|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x^{2} \left (1+y^{2}\right ) y^{\prime }+y^{2} \left (x^{2}+1\right ) = 0
\] |
[_separable] |
✓ |
1.564 |
|
|
\[
{}x \left (-1+x \right ) y^{\prime } = \cot \left (y\right )
\] |
[_separable] |
✓ |
3.173 |
|
|
\[
{}r y^{\prime } = \frac {\left (a^{2}-r^{2}\right ) \tan \left (y\right )}{a^{2}+r^{2}}
\] |
[_separable] |
✓ |
2.054 |
|
|
\[
{}\sqrt {x^{2}+1}\, y^{\prime }+\sqrt {1+y^{2}} = 0
\] |
[_separable] |
✓ |
5.197 |
|
|
\[
{}y^{\prime } = \frac {x \left (1+y^{2}\right )}{y \left (x^{2}+1\right )}
\] |
[_separable] |
✓ |
6.479 |
|
|
\[
{}y^{2} y^{\prime } = 2+3 y^{6}
\] |
[_quadrature] |
✓ |
3.081 |
|
|
\[
{}\cos \left (y\right )^{2}+\left (1+{\mathrm e}^{-x}\right ) \sin \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
7.370 |
|
|
\[
{}y^{\prime } = \frac {x^{3} {\mathrm e}^{x^{2}}}{y \ln \left (y\right )}
\] |
[_separable] |
✓ |
2.526 |
|
|
\[
{}x \cos \left (y\right )^{2}+{\mathrm e}^{x} \tan \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
7.681 |
|
|
\[
{}x \left (1+y^{2}\right )+\left (2 y+1\right ) {\mathrm e}^{-x} y^{\prime } = 0
\] |
[_separable] |
✓ |
2.129 |
|
|
\[
{}x y^{3}+{\mathrm e}^{x^{2}} y^{\prime } = 0
\] |
[_separable] |
✓ |
3.595 |
|
|
\[
{}x \cos \left (y\right )^{2}+\tan \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
21.391 |
|
|
\[
{}x y^{3}+\left (y+1\right ) {\mathrm e}^{-x} y^{\prime } = 0
\] |
[_separable] |
✓ |
4.180 |
|
|
\[
{}y^{\prime }+\frac {x}{y}+2 = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.533 |
|
|
\[
{}x y^{\prime }-y = x \cot \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
5.935 |
|
|
\[
{}x \cos \left (\frac {y}{x}\right )^{2}-y+x y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.461 |
|
|
\[
{}x y^{\prime } = y \left (1+\ln \left (y\right )-\ln \left (x \right )\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
5.134 |
|
|
\[
{}x y+\left (x^{2}+y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
128.031 |
|
|
\[
{}\left (1-{\mathrm e}^{-\frac {y}{x}}\right ) y^{\prime }+1-\frac {y}{x} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.380 |
|
|
\[
{}x^{2}-x y+y^{2}-x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
5.978 |
|
|
\[
{}\left (3+2 x +4 y\right ) y^{\prime } = 1+x +2 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.943 |
|
|
\[
{}y^{\prime } = \frac {2 x +y-1}{x -y-2}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.946 |
|
|
\[
{}y+2 = \left (2 x +y-4\right ) y^{\prime }
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.254 |
|
|
\[
{}y^{\prime } = \sin \left (x -y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
3.999 |
|
|
\[
{}y^{\prime } = \left (x +1\right )^{2}+\left (4 y+1\right )^{2}+8 x y+1
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
26.883 |
|
|
\[
{}3 x^{2}+6 x y^{2}+\left (6 x^{2} y+4 y^{3}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.970 |
|
|
\[
{}2 x^{2}-x y^{2}-2 y+3-\left (x^{2} y+2 x \right ) y^{\prime } = 0
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.733 |
|
|
\[
{}x y^{2}+x -2 y+3+\left (x^{2} y-2 x -2 y\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.786 |
|
|
\[
{}3 y \left (x^{2}-1\right )+\left (x^{3}+8 y-3 x \right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.546 |
|
|
\[
{}x^{2}+\ln \left (y\right )+\frac {x y^{\prime }}{y} = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.623 |
|
|
\[
{}2 x \left (3 x +y-y \,{\mathrm e}^{-x^{2}}\right )+\left (x^{2}+3 y^{2}+{\mathrm e}^{-x^{2}}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
36.674 |
|
|
\[
{}3+y+2 y^{2} \sin \left (x \right )^{2}+\left (x +2 x y-y \sin \left (2 x \right )\right ) y^{\prime } = 0
\] |
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
38.778 |
|
|
