|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } x = y \left (\ln \left (y\right )-\ln \left (x \right )\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.546 |
|
|
\[
{}x^{2} y^{\prime } = y^{2}-y x +x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
1.591 |
|
|
\[
{}y^{\prime } x = y+\sqrt {y^{2}-x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
3.641 |
|
|
\[
{}2 x^{2} y^{\prime } = x^{2}+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
1.575 |
|
|
\[
{}4 x -3 y+\left (2 y-3 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.284 |
|
|
\[
{}y-x +\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.470 |
|
|
\[
{}x +y-2+\left (1-x \right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
1.008 |
|
|
\[
{}3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.063 |
|
|
\[
{}x +y-2+\left (x -y+4\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.584 |
|
|
\[
{}x +y+\left (x -y-2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.457 |
|
|
\[
{}2 x +3 y-5+\left (3 x +2 y-5\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.583 |
|
|
\[
{}8 x +4 y+1+\left (4 x +2 y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.187 |
|
|
\[
{}x -2 y-1+\left (3 x -6 y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.207 |
|
|
\[
{}x +y+\left (x +y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.279 |
|
|
\[
{}2 x y^{\prime } \left (x -y^{2}\right )+y^{3} = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.672 |
|
|
\[
{}4 y^{6}+x^{3} = 6 x y^{5} y^{\prime }
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.609 |
|
|
\[
{}y \left (1+\sqrt {x^{2} y^{4}+1}\right )+2 y^{\prime } x = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.250 |
|
|
\[
{}x +y^{3}+3 \left (y^{3}-x \right ) y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.568 |
|
|
\[
{}y^{\prime }+2 y = {\mathrm e}^{-x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.892 |
|
|
\[
{}x^{2}-y^{\prime } x = y
\] |
[_linear] |
✓ |
1.376 |
|
|
\[
{}y^{\prime }-2 y x = 2 x \,{\mathrm e}^{x^{2}}
\] |
[_linear] |
✓ |
2.152 |
|
|
\[
{}y^{\prime }+2 y x = {\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
1.205 |
|
|
\[
{}y^{\prime } \cos \left (x \right )-y \sin \left (x \right ) = 2 x
\] |
[_linear] |
✓ |
2.148 |
|
|
\[
{}y^{\prime } x -2 y = x^{3} \cos \left (x \right )
\] |
[_linear] |
✓ |
1.536 |
|
|
\[
{}y^{\prime }-y \tan \left (x \right ) = \frac {1}{\cos \left (x \right )^{3}}
\] |
[_linear] |
✓ |
15.315 |
|
|
\[
{}y^{\prime } x \ln \left (x \right )-y = 3 x^{3} \ln \left (x \right )^{2}
\] |
[_linear] |
✓ |
1.371 |
|
|
\[
{}\left (2 x -y^{2}\right ) y^{\prime } = 2 y
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.713 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = \cos \left (x \right )
\] |
[_separable] |
✓ |
1.510 |
|
|
\[
{}y^{\prime } = \frac {y}{2 y \ln \left (y\right )+y-x}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.253 |
|
|
\[
{}\left (\frac {{\mathrm e}^{-y^{2}}}{2}-y x \right ) y^{\prime }-1 = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.313 |
|
|
\[
{}y^{\prime }-y \,{\mathrm e}^{x} = 2 x \,{\mathrm e}^{{\mathrm e}^{x}}
\] |
[_linear] |
✓ |
1.164 |
|
|
\[
{}y^{\prime }+x y \,{\mathrm e}^{x} = {\mathrm e}^{\left (1-x \right ) {\mathrm e}^{x}}
\] |
[_linear] |
✓ |
1.235 |
|
|
\[
{}y^{\prime }-y \ln \left (2\right ) = 2^{\sin \left (x \right )} \left (\cos \left (x \right )-1\right ) \ln \left (2\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.998 |
|
|
\[
{}y^{\prime }-y = -2 \,{\mathrm e}^{-x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.994 |
|
|
\[
{}\sin \left (x \right ) y^{\prime }-y \cos \left (x \right ) = -\frac {\sin \left (x \right )^{2}}{x^{2}}
\] |
[_linear] |
✓ |
5.294 |
|
|
\[
