|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left (x +y+2\right ) y^{\prime } = 1-x -y
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.213 |
|
|
\[
{}\left (3-x -y\right ) y^{\prime } = 1+x -3 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.608 |
|
|
\[
{}\left (3-x +y\right ) y^{\prime } = 11-4 x +3 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.872 |
|
|
\[
{}\left (y+2 x \right ) y^{\prime }+x -2 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.222 |
|
|
\[
{}\left (2 x -y+2\right ) y^{\prime }+3+6 x -3 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.041 |
|
|
\[
{}\left (3+2 x -y\right ) y^{\prime }+2 = 0
\] |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
1.827 |
|
|
\[
{}\left (4+2 x -y\right ) y^{\prime }+5+x -2 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
7.007 |
|
|
\[
{}\left (5-2 x -y\right ) y^{\prime }+4-x -2 y = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
6.343 |
|
|
\[
{}\left (1-3 x +y\right ) y^{\prime } = 2 x -2 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
16.601 |
|
|
\[
{}\left (2-3 x +y\right ) y^{\prime }+5-2 x -3 y = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
6.932 |
|
|
\[
{}\left (4 x -y\right ) y^{\prime }+2 x -5 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
8.945 |
|
|
\[
{}\left (6-4 x -y\right ) y^{\prime } = 2 x -y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.755 |
|
|
\[
{}\left (1+5 x -y\right ) y^{\prime }+5+x -5 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.314 |
|
|
\[
{}\left (a +b x +y\right ) y^{\prime }+a -b x -y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.034 |
|
|
\[
{}\left (x^{2}-y\right ) y^{\prime }+x = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
2.375 |
|
|
\[
{}\left (x^{2}-y\right ) y^{\prime } = 4 y x
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.773 |
|
|
\[
{}\left (y-\cot \left (x \right ) \csc \left (x \right )\right ) y^{\prime }+\csc \left (x \right ) \left (1+y \cos \left (x \right )\right ) y = 0
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
82.776 |
|
|
\[
{}2 y y^{\prime }+2 x +x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
4.411 |
|
|
\[
{}2 y y^{\prime } = x y^{2}+x^{3}
\] |
[_rational, _Bernoulli] |
✓ |
2.596 |
|
|
\[
{}\left (x -2 y\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.935 |
|
|
\[
{}\left (x +2 y\right ) y^{\prime }+2 x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.967 |
|
|
\[
{}\left (x -2 y\right ) y^{\prime }+2 x +y = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
7.643 |
|
|
\[
{}\left (1+x -2 y\right ) y^{\prime } = 1+2 x -y
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.483 |
|
|
\[
{}\left (1+x +2 y\right ) y^{\prime }+1-x -2 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.234 |
|
|
\[
{}\left (1+x +2 y\right ) y^{\prime }+7+x -4 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
6.210 |
|
|
\[
{}2 \left (x +y\right ) y^{\prime }+x^{2}+2 y = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.806 |
|
|
\[
{}\left (3+2 x -2 y\right ) y^{\prime } = 1+6 x -2 y
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.481 |
|
|
\[
{}\left (1-4 x -2 y\right ) y^{\prime }+2 x +y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.228 |
|
|
\[
{}\left (6 x -2 y\right ) y^{\prime } = 2+3 x -y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.299 |
|
|
\[
{}\left (19+9 x +2 y\right ) y^{\prime }+18-2 x -6 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
9.527 |
|
|
\[
{}\left (x^{3}+2 y\right ) y^{\prime } = 3 x \left (2-y x \right )
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.495 |
|
|
\[
{}\left (\tan \left (x \right ) \sec \left (x \right )-2 y\right ) y^{\prime }+\sec \left (x \right ) \left (1+2 y \sin \left (x \right )\right ) = 0
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
