|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}4 x -2 y y^{\prime }+{y^{\prime }}^{2} x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.500 |
|
|
\[
{}2 x^{2} y+{y^{\prime }}^{2} = x^{3} y^{\prime }
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.467 |
|
|
\[
{}y {y^{\prime }}^{2} = 3 y^{\prime } x +y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
56.735 |
|
|
\[
{}8 x +1 = y {y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
2.908 |
|
|
\[
{}y {y^{\prime }}^{2}+2 y^{\prime }+1 = 0
\] |
[_quadrature] |
✓ |
0.338 |
|
|
\[
{}\left (1+{y^{\prime }}^{2}\right ) x = \left (x +y\right ) y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.589 |
|
|
\[
{}x^{2}-3 y y^{\prime }+{y^{\prime }}^{2} x = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
6.821 |
|
|
\[
{}y+2 y^{\prime } x = {y^{\prime }}^{2} x
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.525 |
|
|
\[
{}x = {y^{\prime }}^{2}+y^{\prime }
\] |
[_quadrature] |
✓ |
0.191 |
|
|
\[
{}x = y-{y^{\prime }}^{3}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
3.463 |
|
|
\[
{}x +2 y y^{\prime } = {y^{\prime }}^{2} x
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.329 |
|
|
\[
{}4 x -2 y y^{\prime }+{y^{\prime }}^{2} x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.511 |
|
|
\[
{}x {y^{\prime }}^{3} = y y^{\prime }+1
\] |
[_dAlembert] |
✓ |
0.271 |
|
|
\[
{}y \left (1+{y^{\prime }}^{2}\right ) = 2 y^{\prime } x
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.902 |
|
|
\[
{}2 x +{y^{\prime }}^{2} x = 2 y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.511 |
|
|
\[
{}x = y y^{\prime }+{y^{\prime }}^{2}
\] |
[_dAlembert] |
✓ |
2.454 |
|
|
\[
{}4 {y^{\prime }}^{2} x +2 y^{\prime } x = y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.045 |
|
|
\[
{}y = y^{\prime } x \left (y^{\prime }+1\right )
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.800 |
|
|
\[
{}2 x {y^{\prime }}^{3}+1 = y {y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
143.580 |
|
|
\[
{}{y^{\prime }}^{3}+x y y^{\prime } = 2 y^{2}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
9.846 |
|
|
\[
{}3 {y^{\prime }}^{4} x = {y^{\prime }}^{3} y+1
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
4.960 |
|
|
\[
{}2 {y^{\prime }}^{5}+2 y^{\prime } x = y
\] |
[_dAlembert] |
✓ |
4.808 |
|
|
\[
{}\frac {1}{{y^{\prime }}^{2}}+y^{\prime } x = 2 y
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
141.075 |
|
|
\[
{}2 y = 3 y^{\prime } x +4+2 \ln \left (y^{\prime }\right )
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
38.707 |
|
|
\[
{}y = y^{\prime } x +{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.365 |
|
|
\[
{}y = y^{\prime } x +\frac {1}{y^{\prime }}
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.379 |
|
|
\[
{}y = y^{\prime } x -\sqrt {y^{\prime }}
\] |
[[_homogeneous, ‘class G‘], _Clairaut] |
✓ |
0.929 |
|
|
\[
{}y = y^{\prime } x +\ln \left (y^{\prime }\right )
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
1.877 |
|
|
\[
{}y = y^{\prime } x +\frac {3}{{y^{\prime }}^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.606 |
|
|
\[
{}y = y^{\prime } x -{y^{\prime }}^{{2}/{3}}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
1.671 |
|
|
\[
{}y = y^{\prime } x +{\mathrm e}^{y^{\prime }}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
1.478 |
|
|
\[
{}\left (y-y^{\prime } x \right )^{2} = 1+{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.537 |
|
|
\[
{}{y^{\prime }}^{2} x -y y^{\prime }-2 = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.372 |
|
|
\[
{}y^{2}-2 x y y^{\prime }+{y^{\prime }}^{2} \left (x^{2}-1\right ) = 0
\] |
[_separable] |
✓ |
0.745 |
|
|
\[
{}y^{\prime } = \sqrt {1-y}
\] |
[_quadrature] |
✓ |
0.286 |
|
|
\[
{}y^{\prime } = x y-x^{2}
\] |
[_linear] |
✓ |
0.630 |
|
|
\[
{}y^{\prime } = x^{2} y^{2}
\] |
[_separable] |
✓ |
0.330 |
|
|
\[
{}y^{\prime } = 3 x +\frac {y}{x}
\] |
[_linear] |
✓ |
0.605 |
|
|
\[
{}y^{\prime } = \ln \left (x y\right )
\] |
[‘y=_G(x,y’)‘] |
✓ |
0.380 |
|
|
\[
{}y^{\prime } = 1+y^{2}
\] |
[_quadrature] |
✓ |
0.329 |
|
|
\[
{}y^{\prime } = x^{2}+y^{2}
\] |
[[_Riccati, _special]] |
✓ |
0.392 |
|
|
\[
{}y^{\prime } = \sqrt {x y+1}
\] |
[‘y=_G(x,y’)‘] |
✓ |
0.217 |
|
|
\[
{}y^{\prime } = \cos \left (x \right )+\sin \left (y\right )
\] |
[‘y=_G(x,y’)‘] |
✓ |
0.387 |
|
|
\[
{}y^{\prime \prime }-y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.693 |
|
|
\[
{}y^{\prime \prime }-2 y = {\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.654 |
|
|
\[
{}y^{\prime \prime }+2 y y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.190 |
|
|
\[
{}y^{\prime \prime } = \sin \left (y\right )
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
0.460 |
|
|
\[
{}y^{\prime \prime }+\frac {{y^{\prime }}^{2}}{2}-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.230 |
|
|
\[
{}y^{\prime \prime } = \sin \left (x y\right )
\] |
[NONE] |
✓ |
0.738 |
|
|
\[
{}y^{\prime \prime } = \cos \left (x y\right )
\] |
[NONE] |
✓ |
0.795 |
|
|
\[
{}2 x y^{\prime \prime }+5 y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.729 |
|
|
\[
{}3 x \left (2+3 x \right ) y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.962 |
|
|
\[
{}x^{2} \left (4+x \right ) y^{\prime \prime }+7 y^{\prime } x -y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.910 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.897 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 y^{\prime } x +\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.875 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+\left (2+3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.862 |