{}x^{2} y^{\prime } \cos \left (\frac {1}{x}\right )-y \sin \left (\frac {1}{x}\right ) = -1
\] |
[_linear] |
✓ |
2.493 |
|
|
\[
{}2 y^{\prime } x -y = 1-\frac {2}{\sqrt {x}}
\] |
[_linear] |
✓ |
1.233 |
|
|
\[
{}x^{2} y^{\prime }+y = \left (x^{2}+1\right ) {\mathrm e}^{x}
\] |
[_linear] |
✓ |
1.579 |
|
|
\[
{}y^{\prime } x +y = 2 x
\] |
[_linear] |
✓ |
1.624 |
|
|
\[
{}\sin \left (x \right ) y^{\prime }+y \cos \left (x \right ) = 1
\] |
[_linear] |
✓ |
1.760 |
|
|
\[
{}y^{\prime } \cos \left (x \right )-y \sin \left (x \right ) = -\sin \left (2 x \right )
\] |
[_linear] |
✓ |
2.701 |
|
|
\[
{}y^{\prime }+2 y x = 2 x y^{2}
\] |
[_separable] |
✓ |
1.775 |
|
|
\[
{}3 x y^{2} y^{\prime }-2 y^{3} = x^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
8.077 |
|
|
\[
{}\left (x^{3}+{\mathrm e}^{y}\right ) y^{\prime } = 3 x^{2}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.128 |
|
|
\[
{}y^{\prime }+3 y x = y \,{\mathrm e}^{x^{2}}
\] |
[_separable] |
✓ |
1.301 |
|
|
\[
{}y^{\prime }-2 y \,{\mathrm e}^{x} = 2 \sqrt {y \,{\mathrm e}^{x}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
2.132 |
|
|
\[
{}2 y^{\prime } \ln \left (x \right )+\frac {y}{x} = \frac {\cos \left (x \right )}{y}
\] |
[_Bernoulli] |
✓ |
6.523 |
|
|
\[
{}2 \sin \left (x \right ) y^{\prime }+y \cos \left (x \right ) = y^{3} \sin \left (x \right )^{2}
\] |
[_Bernoulli] |
✓ |
13.042 |
|
|
\[
{}\left (1+x^{2}+y^{2}\right ) y^{\prime }+y x = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.256 |
|
|
\[
{}y^{\prime }-y \cos \left (x \right ) = y^{2} \cos \left (x \right )
\] |
[_separable] |
✓ |
2.410 |
|
|
\[
{}y^{\prime }-\tan \left (y\right ) = \frac {{\mathrm e}^{x}}{\cos \left (y\right )}
\] |
[‘y=_G(x,y’)‘] |
✓ |
2.576 |
|
|
\[
{}y^{\prime } = y \left ({\mathrm e}^{x}+\ln \left (y\right )\right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
1.052 |
|
|
\[
{}y^{\prime } \cos \left (y\right )+\sin \left (y\right ) = x +1
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
2.609 |
|
|
\[
{}y y^{\prime }+1 = \left (x -1\right ) {\mathrm e}^{-\frac {y^{2}}{2}}
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.500 |
|
|
\[
{}y^{\prime }+x \sin \left (2 y\right ) = 2 x \,{\mathrm e}^{-x^{2}} \cos \left (y\right )^{2}
\] |
[‘y=_G(x,y’)‘] |
✗ |
2.681 |
|
|
\[
{}x \left (2 x^{2}+y^{2}\right )+y \left (x^{2}+2 y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
123.224 |
|
|
\[
{}3 x^{2}+6 x y^{2}+\left (6 x^{2} y+4 y^{3}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.637 |
|
|
\[
{}\frac {x}{\sqrt {x^{2}+y^{2}}}+\frac {1}{x}+\frac {1}{y}+\left (\frac {y}{\sqrt {x^{2}+y^{2}}}+\frac {1}{y}-\frac {x}{y^{2}}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
38.891 |
|
|
\[
{}3 x^{2} \tan \left (y\right )-\frac {2 y^{3}}{x^{3}}+\left (x^{3} \sec \left (y\right )^{2}+4 y^{3}+\frac {3 y^{2}}{x^{2}}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
78.440 |
|
|
\[
{}2 x +\frac {x^{2}+y^{2}}{x^{2} y} = \frac {\left (x^{2}+y^{2}\right ) y^{\prime }}{x y^{2}}
\] |
[[_homogeneous, ‘class D‘], _exact, _rational] |
✓ |
3.389 |
|
|
\[
{}\frac {\sin \left (2 x \right )}{y}+x +\left (y-\frac {\sin \left (x \right )^{2}}{y^{2}}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
63.323 |
|
|
\[
{}3 x^{2}-2 x -y+\left (2 y-x +3 y^{2}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.209 |
|
|
\[
{}\frac {x y}{\sqrt {x^{2}+1}}+2 y x -\frac {y}{x}+\left (\sqrt {x^{2}+1}+x^{2}-\ln \left (x \right )\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
19.932 |
|
|
\[
{}\sin \left (y\right )+y \sin \left (x \right )+\frac {1}{x}+\left (x \cos \left (y\right )-\cos \left (x \right )+\frac {1}{y}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
65.966 |
|
|
\[