11.108 |
|
|
\[
{}\left (x \,{\mathrm e}^{-x}-2 y\right ) y^{\prime } = 2 x \,{\mathrm e}^{-2 x}-\left ({\mathrm e}^{-x}+x \,{\mathrm e}^{-x}-2 y\right ) y
\] |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
5.152 |
|
|
\[
{}3 y y^{\prime }+5 \cot \left (x \right ) \cot \left (y\right ) \cos \left (y\right )^{2} = 0
\] |
[_separable] |
✓ |
16.507 |
|
|
\[
{}3 \left (2-y\right ) y^{\prime }+y x = 0
\] |
[_separable] |
✓ |
2.816 |
|
|
\[
{}\left (x -3 y\right ) y^{\prime }+4+3 x -y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
8.053 |
|
|
\[
{}\left (4-x -3 y\right ) y^{\prime }+3-x -3 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.908 |
|
|
\[
{}\left (2+2 x +3 y\right ) y^{\prime } = 1-2 x -3 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.872 |
|
|
\[
{}\left (5-2 x -3 y\right ) y^{\prime }+1-2 x -3 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.841 |
|
|
\[
{}\left (1+9 x -3 y\right ) y^{\prime }+2+3 x -y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.143 |
|
|
\[
{}\left (x +4 y\right ) y^{\prime }+4 x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.491 |
|
|
\[
{}\left (3+2 x +4 y\right ) y^{\prime } = 1+x +2 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.332 |
|
|
\[
{}\left (5+2 x -4 y\right ) y^{\prime } = 3+x -2 y
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.512 |
|
|
\[
{}\left (5+3 x -4 y\right ) y^{\prime } = 2+7 x -3 y
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.581 |
|
|
\[
{}4 \left (1-x -y\right ) y^{\prime }+2-x = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
2.804 |
|
|
\[
{}\left (11-11 x -4 y\right ) y^{\prime } = 62-8 x -25 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
14.534 |
|
|
\[
{}\left (6+3 x +5 y\right ) y^{\prime } = 2+x +7 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
83.806 |
|
|
\[
{}\left (7 x +5 y\right ) y^{\prime }+10 x +8 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
9.135 |
|
|
\[
{}\left (x +4 x^{3}+5 y\right ) y^{\prime }+7 x^{3}+3 x^{2} y+4 y = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.296 |
|
|
\[
{}\left (5-x +6 y\right ) y^{\prime } = 3-x +4 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
12.152 |
|
|
\[
{}3 \left (x +2 y\right ) y^{\prime } = 1-x -2 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.461 |
|
|
\[
{}\left (7 y-3 x +3\right ) y^{\prime }+7-7 x +3 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
9.167 |
|
|
\[
{}\left (1+x +9 y\right ) y^{\prime }+1+x +5 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.006 |
|
|
\[
{}\left (8+5 x -12 y\right ) y^{\prime } = 3+2 x -5 y
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
8.829 |
|
|
\[
{}\left (140+7 x -16 y\right ) y^{\prime }+25+8 x +y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
15.071 |
|
|
\[
{}\left (3+9 x +21 y\right ) y^{\prime } = 45+7 x -5 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
12.946 |
|
|
\[
{}\left (a x +b y\right ) y^{\prime }+x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
33.847 |
|
|
\[
{}\left (a x +b y\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
11.898 |
|
|
\[
{}\left (a x +b y\right ) y^{\prime }+b x +a y = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
14.793 |
|
|
\[
{}\left (a x +b y\right ) y^{\prime } = b x +a y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
11.078 |
|
|
\[
{}x y y^{\prime }+1+y^{2} = 0
\] |
[_separable] |
✓ |
7.392 |
|
|
\[
{}x y y^{\prime } = x +y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
7.946 |
|
|
\[
{}x y y^{\prime }+x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
16.468 |
|
|
\[
{}x y y^{\prime }+x^{4}-y^{2} = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
7.872 |
|
|
\[
{}x y y^{\prime } = a \,x^{3} \cos \left (x \right )+y^{2}
\] |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
