 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+x \left (x^{2}-4\right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.691 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-3 \left (x^{2}+x \right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.058 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+9 \left (-x^{2}+x \right ) y^{\prime }+\left (-1+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.782 |
|
|
\[
{}4 x^{2} \left (1-x \right ) y^{\prime \prime }+3 x \left (2 x +1\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.763 |
|
|
\[
{}2 x^{2} \left (1-3 x \right ) y^{\prime \prime }+5 x y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.779 |
|
|
\[
{}4 x^{2} \left (x +1\right ) y^{\prime \prime }-5 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.752 |
|
|
\[
{}x^{2} \left (x +4\right ) y^{\prime \prime }+x \left (-1+x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.743 |
|
|
\[
{}\left (8-x \right ) x^{2} y^{\prime \prime }+6 x y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.775 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x \left (x^{2}+1\right ) y^{\prime }-\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.760 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.646 |
|
|
\[
{}3 x^{2} y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.624 |
|
|
\[
{}x^{3} \left (x^{2}+3\right ) y^{\prime \prime }+5 x y^{\prime }-\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.124 |
|
|
\[
{}2 x y^{\prime \prime }-\left (x^{3}+1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.708 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.572 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.423 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 \left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.653 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x +1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.621 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (2 x +3\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.674 |
|
|
\[
{}x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }-5 x y^{\prime }+9 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.527 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x^{2}-1\right ) y^{\prime }+\left (-x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.546 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (2 x -1\right ) y^{\prime }+x \left (-1+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.687 |
|
|
\[
{}x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.743 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-\left (3 x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.755 |
|
|
\[
{}x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-9 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.816 |
|
|
\[
{}\left (-x^{2}+x \right ) y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.659 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x -7\right ) y^{\prime }+\left (x +12\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.424 |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (x -4\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.444 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (-x^{2}+3\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.329 |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime }-y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.287 |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime }-y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.324 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-2 x y = x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.524 |
|
|
\[
{}x y^{\prime \prime }-x y^{\prime }+y = x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.326 |
|
|
\[
{}\left (1-2 x \right ) y^{\prime \prime }+4 x y^{\prime }-4 y = x^{2}-x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.411 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x +12\right ) y = x^{2}+x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.921 |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (x^{2}+3\right ) y^{\prime }+y = -2 x^{2}+x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.875 |
|
|
\[
{}3 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y = -x^{3}+x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.072 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+\left (3 x +2\right ) y = x^{4}+x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.840 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+10 x y^{\prime }+y = -1+x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.644 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y = x^{3}+1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.837 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 6 \left (-x^{2}+1\right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.335 |
|
|
\[
{}\left (x^{2}+2 x \right ) y^{\prime \prime }-\left (2+2 x \right ) y^{\prime }+2 y = x^{2} \left (x +2\right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.913 |
|