|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}4 x -2 y y^{\prime }+{y^{\prime }}^{2} x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.503 |
|
|
\[
{}2 x^{2} y+{y^{\prime }}^{2} = x^{3} y^{\prime }
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.506 |
|
|
\[
{}y {y^{\prime }}^{2} = 3 y^{\prime } x +y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
56.000 |
|
|
\[
{}8 x +1 = y {y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
2.947 |
|
|
\[
{}y {y^{\prime }}^{2}+2 y^{\prime }+1 = 0
\] |
[_quadrature] |
✓ |
0.334 |
|
|
\[
{}\left (1+{y^{\prime }}^{2}\right ) x = \left (x +y\right ) y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.608 |
|
|
\[
{}x^{2}-3 y y^{\prime }+{y^{\prime }}^{2} x = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
6.897 |
|
|
\[
{}y+2 y^{\prime } x = {y^{\prime }}^{2} x
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.562 |
|
|
\[
{}x = {y^{\prime }}^{2}+y^{\prime }
\] |
[_quadrature] |
✓ |
0.191 |
|
|
\[
{}x = y-{y^{\prime }}^{3}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
4.576 |
|
|
\[
{}x +2 y y^{\prime } = {y^{\prime }}^{2} x
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.350 |
|
|
\[
{}4 x -2 y y^{\prime }+{y^{\prime }}^{2} x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.500 |
|
|
\[
{}x {y^{\prime }}^{3} = y y^{\prime }+1
\] |
[_dAlembert] |
✓ |
0.230 |
|
|
\[
{}y \left (1+{y^{\prime }}^{2}\right ) = 2 y^{\prime } x
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.883 |
|
|
\[
{}2 x +{y^{\prime }}^{2} x = 2 y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.492 |
|
|
\[
{}x = y y^{\prime }+{y^{\prime }}^{2}
\] |
[_dAlembert] |
✓ |
1.421 |
|
|
\[
{}4 {y^{\prime }}^{2} x +2 y^{\prime } x = y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.054 |
|
|
\[
{}y = y^{\prime } x \left (y^{\prime }+1\right )
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.852 |
|
|
\[
{}2 x {y^{\prime }}^{3}+1 = y {y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.554 |
|
|
\[
{}{y^{\prime }}^{3}+x y y^{\prime } = 2 y^{2}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
7.321 |
|
|
\[
{}3 {y^{\prime }}^{4} x = {y^{\prime }}^{3} y+1
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
4.281 |
|
|
\[
{}2 {y^{\prime }}^{5}+2 y^{\prime } x = y
\] |
[_dAlembert] |
✓ |
0.663 |
|
|
\[
{}\frac {1}{{y^{\prime }}^{2}}+y^{\prime } x = 2 y
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
23.484 |
|
|
\[
{}2 y = 3 y^{\prime } x +4+2 \ln \left (y^{\prime }\right )
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
8.315 |
|
|
\[
{}y = y^{\prime } x +{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.355 |
|
|
\[
{}y = y^{\prime } x +\frac {1}{y^{\prime }}
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.374 |
|
|
\[
{}y = y^{\prime } x -\sqrt {y^{\prime }}
\] |
[[_homogeneous, ‘class G‘], _Clairaut] |
✓ |
0.917 |
|
|
\[
{}y = y^{\prime } x +\ln \left (y^{\prime }\right )
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
1.869 |
|
|
\[
{}y = y^{\prime } x +\frac {3}{{y^{\prime }}^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.607 |
|
|
\[
{}y = y^{\prime } x -{y^{\prime }}^{{2}/{3}}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
1.571 |
|
|
\[
{}y = y^{\prime } x +{\mathrm e}^{y^{\prime }}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
1.418 |
|
|
\[
{}\left (y-y^{\prime } x \right )^{2} = 1+{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.590 |
|
|
\[
{}{y^{\prime }}^{2} x -y y^{\prime }-2 = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.377 |
|
|
\[
{}y^{2}-2 x y y^{\prime }+{y^{\prime }}^{2} \left (x^{2}-1\right ) = 0
\] |
[_separable] |
✓ |
3.450 |
|
|
\[
{}y^{\prime } = \sqrt {1-y}
\] |
[_quadrature] |
✓ |
0.300 |
|
|
\[
{}y^{\prime } = x y-x^{2}
\] |
[_linear] |
✓ |
0.651 |
|
|
\[
{}y^{\prime } = x^{2} y^{2}
\] |
[_separable] |
✓ |
0.381 |
|
|
\[
{}y^{\prime } = 3 x +\frac {y}{x}
\] |
[_linear] |
✓ |
0.618 |
|
|
\[
{}y^{\prime } = \ln \left (x y\right )
\] |
[‘y=_G(x,y’)‘] |
✓ |
0.375 |
|
|
\[
{}y^{\prime } = 1+y^{2}
\] |
[_quadrature] |
✓ |
0.335 |
|
|
\[
{}y^{\prime } = x^{2}+y^{2}
\] |
[[_Riccati, _special]] |
✓ |
0.397 |
|
|
\[
{}y^{\prime } = \sqrt {x y+1}
\] |
[‘y=_G(x,y’)‘] |
✓ |
0.227 |
|
|
\[
{}y^{\prime } = \cos \left (x \right )+\sin \left (y\right )
\] |
[‘y=_G(x,y’)‘] |
✓ |
0.384 |
|
|
\[
{}y^{\prime \prime }-y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.703 |
|
|
\[
{}y^{\prime \prime }-2 y = {\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.596 |
|
|
\[
{}y^{\prime \prime }+2 y y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.199 |
|
|
\[
{}y^{\prime \prime } = \sin \left (y\right )
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
0.471 |
|
|
\[
{}y^{\prime \prime }+\frac {{y^{\prime }}^{2}}{2}-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.234 |
|
|
\[
{}y^{\prime \prime } = \sin \left (x y\right )
\] |
[NONE] |
✓ |
0.789 |
|
|
\[
{}y^{\prime \prime } = \cos \left (x y\right )
\] |
[NONE] |
✓ |
0.791 |
|
|
\[
{}2 x y^{\prime \prime }+5 y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.735 |
|
|
\[
{}3 x \left (2+3 x \right ) y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.986 |
|
|
\[
{}x^{2} \left (4+x \right ) y^{\prime \prime }+7 y^{\prime } x -y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.938 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.929 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 y^{\prime } x +\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.941 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+\left (2+3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.854 |