{}\frac {y+\sin \left (x \right ) \cos \left (y x \right )^{2}}{\cos \left (y x \right )^{2}}+\left (\frac {x}{\cos \left (y x \right )^{2}}+\sin \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
90.285 |
|
|
\[
{}\frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
10.261 |
|
|
\[
{}y \left (x^{2}+y^{2}+a^{2}\right ) y^{\prime }+x \left (x^{2}+y^{2}-a^{2}\right ) = 0
\] |
[_exact, _rational] |
✓ |
1.688 |
|
|
\[
{}3 x^{2} y+y^{3}+\left (x^{3}+3 x y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
109.940 |
|
|
\[
{}1-x^{2} y+x^{2} \left (-x +y\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.209 |
|
|
\[
{}x^{2}+y-y^{\prime } x = 0
\] |
[_linear] |
✓ |
1.039 |
|
|
\[
{}x +y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.498 |
|
|
\[
{}2 x^{2} y+2 y+5+\left (2 x^{3}+2 x \right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
1.197 |
|
|
\[
{}x^{4} \ln \left (x \right )-2 x y^{3}+3 x^{2} y^{2} y^{\prime } = 0
\] |
[_Bernoulli] |
✓ |
1.664 |
|
|
\[
{}x +\sin \left (x \right )+\sin \left (y\right )+y^{\prime } \cos \left (y\right ) = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
4.709 |
|
|
\[
{}2 x y^{2}-3 y^{3}+\left (7-3 x y^{2}\right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
2.371 |
|
|
\[
{}3 y^{2}-x +\left (2 y^{3}-6 y x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.133 |
|
|
\[
{}x^{2}+y^{2}+1-2 x y y^{\prime } = 0
\] |
[_rational, _Bernoulli] |
✓ |
150.857 |
|
|
\[
{}x -y x +\left (y+x^{2}\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.247 |
|
|
\[
{}4 {y^{\prime }}^{2}-9 x = 0
\] |
[_quadrature] |
✓ |
0.224 |
|
|
\[
{}{y^{\prime }}^{2}-2 y y^{\prime } = y^{2} \left ({\mathrm e}^{2 x}-1\right )
\] |
[_separable] |
✓ |
0.361 |
|
|
\[
{}{y^{\prime }}^{2}-2 y^{\prime } x -8 x^{2} = 0
\] |
[_quadrature] |
✓ |
0.423 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+3 x y y^{\prime }+2 y^{2} = 0
\] |
[_separable] |
✓ |
2.717 |
|
|
\[
{}{y^{\prime }}^{2}-\left (2 x +y\right ) y^{\prime }+x^{2}+y x = 0
\] |
[_quadrature] |
✓ |
1.025 |
|
|
\[
{}{y^{\prime }}^{3}+\left (x +2\right ) {\mathrm e}^{y} = 0
\] |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
0.782 |
|
|
\[
{}{y^{\prime }}^{3} = y {y^{\prime }}^{2}-x^{2} y^{\prime }+x^{2} y
\] |
[_quadrature] |
✓ |
0.627 |
|
|
\[
{}{y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.602 |
|
|
\[
{}{y^{\prime }}^{2}-4 y^{\prime } x +2 y+2 x^{2} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.297 |
|
|
\[
{}y = {y^{\prime }}^{2} {\mathrm e}^{y^{\prime }}
\] |
[_quadrature] |
✓ |
1.592 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{\frac {y^{\prime }}{y}}
\] |
[_quadrature] |
✓ |
0.533 |
|
|
\[
{}x = \ln \left (y^{\prime }\right )+\sin \left (y^{\prime }\right )
\] |
[_quadrature] |
✓ |
1.204 |
|
|
\[
{}x = {y^{\prime }}^{2}-2 y^{\prime }+2
\] |
[_quadrature] |
✓ |
0.190 |
|
|
\[
{}y = y^{\prime } \ln \left (y^{\prime }\right )
\] |
[_quadrature] |
✓ |
1.608 |
|
|
\[
{}y = \left (y^{\prime }-1\right ) {\mathrm e}^{y^{\prime }}
\] |
[_quadrature] |
✓ |
0.536 |
|
|
\[
{}{y^{\prime }}^{2} x = {\mathrm e}^{\frac {1}{y^{\prime }}}
\] |
[_quadrature] |
✓ |
0.404 |
|
|
\[
{}x \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = a
\] |
[_quadrature] |
✓ |
1.700 |
|
|
\[
{}y^{{2}/{5}}+{y^{\prime }}^{{2}/{5}} = a^{{2}/{5}}
\] |
[_quadrature] |
✓ |
1.803 |
|
|
\[
{}x = y^{\prime }+\sin \left (y^{\prime }\right )
\] |
[_quadrature] |
✓ |
0.451 |
|
|
\[
{}y = y^{\prime } \left (1+y^{\prime } \cos \left (y^{\prime }\right )\right )
\] |
[_quadrature] |
✓ |
0.579 |
|
|
\[
{}y = \arcsin \left (y^{\prime }\right )+\ln \left (1+{y^{\prime }}^{2}\right )
\] |
[_quadrature] |
✓ |
1.535 |
|
|
\[
{}y = 2 y^{\prime } x +\ln \left (y^{\prime }\right )
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
5.090 |
|