|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y+x +y^{\prime } x = 0
\] |
[_linear] |
✓ |
2.434 |
|
|
\[
{}6 x -2 y+1+\left (2 y-2 x -3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.570 |
|
|
\[
{}\sec \left (x \right ) \cos \left (y\right )^{2}-\cos \left (x \right ) \sin \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
7.101 |
|
|
\[
{}\left (x +1\right ) y^{2}-x^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
1.575 |
|
|
\[
{}2 \left (1-y^{2}\right ) x y+\left (x^{2}+1\right ) \left (1+y^{2}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
21.224 |
|
|
\[
{}\sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
3.522 |
|
|
\[
{}x \,{\mathrm e}^{\frac {y}{x}}+y-y^{\prime } x = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
10.569 |
|
|
\[
{}2 x^{2} y+3 y^{3}-\left (x^{3}+2 x y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
22.274 |
|
|
\[
{}y^{2}-x y+x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.429 |
|
|
\[
{}2 x^{2} y+y^{3}-x^{3} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
88.555 |
|
|
\[
{}y^{3}+x^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
4.067 |
|
|
\[
{}x +y \cos \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
5.849 |
|
|
\[
{}4 x +3 y+1+\left (x +y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.465 |
|
|
\[
{}4 x -y+2+\left (x +y+3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.472 |
|
|
\[
{}2 x +y-\left (4 x +2 y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.969 |
|
|
\[
{}y+2 x y^{2}-x^{2} y^{3}+2 x^{2} y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.964 |
|
|
\[
{}2 y+3 x y^{2}+\left (x +2 x^{2} y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
9.149 |
|
|
\[
{}y+x y^{2}+\left (x -x^{2} y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.815 |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = \sec \left (x \right )
\] |
[_linear] |
✓ |
1.681 |
|
|
\[
{}y^{\prime } x +\left (x +1\right ) y = {\mathrm e}^{x}
\] |
[_linear] |
✓ |
1.355 |
|
|
\[
{}y^{\prime }-\frac {2 y}{x +1} = \left (x +1\right )^{3}
\] |
[_linear] |
✓ |
1.532 |
|
|
\[
{}\left (x^{3}+x \right ) y^{\prime }+4 x^{2} y = 2
\] |
[_linear] |
✓ |
1.309 |
|
|
\[
{}x^{2} y^{\prime }+\left (1-2 x \right ) y = x^{2}
\] |
[_linear] |
✓ |
1.724 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }-2 \left (x +1\right ) y = y^{{5}/{2}}
\] |
[_rational, _Bernoulli] |
✓ |
1.781 |
|
|
\[
{}y y^{\prime }+x y^{2} = x
\] |
[_separable] |
✓ |
2.043 |
|
|
\[
{}\sin \left (y\right ) y^{\prime }+\sin \left (x \right ) \cos \left (y\right ) = \sin \left (x \right )
\] |
[_separable] |
✓ |
40.056 |
|
|
\[
{}4 y^{\prime } x +3 y+{\mathrm e}^{x} x^{4} y^{5} = 0
\] |
[_Bernoulli] |
✓ |
1.725 |
|
|
\[
{}y^{\prime }-\frac {1+y}{x +1} = \sqrt {1+y}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
3.558 |
|
|
\[
{}x^{4} y \left (3 y+2 y^{\prime } x \right )+x^{2} \left (4 y+3 y^{\prime } x \right ) = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
5.897 |
|
|
\[
{}y^{2} \left (3 y-6 y^{\prime } x \right )-x \left (y-2 y^{\prime } x \right ) = 0
\] |
[_separable] |
✓ |
2.245 |
|
|
\[
{}2 x^{3} y-y^{2}-\left (2 x^{4}+x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.724 |
|
|
\[
{}y^{2}-x y+x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.395 |
|
|
\[
{}\frac {-y+y^{\prime } x}{\sqrt {x^{2}-y^{2}}} = y^{\prime } x
\] |
[‘y=_G(x,y’)‘] |
✓ |
1.942 |
|
|
\[
{}x +y-\left (x -y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.588 |
|
|
\[
{}x^{2}+y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
8.154 |
|
|
\[
{}x -y^{2}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.865 |