|
|
\[
{}\left (x^{3}+2 x^{2}\right ) y^{\prime \prime }-y^{\prime } x +\left (1-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.977 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-3 \left (x^{2}+x \right ) y^{\prime }+\left (2+3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.888 |
|
|
\[
{}3 x^{2} y^{\prime \prime }+\left (-x^{2}+5 x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.997 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+x \left (x^{2}-4\right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.904 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-3 \left (x^{2}+x \right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.271 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+9 \left (-x^{2}+x \right ) y^{\prime }+\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.996 |
|
|
\[
{}4 x^{2} \left (1-x \right ) y^{\prime \prime }+3 x \left (2 x +1\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.994 |
|
|
\[
{}2 x^{2} \left (1-3 x \right ) y^{\prime \prime }+5 y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.931 |
|
|
\[
{}4 x^{2} \left (x +1\right ) y^{\prime \prime }-5 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.900 |
|
|
\[
{}x^{2} \left (4+x \right ) y^{\prime \prime }+x \left (x -1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.911 |
|
|
\[
{}\left (8-x \right ) x^{2} y^{\prime \prime }+6 y^{\prime } x -y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.974 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x \left (x^{2}+1\right ) y^{\prime }-\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.963 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.810 |
|
|
\[
{}3 x^{2} y^{\prime \prime }+2 y^{\prime } x +\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.863 |
|
|
\[
{}x^{3} \left (x^{2}+3\right ) y^{\prime \prime }+5 y^{\prime } x -\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.153 |
|
|
\[
{}2 x y^{\prime \prime }-\left (x^{3}+1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.849 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.728 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.664 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 \left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.816 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x +1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.843 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (2 x +3\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.836 |
|
|
\[
{}x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }-5 y^{\prime } x +9 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.824 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x^{2}-1\right ) y^{\prime }+\left (-x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.828 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (2 x -1\right ) y^{\prime }+x \left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.923 |
|
|
\[
{}x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.951 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-\left (3 x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.969 |
|
|
\[
{}x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-9 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.071 |
|
|
\[
{}\left (-x^{2}+x \right ) y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.891 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x -7\right ) y^{\prime }+\left (x +12\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.385 |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (x -4\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.310 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (-x^{2}+3\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.311 |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime }-y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.278 |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime }-y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.310 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-2 x y = x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.736 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime } x +y = x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.238 |
|
|
\[
{}\left (1-2 x \right ) y^{\prime \prime }+4 y^{\prime } x -4 y = x^{2}-x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.620 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x +12\right ) y = x^{2}+x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.051 |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (x^{2}+3\right ) y^{\prime }+y = -2 x^{2}+x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.114 |
|
|
\[
{}3 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y = -x^{3}+x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.297 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+\left (2+3 x \right ) y = x^{4}+x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.070 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+10 y^{\prime } x +y = x -1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.836 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y = x^{3}+1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.055 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y = 6 \left (-x^{2}+1\right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.499 |
|
|
\[
{}\left (x^{2}+2 x \right ) y^{\prime \prime }-\left (2+2 x \right ) y^{\prime }+2 y = x^{2} \left (x +2\right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.127 |
|