\[
{}2 x y+\left (x^{2}+2 x y+y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
72.823 |
|
|
\[
{}x^{2}-\sin \left (y\right )^{2}+x \sin \left (2 y\right ) y^{\prime } = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
3.527 |
|
|
\[
{}y \left (2 x -y+2\right )+2 \left (x -y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.206 |
|
|
\[
{}4 x y+3 y^{2}-x +x \left (x +2 y\right ) y^{\prime } = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.782 |
|
|
\[
{}y+x \left (y^{2}+\ln \left (x \right )\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
2.935 |
|
|
\[
{}x^{2}+2 x +y+\left (3 x^{2} y-x \right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.680 |
|
|
\[
{}y^{2}+\left (x y+y^{2}-1\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
1.310 |
|
|
\[
{}3 x^{2}+3 y^{2}+x \left (x^{2}+3 y^{2}+6 y\right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
1.616 |
|
|
\[
{}2 y \left (x +y+2\right )+\left (y^{2}-x^{2}-4 x -1\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
3.478 |
|
|
\[
{}2+y^{2}+2 x +2 y y^{\prime } = 0
\] |
[_rational, _Bernoulli] |
✓ |
1.803 |
|
|
\[
{}2 x y^{2}-y+\left (y^{2}+x +y\right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
1.549 |
|
|
\[
{}y \left (x +y\right )+\left (x +2 y-1\right ) y^{\prime } = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.471 |
|
|
\[
{}2 x \left (x^{2}-\sin \left (y\right )+1\right )+\left (x^{2}+1\right ) \cos \left (y\right ) y^{\prime } = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
3.638 |
|
|
\[
{}x^{2}+y+y^{2}-x y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
1.736 |
|
|
\[
{}x -\sqrt {x^{2}+y^{2}}+\left (y-\sqrt {x^{2}+y^{2}}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
75.553 |
|
|
\[
{}y \sqrt {1+y^{2}}+\left (x \sqrt {1+y^{2}}-y\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
5.598 |
|
|
\[
{}y^{2}-\left (x y+x^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.707 |
|
|
\[
{}y-2 x^{3} \tan \left (\frac {y}{x}\right )-x y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘]] |
✓ |
2.679 |
|
|
\[
{}2 y^{2} x^{2}+y+\left (x^{3} y-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.927 |
|
|
\[
{}y^{2}+\left (x y+\tan \left (x y\right )\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
38.916 |
|
|
\[
{}2 x^{2} y^{4}-y+\left (4 x^{3} y^{3}-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
196.194 |
|
|
\[
{}x^{2}+y^{3}+y+\left (x^{3}+y^{2}-x \right ) y^{\prime } = 0
\] |
[_rational] |
✗ |
1.872 |
|
|
\[
{}y \left (1+y^{2}\right )+x \left (y^{2}-x +1\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.508 |
|
|
\[
{}y^{2}+\left ({\mathrm e}^{x}-y\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.318 |
|
|
\[
{}y^{2} x^{2}-2 y+\left (x^{3} y-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.675 |
|
|
\[
{}2 x^{3} y+y^{3}-\left (x^{4}+2 x y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
4.087 |
|
|
\[
{}1+y \cos \left (x \right )-\sin \left (x \right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
0.322 |
|
|
\[
{}\left (\sin \left (y\right )^{2}+x \cot \left (y\right )\right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
2.686 |
|
|
\[
{}1-\left (y-2 x y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.263 |
|
|
\[
{}1-\left (1+2 x \tan \left (y\right )\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.615 |
|
|
\[
{}\left (y^{3}+\frac {x}{y}\right ) y^{\prime } = 1
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.833 |
|
|
\[
{}1+\left (x -y^{2}\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
1.190 |
|
|
\[
{}y^{2}+\left (x y+y^{2}-1\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
1.293 |
|
|
\[
{}y = \left ({\mathrm e}^{y}+2 x y-2 x \right ) y^{\prime }