|
|
\[
{}-y+y^{\prime } x = x^{2}+y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
1.660 |
|
|
\[
{}3 x^{2}+6 x y+3 y^{2}+\left (2 x^{2}+3 x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
6.175 |
|
|
\[
{}2 x +\left (x^{2}+y^{2}+2 y\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.243 |
|
|
\[
{}y^{4}+2 y+\left (x y^{3}+2 y^{4}-4 x \right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.986 |
|
|
\[
{}x^{3} y-y^{4}+\left (x y^{3}-x^{4}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.633 |
|
|
\[
{}y^{2}-x^{2}+2 m x y+\left (m y^{2}-m \,x^{2}-2 x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
8.523 |
|
|
\[
{}y^{\prime } x -y+2 x^{2} y-x^{3} = 0
\] |
[_linear] |
✓ |
1.572 |
|
|
\[
{}\left (x +y\right ) y^{\prime }-1 = 0
\] |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
1.709 |
|
|
\[
{}x +y y^{\prime }+y-y^{\prime } x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.581 |
|
|
\[
{}y^{\prime } x -a y+b y^{2} = c \,x^{2 a}
\] |
[_rational, _Riccati] |
✓ |
2.749 |
|
|
\[
{}x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime } = 0
\] |
[_separable] |
✓ |
2.822 |
|
|
\[
{}\sqrt {1-y^{2}}+\sqrt {-x^{2}+1}\, y^{\prime } = 0
\] |
[_separable] |
✓ |
16.403 |
|
|
\[
{}y^{\prime }-x^{2} y = x^{5}
\] |
[_linear] |
✓ |
2.011 |
|
|
\[
{}\left (y-x \right )^{2} y^{\prime } = 1
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.612 |
|
|
\[
{}y^{\prime } x +y+x^{4} y^{4} {\mathrm e}^{x} = 0
\] |
[_Bernoulli] |
✓ |
3.412 |
|
|
\[
{}\left (1-x \right ) y+\left (1-y\right ) x y^{\prime } = 0
\] |
[_separable] |
✓ |
1.416 |
|
|
\[
{}\left (y-x \right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.015 |
|
|
\[
{}-y+y^{\prime } x = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
6.560 |
|
|
\[
{}-y+y^{\prime } x = \sqrt {x^{2}-y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
57.979 |
|
|
\[
{}x \sin \left (\frac {y}{x}\right )-y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.121 |
|
|
\[
{}x -2 y+5+\left (2 x -y+4\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.072 |
|
|
\[
{}y^{\prime }+\frac {y}{\left (-x^{2}+1\right )^{{3}/{2}}} = \frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}}
\] |
[_linear] |
✓ |
3.379 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }-x y = a x y^{2}
\] |
[_separable] |
✓ |
2.160 |
|
|
\[
{}x y^{2} \left (3 y+y^{\prime } x \right )-2 y+y^{\prime } x = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
5.063 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+y = \arctan \left (x \right )
\] |
[_linear] |
✓ |
1.968 |
|
|
\[
{}5 x y-3 y^{3}+\left (3 x^{2}-7 x y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.450 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = \frac {\sin \left (2 x \right )}{2}
\] |
[_linear] |
✓ |
2.250 |
|
|
\[
{}x y^{2}+y-y^{\prime } x = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.181 |
|
|
\[
{}\left (1-x \right ) y-\left (1+y\right ) x y^{\prime } = 0
\] |
[_separable] |
✓ |
1.356 |
|
|
\[
{}3 x^{2} y+\left (x^{3}+x^{3} y^{2}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.731 |
|
|
\[
{}\left (x^{2}+y^{2}\right ) \left (x +y y^{\prime }\right ) = \left (x^{2}+y^{2}+x \right ) \left (-y+y^{\prime } x \right )
\] |
[_rational] |
✗ |
2.868 |
|
|
\[
{}2 x +3 y-1+\left (2 x +3 y-5\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.805 |
|
|
\[
{}y^{3}-2 x^{2} y+\left (2 x y^{2}-x^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
28.628 |
|
|
\[
{}2 x^{3} y^{2}-y+\left (2 x^{2} y^{3}-x \right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
1.594 |
|
|
\[
