|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime }+2 x y = 2 x y^{2}
\] |
[_separable] |
✓ |
2.494 |
|
|
\[
{}3 x y^{2} y^{\prime }-2 y^{3} = x^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
13.415 |
|
|
\[
{}\left (x^{3}+{\mathrm e}^{y}\right ) y^{\prime } = 3 x^{2}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.447 |
|
|
\[
{}y^{\prime }+3 x y = y \,{\mathrm e}^{x^{2}}
\] |
[_separable] |
✓ |
2.085 |
|
|
\[
{}y^{\prime }-2 y \,{\mathrm e}^{x} = 2 \sqrt {y \,{\mathrm e}^{x}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
4.032 |
|
|
\[
{}2 y^{\prime } \ln \left (x \right )+\frac {y}{x} = \frac {\cos \left (x \right )}{y}
\] |
[_Bernoulli] |
✓ |
5.118 |
|
|
\[
{}2 \sin \left (x \right ) y^{\prime }+y \cos \left (x \right ) = y^{3} \sin \left (x \right )^{2}
\] |
[_Bernoulli] |
✓ |
10.136 |
|
|
\[
{}\left (1+x^{2}+y^{2}\right ) y^{\prime }+x y = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.751 |
|
|
\[
{}y^{\prime }-y \cos \left (x \right ) = y^{2} \cos \left (x \right )
\] |
[_separable] |
✓ |
2.984 |
|
|
\[
{}y^{\prime }-\tan \left (y\right ) = \frac {{\mathrm e}^{x}}{\cos \left (y\right )}
\] |
[‘y=_G(x,y’)‘] |
✓ |
2.570 |
|
|
\[
{}y^{\prime } = y \left ({\mathrm e}^{x}+\ln \left (y\right )\right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
2.398 |
|
|
\[
{}y^{\prime } \cos \left (y\right )+\sin \left (y\right ) = x +1
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
3.313 |
|
|
\[
{}y y^{\prime }+1 = \left (-1+x \right ) {\mathrm e}^{-\frac {y^{2}}{2}}
\] |
[‘y=_G(x,y’)‘] |
✗ |
3.020 |
|
|
\[
{}y^{\prime }+x \sin \left (2 y\right ) = 2 x \,{\mathrm e}^{-x^{2}} \cos \left (y\right )^{2}
\] |
[‘y=_G(x,y’)‘] |
✗ |
6.570 |
|
|
\[
{}x \left (2 x^{2}+y^{2}\right )+y \left (x^{2}+2 y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
89.151 |
|
|
\[
{}3 x^{2}+6 x y^{2}+\left (6 x^{2} y+4 y^{3}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
2.075 |
|
|
\[
{}\frac {x}{\sqrt {x^{2}+y^{2}}}+\frac {1}{x}+\frac {1}{y}+\left (\frac {y}{\sqrt {x^{2}+y^{2}}}+\frac {1}{y}-\frac {x}{y^{2}}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
27.219 |
|
|
\[
{}3 x^{2} \tan \left (y\right )-\frac {2 y^{3}}{x^{3}}+\left (x^{3} \sec \left (y\right )^{2}+4 y^{3}+\frac {3 y^{2}}{x^{2}}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
47.975 |
|
|
\[
{}2 x +\frac {x^{2}+y^{2}}{x^{2} y} = \frac {\left (x^{2}+y^{2}\right ) y^{\prime }}{x y^{2}}
\] |
[[_homogeneous, ‘class D‘], _exact, _rational] |
✓ |
3.641 |
|
|
\[
{}\frac {\sin \left (2 x \right )}{y}+x +\left (y-\frac {\sin \left (x \right )^{2}}{y^{2}}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
33.999 |
|
|
\[
{}3 x^{2}-2 x -y+\left (2 y-x +3 y^{2}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.388 |
|
|
\[
{}\frac {x y}{\sqrt {x^{2}+1}}+2 x y-\frac {y}{x}+\left (\sqrt {x^{2}+1}+x^{2}-\ln \left (x \right )\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
19.395 |
|
|
\[
{}\sin \left (y\right )+y \sin \left (x \right )+\frac {1}{x}+\left (x \cos \left (y\right )-\cos \left (x \right )+\frac {1}{y}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
38.336 |
|
|
\[
{}\frac {y+\sin \left (x \right ) \cos \left (x y\right )^{2}}{\cos \left (x y\right )^{2}}+\left (\frac {x}{\cos \left (x y\right )^{2}}+\sin \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
44.484 |
|
|
\[
{}\frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
8.524 |
|
|
\[
{}y \left (x^{2}+y^{2}+a^{2}\right ) y^{\prime }+x \left (x^{2}+y^{2}-a^{2}\right ) = 0
\] |
[_exact, _rational] |
✓ |
2.168 |
|
|
\[
{}3 x^{2} y+y^{3}+\left (x^{3}+3 x y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
14.911 |
|
|
\[
{}1-x^{2} y+x^{2} \left (y-x \right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.573 |
|
|
\[
{}x^{2}+y-x y^{\prime } = 0
\] |
[_linear] |
✓ |