|
|
\[
{}\left (x^{3}+2 x^{2}\right ) y^{\prime \prime }-y^{\prime } x +\left (1-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.987 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-3 \left (x^{2}+x \right ) y^{\prime }+\left (2+3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.918 |
|
|
\[
{}3 x^{2} y^{\prime \prime }+\left (-x^{2}+5 x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.914 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+x \left (x^{2}-4\right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.830 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-3 \left (x^{2}+x \right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.183 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+9 \left (-x^{2}+x \right ) y^{\prime }+\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.918 |
|
|
\[
{}4 x^{2} \left (1-x \right ) y^{\prime \prime }+3 x \left (2 x +1\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.971 |
|
|
\[
{}2 x^{2} \left (1-3 x \right ) y^{\prime \prime }+5 y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.972 |
|
|
\[
{}4 x^{2} \left (x +1\right ) y^{\prime \prime }-5 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.950 |
|
|
\[
{}x^{2} \left (4+x \right ) y^{\prime \prime }+x \left (x -1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.939 |
|
|
\[
{}\left (8-x \right ) x^{2} y^{\prime \prime }+6 y^{\prime } x -y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.912 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x \left (x^{2}+1\right ) y^{\prime }-\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.971 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.775 |
|
|
\[
{}3 x^{2} y^{\prime \prime }+2 y^{\prime } x +\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.791 |
|
|
\[
{}x^{3} \left (x^{2}+3\right ) y^{\prime \prime }+5 y^{\prime } x -\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.151 |
|
|
\[
{}2 x y^{\prime \prime }-\left (x^{3}+1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.856 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.720 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.660 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 \left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.802 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x +1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.825 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (2 x +3\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.873 |
|
|
\[
{}x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }-5 y^{\prime } x +9 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.819 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x^{2}-1\right ) y^{\prime }+\left (-x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.796 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (2 x -1\right ) y^{\prime }+x \left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.852 |
|
|
\[
{}x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.878 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-\left (3 x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.966 |
|
|
\[
{}x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-9 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.013 |
|
|
\[
{}\left (-x^{2}+x \right ) y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.825 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x -7\right ) y^{\prime }+\left (x +12\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.300 |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (x -4\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.360 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (-x^{2}+3\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.219 |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime }-y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.250 |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime }-y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.248 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-2 x y = x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.740 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime } x +y = x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.243 |
|
|
\[
{}\left (1-2 x \right ) y^{\prime \prime }+4 y^{\prime } x -4 y = x^{2}-x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.558 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x +12\right ) y = x^{2}+x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.105 |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (x^{2}+3\right ) y^{\prime }+y = -2 x^{2}+x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.061 |
|
|
\[
{}3 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y = -x^{3}+x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.280 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+\left (2+3 x \right ) y = x^{4}+x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.080 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+10 y^{\prime } x +y = x -1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.787 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y = x^{3}+1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.025 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y = 6 \left (-x^{2}+1\right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.505 |
|
|
\[
{}\left (x^{2}+2 x \right ) y^{\prime \prime }-\left (2+2 x \right ) y^{\prime }+2 y = x^{2} \left (x +2\right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.080 |
|