{}\left (x^{2}+y^{2}\right ) \left (x +y y^{\prime }\right )+\sqrt {1+x^{2}+y^{2}}\, \left (y-y^{\prime } x \right ) = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.528 |
|
|
\[
{}1+{\mathrm e}^{\frac {y}{x}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
5.187 |
|
|
\[
{}y^{\prime } x +y-y^{2} \ln \left (x \right ) = 0
\] |
[_Bernoulli] |
✓ |
2.042 |
|
|
\[
{}x^{3} y^{4}+x^{2} y^{3}+x y^{2}+y+\left (x^{4} y^{3}-x^{3} y^{2}-x^{3} y+x \right ) y^{\prime } = 0
\] |
[_rational] |
✗ |
3.040 |
|
|
\[
{}\left (2 \sqrt {x y}-x \right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
93.860 |
|
|
\[
{}{y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+x y = 0
\] |
[_quadrature] |
✓ |
1.782 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }-x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.297 |
|
|
\[
{}y^{2}+{y^{\prime }}^{2} = 1
\] |
[_quadrature] |
✓ |
0.556 |
|
|
\[
{}\left (2 y^{\prime } x -y\right )^{2} = 8 x^{3}
\] |
[_linear] |
✓ |
0.558 |
|
|
\[
{}\left (x^{2}+1\right ) {y^{\prime }}^{2} = 1
\] |
[_quadrature] |
✓ |
0.224 |
|
|
\[
{}{y^{\prime }}^{3}-\left (2 x +y^{2}\right ) {y^{\prime }}^{2}+\left (x^{2}-y^{2}+2 x y^{2}\right ) y^{\prime }-\left (x^{2}-y^{2}\right ) y^{2} = 0
\] |
[_quadrature] |
✓ |
3.400 |
|
|
\[
{}2 y^{\prime } x -y+\ln \left (y^{\prime }\right ) = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
2.393 |
|
|
\[
{}4 x {y^{\prime }}^{2}+2 y^{\prime } x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.057 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }-x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.313 |
|
|
\[
{}y^{\prime }+2 x y = x^{2}+y^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
1.855 |
|
|
\[
{}y = -y^{\prime } x +x^{4} {y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.988 |
|
|
\[
{}{y^{\prime }}^{2}+2 y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.421 |
|
|
\[
{}x +y^{\prime } y \left (2 {y^{\prime }}^{2}+3\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
5.016 |
|
|
\[
{}a^{2} y {y^{\prime }}^{2}-2 y^{\prime } x +y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.394 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }-x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.279 |
|
|
\[
{}{y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
7.257 |
|
|
\[
{}\left (-y+y^{\prime } x \right )^{2} = {y^{\prime }}^{2}+1
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.547 |
|
|
\[
{}4 \,{\mathrm e}^{2 y} {y^{\prime }}^{2}+2 y^{\prime } x -1 = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
7.461 |
|
|
\[
{}4 \,{\mathrm e}^{2 y} {y^{\prime }}^{2}+2 \,{\mathrm e}^{2 x} y^{\prime }-{\mathrm e}^{2 x} = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.046 |
|
|
\[
{}{\mathrm e}^{2 y} {y^{\prime }}^{3}+\left ({\mathrm e}^{2 x}+{\mathrm e}^{3 x}\right ) y^{\prime }-{\mathrm e}^{3 x} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
299.631 |
|
|
\[
{}x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }+x = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
10.450 |
|
|
\[
{}\left (x^{2}+y^{2}\right ) \left (1+y^{\prime }\right )^{2}-2 \left (x +y\right ) \left (1+y^{\prime }\right ) \left (x +y y^{\prime }\right )+\left (x +y y^{\prime }\right )^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.037 |
|
|
\[
{}y = 2 y^{\prime } x +y^{2} {y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
107.704 |
|
|
\[
{}a^{2} y {y^{\prime }}^{2}-2 y^{\prime } x +y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.421 |
|
|
\[
{}\left (x -y^{\prime }-y\right )^{2} = x^{2} \left (2 x y-x^{2} y^{\prime }\right )
\] |
[‘y=_G(x,y’)‘] |
✓ |
80.129 |
|