1.708 |
|
|
\[
{}x +y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.471 |
|
|
\[
{}2 x^{2} y+2 y+5+\left (2 x^{3}+2 x \right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
1.464 |
|
|
\[
{}x^{4} \ln \left (x \right )-2 x y^{3}+3 x^{2} y^{2} y^{\prime } = 0
\] |
[_Bernoulli] |
✓ |
2.100 |
|
|
\[
{}x +\sin \left (x \right )+\sin \left (y\right )+y^{\prime } \cos \left (y\right ) = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
4.213 |
|
|
\[
{}2 x y^{2}-3 y^{3}+\left (7-3 x y^{2}\right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
2.817 |
|
|
\[
{}3 y^{2}-x +\left (2 y^{3}-6 x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
4.110 |
|
|
\[
{}x^{2}+y^{2}+1-2 x y y^{\prime } = 0
\] |
[_rational, _Bernoulli] |
✓ |
2.535 |
|
|
\[
{}x -x y+\left (y+x^{2}\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.892 |
|
|
\[
{}4 {y^{\prime }}^{2}-9 x = 0
\] |
[_quadrature] |
✓ |
0.339 |
|
|
\[
{}{y^{\prime }}^{2}-2 y y^{\prime } = y^{2} \left ({\mathrm e}^{2 x}-1\right )
\] |
[_separable] |
✓ |
0.459 |
|
|
\[
{}{y^{\prime }}^{2}-2 x y^{\prime }-8 x^{2} = 0
\] |
[_quadrature] |
✓ |
0.409 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+3 x y y^{\prime }+2 y^{2} = 0
\] |
[_separable] |
✓ |
1.131 |
|
|
\[
{}{y^{\prime }}^{2}-\left (2 x +y\right ) y^{\prime }+x^{2}+x y = 0
\] |
[_quadrature] |
✓ |
0.510 |
|
|
\[
{}{y^{\prime }}^{3}+\left (x +2\right ) {\mathrm e}^{y} = 0
\] |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
1.023 |
|
|
\[
{}{y^{\prime }}^{3} = y {y^{\prime }}^{2}-x^{2} y^{\prime }+x^{2} y
\] |
[_quadrature] |
✓ |
0.832 |
|
|
\[
{}{y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
3.925 |
|
|
\[
{}{y^{\prime }}^{2}-4 x y^{\prime }+2 y+2 x^{2} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
1.726 |
|
|
\[
{}y = {y^{\prime }}^{2} {\mathrm e}^{y^{\prime }}
\] |
[_quadrature] |
✓ |
0.726 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{\frac {y^{\prime }}{y}}
\] |
[_quadrature] |
✓ |
4.386 |
|
|
\[
{}x = \ln \left (y^{\prime }\right )+\sin \left (y^{\prime }\right )
\] |
[_quadrature] |
✓ |
2.720 |
|
|
\[
{}x = {y^{\prime }}^{2}-2 y^{\prime }+2
\] |
[_quadrature] |
✓ |
0.256 |
|
|
\[
{}y = y^{\prime } \ln \left (y^{\prime }\right )
\] |
[_quadrature] |
✓ |
3.409 |
|
|
\[
{}y = \left (y^{\prime }-1\right ) {\mathrm e}^{y^{\prime }}
\] |
[_quadrature] |
✓ |
2.219 |
|
|
\[
{}{y^{\prime }}^{2} x = {\mathrm e}^{\frac {1}{y^{\prime }}}
\] |
[_quadrature] |
✓ |
0.557 |
|
|
\[
{}x \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = a
\] |
[_quadrature] |
✓ |
2.467 |
|
|
\[
{}y^{{2}/{5}}+{y^{\prime }}^{{2}/{5}} = a^{{2}/{5}}
\] |
[_quadrature] |
✓ |
214.365 |
|
|
\[
{}x = y^{\prime }+\sin \left (y^{\prime }\right )
\] |
[_quadrature] |
✓ |
0.645 |
|
|
\[
{}y = y^{\prime } \left (1+y^{\prime } \cos \left (y^{\prime }\right )\right )
\] |
[_quadrature] |
✓ |
1.920 |
|
|
\[
{}y = \arcsin \left (y^{\prime }\right )+\ln \left (1+{y^{\prime }}^{2}\right )
\] |
[_quadrature] |
✓ |
6.031 |
|
|
\[
{}y = 2 x y^{\prime }+\ln \left (y^{\prime }\right )
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
2.319 |
|
|
\[
{}y = x \left (1+y^{\prime }\right )+{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.525 |
|
|
\[
{}y = 2 x y^{\prime }+\sin \left (y^{\prime }\right )
\] |
[_dAlembert] |
✓ |
1.220 |
|
|
\[
{}y = {y^{\prime }}^{2} x -\frac {1}{y^{\prime }}
\] |
[_dAlembert] |
✓ |
3.419 |
|
|
\[
{}y = \frac {3 x y^{\prime }}{2}+{\mathrm e}^{y^{\prime }}
\] |
[_dAlembert] |
✓ |
2.426 |
|
|
\[
{}y = x y^{\prime }+\frac {a}{{y^{\prime }}^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.821 |
|
|
\[
{}y = x y^{\prime }+{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.430 |
|
|
\[
{}{y^{\prime }}^{2} x -y y^{\prime }-y^{\prime }+1 = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.481 |
|
|
\[