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.659 |
|
|
\[
{}\left (2 x +3\right ) y^{\prime } = y+\sqrt {2 x +3}
\] |
[_linear] |
✓ |
0.225 |
|
|
\[
{}y+\left (y^{2} {\mathrm e}^{y}-x \right ) y^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.315 |
|
|
\[
{}y^{\prime } = 1+3 y \tan \left (x \right )
\] |
[_linear] |
✓ |
0.360 |
|
|
\[
{}\left (\cos \left (x \right )+1\right ) y^{\prime } = \sin \left (x \right ) \left (\sin \left (x \right )+\sin \left (x \right ) \cos \left (x \right )-y\right )
\] |
[_linear] |
✓ |
0.356 |
|
|
\[
{}y^{\prime } = \left (\sin \left (x \right )^{2}-y\right ) \cos \left (x \right )
\] |
[_linear] |
✓ |
0.353 |
|
|
\[
{}\left (x +1\right ) y^{\prime }-y = x \left (x +1\right )^{2}
\] |
[_linear] |
✓ |
0.230 |
|
|
\[
{}1+y+\left (x -y \left (y+1\right )^{2}\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.509 |
|
|
\[
{}y^{\prime }+y^{2} = x^{2}+1
\] |
[_Riccati] |
✓ |
0.526 |
|
|
\[
{}3 x y^{\prime }-3 x y^{4} \ln \left (x \right )-y = 0
\] |
[_Bernoulli] |
✓ |
0.776 |
|
|
\[
{}y^{\prime } = \frac {4 x^{3} y^{2}}{x^{4} y+2}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
8.454 |
|
|
\[
{}y \left (6 y^{2}-x -1\right )+2 x y^{\prime } = 0
\] |
[_rational, _Bernoulli] |
✓ |
0.684 |
|
|
\[
{}\left (x +1\right ) \left (y^{\prime }+y^{2}\right )-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
0.321 |
|
|
\[
{}x y y^{\prime }+y^{2}-\sin \left (x \right ) = 0
\] |
[_Bernoulli] |
✓ |
0.658 |
|
|
\[
{}2 x^{3}-y^{4}+x y^{3} y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
0.880 |
|
|
\[
{}y^{\prime }-y \tan \left (x \right )+y^{2} \cos \left (x \right ) = 0
\] |
[_Bernoulli] |
✓ |
0.394 |
|
|
\[
{}6 y^{2}-x \left (2 x^{3}+y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
5.141 |
|
|
\[
{}x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+1 = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.581 |
|
|
\[
{}y = x y^{\prime }+{y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.420 |
|
|
\[
{}x \left ({y^{\prime }}^{2}-1\right ) = 2 y^{\prime }
\] |
[_quadrature] |
✓ |
0.217 |
|
|
\[
{}x y^{\prime } \left (y^{\prime }+2\right ) = y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
12.787 |
|
|
\[
{}x = y^{\prime } \sqrt {1+{y^{\prime }}^{2}}
\] |
[_quadrature] |
✓ |
1.111 |
|
|
\[
{}2 {y^{\prime }}^{2} \left (y-x y^{\prime }\right ) = 1
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.537 |
|
|
\[
{}y = 2 x y^{\prime }+y^{2} {y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
108.203 |
|
|
\[
{}{y^{\prime }}^{3}+y^{2} = x y y^{\prime }
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
13.088 |
|
|
\[
{}2 x y^{\prime }-y = y^{\prime } \ln \left (y y^{\prime }\right )
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.975 |
|
|
\[
{}y = x y^{\prime }-x^{2} {y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
13.098 |
|
|
\[
{}y \left (y-2 x y^{\prime }\right )^{3} = {y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
122.606 |
|
|
\[
{}x y^{\prime }+y = 4 \sqrt {y^{\prime }}
\] |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
34.067 |
|
|
\[
{}2 x y^{\prime }-y = \ln \left (y^{\prime }\right )
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
2.341 |
|
|
\[
{}x y^{2} \left (x y^{\prime }+y\right ) = 1
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.990 |
|
|
\[
{}5 y+{y^{\prime }}^{2} = x \left (x +y^{\prime }\right )
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
1.922 |
|
|
\[
{}y^{\prime } = \frac {y+2}{x +1}
\] |
[_separable] |
✓ |
1.959 |
|
|
\[
{}x y^{\prime } = y-x \,{\mathrm e}^{\frac {y}{x}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
11.723 |
|
|
\[
{}1+y^{2} \sin \left (2 x \right )-2 y \cos \left (x \right )^{2} y^{\prime } = 0
\] |
[_exact, _Bernoulli] |
✓ |
7.318 |
|