7.734 |
|
|
\[
{}x y y^{\prime } = x^{2}-y x +y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
14.224 |
|
|
\[
{}x y y^{\prime }+2 x^{2}-2 y x -y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
7.055 |
|
|
\[
{}x y y^{\prime } = a +b y^{2}
\] |
[_separable] |
✓ |
7.540 |
|
|
\[
{}x y y^{\prime } = a \,x^{n}+b y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
6.862 |
|
|
\[
{}x y y^{\prime } = \left (x^{2}+1\right ) \left (1-y^{2}\right )
\] |
[_separable] |
✓ |
5.174 |
|
|
\[
{}x y y^{\prime }+x^{2} \operatorname {arccot}\left (\frac {y}{x}\right )-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
26.875 |
|
|
\[
{}x y y^{\prime }+x^{2} {\mathrm e}^{-\frac {2 y}{x}}-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
6.402 |
|
|
\[
{}\left (y x +1\right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.120 |
|
|
\[
{}x \left (1+y\right ) y^{\prime }-\left (1-x \right ) y = 0
\] |
[_separable] |
✓ |
1.782 |
|
|
\[
{}x \left (1-y\right ) y^{\prime }+\left (x +1\right ) y = 0
\] |
[_separable] |
✓ |
3.410 |
|
|
\[
{}x \left (1-y\right ) y^{\prime }+\left (1-x \right ) y = 0
\] |
[_separable] |
✓ |
1.805 |
|
|
\[
{}x \left (2+y\right ) y^{\prime }+a x = 0
\] |
[_quadrature] |
✓ |
0.705 |
|
|
\[
{}\left (2+3 x -y x \right ) y^{\prime }+y = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.411 |
|
|
\[
{}x \left (4+y\right ) y^{\prime } = 2 x +2 y+y^{2}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
10.609 |
|
|
\[
{}x \left (a +y\right ) y^{\prime }+b x +c y = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.737 |
|
|
\[
{}x \left (a +y\right ) y^{\prime } = y \left (B x +A \right )
\] |
[_separable] |
✓ |
3.624 |
|
|
\[
{}x \left (x +y\right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
21.955 |
|
|
\[
{}x \left (x -y\right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
47.871 |
|
|
\[
{}x \left (x +y\right ) y^{\prime } = x^{2}+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
9.638 |
|
|
\[
{}x \left (x -y\right ) y^{\prime }+2 x^{2}+3 y x -y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
19.175 |
|
|
\[
{}x \left (x +y\right ) y^{\prime }-y \left (x +y\right )+x \sqrt {x^{2}-y^{2}} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
15.257 |
|
|
\[
{}\left (a +x \left (x +y\right )\right ) y^{\prime } = b \left (x +y\right ) y
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
3.062 |
|
|
\[
{}x \left (y+2 x \right ) y^{\prime } = x^{2}+y x -y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
19.205 |
|
|
\[
{}x \left (4 x -y\right ) y^{\prime }+4 x^{2}-6 y x -y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
22.183 |
|
|
\[
{}x \left (x^{3}+y\right ) y^{\prime } = \left (x^{3}-y\right ) y
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
9.875 |
|
|
\[
{}x \left (2 x^{3}+y\right ) y^{\prime } = \left (2 x^{3}-y\right ) y
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
10.304 |
|
|
\[
{}x \left (2 x^{3}+y\right ) y^{\prime } = 6 y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
11.635 |
|
|
\[
{}y \left (1-x \right ) y^{\prime }+x \left (1-y\right ) = 0
\] |
[_separable] |
✓ |
2.124 |
|
|
\[
{}\left (x +a \right ) \left (x +b \right ) y^{\prime } = y x
\] |
[_separable] |
✓ |
4.711 |
|
|
\[
{}2 x y y^{\prime }+1-2 x^{3}-y^{2} = 0
\] |
[_rational, _Bernoulli] |
✓ |
2.284 |
|
|
\[
{}2 x y y^{\prime }+a +y^{2} = 0
\] |
[_separable] |
✓ |
6.432 |
|
|
\[
{}2 x y y^{\prime } = a x +y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.677 |
|
|
\[
{}2 x y y^{\prime }+x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
12.214 |
|
|
\[
{}2 x y y^{\prime } = x^{2}+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
23.112 |
|
|
\[
{}2 x y y^{\prime } = 4 x^{2} \left (2 x +1\right )+y^{2}
\] |
[_rational, _Bernoulli] |
✓ |
10.089 |
|