{}y = x y^{\prime }+a \sqrt {1+{y^{\prime }}^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
1.747 |
|
|
\[
{}x = \frac {y}{y^{\prime }}+\frac {1}{{y^{\prime }}^{2}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.445 |
|
|
\[
{}y^{\prime } {\mathrm e}^{-x}+y^{2}-2 y \,{\mathrm e}^{x} = 1-{\mathrm e}^{2 x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
2.285 |
|
|
\[
{}y^{\prime }+y^{2}-2 y \sin \left (x \right )+\sin \left (x \right )^{2}-\cos \left (x \right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
3.135 |
|
|
\[
{}x y^{\prime }-y^{2}+\left (2 x +1\right ) y = x^{2}+2 x
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Riccati] |
✓ |
1.734 |
|
|
\[
{}x^{2} y^{\prime } = y^{2} x^{2}+x y+1
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.758 |
|
|
\[
{}\left (1+{y^{\prime }}^{2}\right ) y^{2}-4 y y^{\prime }-4 x = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
8.563 |
|
|
\[
{}{y^{\prime }}^{2}-4 y = 0
\] |
[_quadrature] |
✓ |
0.393 |
|
|
\[
{}{y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
11.202 |
|
|
\[
{}{y^{\prime }}^{2}-y^{2} = 0
\] |
[_quadrature] |
✓ |
0.738 |
|
|
\[
{}y^{\prime } = y^{{2}/{3}}+a
\] |
[_quadrature] |
✓ |
5.457 |
|
|
\[
{}\left (x y^{\prime }+y\right )^{2}+3 x^{5} \left (x y^{\prime }-2 y\right ) = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
9.540 |
|
|
\[
{}y \left (y-2 x y^{\prime }\right )^{2} = 2 y^{\prime }
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.665 |
|
|
\[
{}8 {y^{\prime }}^{3}-12 {y^{\prime }}^{2} = 27 y-27 x
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
0.517 |
|
|
\[
{}\left (y^{\prime }-1\right )^{2} = y^{2}
\] |
[_quadrature] |
✓ |
0.739 |
|
|
\[
{}y = {y^{\prime }}^{2}-x y^{\prime }+x
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.496 |
|
|
\[
{}\left (x y^{\prime }+y\right )^{2} = y^{2} y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
67.687 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}+y^{2} = 1
\] |
[_quadrature] |
✓ |
0.484 |
|
|
\[
{}{y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
4.107 |
|
|
\[
{}3 {y^{\prime }}^{2} x -6 y y^{\prime }+x +2 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.871 |
|
|
\[
{}y = x y^{\prime }+\sqrt {a^{2} {y^{\prime }}^{2}+b^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
3.405 |
|
|
\[
{}y^{\prime } = \left (x -y\right )^{2}+1
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
1.887 |
|
|
\[
{}x \sin \left (x \right ) y^{\prime }+\left (\sin \left (x \right )-x \cos \left (x \right )\right ) y = \sin \left (x \right ) \cos \left (x \right )-x
\] |
[_linear] |
✓ |
7.590 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = y^{n} \sin \left (2 x \right )
\] |
[_Bernoulli] |
✓ |
6.309 |
|
|
\[
{}x^{3}-3 x y^{2}+\left (y^{3}-3 x^{2} y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
43.332 |
|
|
\[
{}5 x y-4 y^{2}-6 x^{2}+\left (y^{2}-8 x y+\frac {5 x^{2}}{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
147.244 |
|
|
\[
{}3 x y^{2}-x^{2}+\left (3 x^{2} y-6 y^{2}-1\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.676 |
|
|
\[
{}y-x y^{2} \ln \left (x \right )+x y^{\prime } = 0
\] |
[_Bernoulli] |
✓ |
2.533 |
|
|
\[
{}2 x y \,{\mathrm e}^{x^{2}}-x \sin \left (x \right )+{\mathrm e}^{x^{2}} y^{\prime } = 0
\] |
[_linear] |
✓ |
2.621 |
|
|
\[
{}y^{\prime } = \frac {1}{2 x -y^{2}}
\] |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
1.194 |
|
|
\[
{}x^{2}+x y^{\prime } = 3 x +y^{\prime }
\] |
[_quadrature] |
✓ |
0.604 |
|
|
\[
{}x y y^{\prime }-y^{2} = x^{4}
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
4.262 |
|
|
\[
{}\frac {1}{y^{2}-x y+x^{2}} = \frac {y^{\prime }}{2 y^{2}-x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
19.638 |
|
|
\[
{}\left (2 x -1\right ) y^{\prime }-2 y = \frac {1-4 x}{x^{2}}
\] |
[_linear] |
✓ |
1.352 |
|