|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}2 x y y^{\prime }+x^{2} \left (a \,x^{3}+1\right ) = 6 y^{2}
\] |
[_rational, _Bernoulli] |
✓ |
4.543 |
|
|
\[
{}\left (3-x +2 y x \right ) y^{\prime }+3 x^{2}-y+y^{2} = 0
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.077 |
|
|
\[
{}x \left (x -2 y\right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
32.533 |
|
|
\[
{}x \left (x +2 y\right ) y^{\prime }+\left (2 x -y\right ) y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
92.453 |
|
|
\[
{}x \left (x -2 y\right ) y^{\prime }+\left (2 x -y\right ) y = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
15.019 |
|
|
\[
{}x \left (1+x -2 y\right ) y^{\prime }+\left (1-2 x +y\right ) y = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.569 |
|
|
\[
{}x \left (1-x -2 y\right ) y^{\prime }+\left (2 x +y+1\right ) y = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.102 |
|
|
\[
{}2 x \left (2 x^{2}+y\right ) y^{\prime }+\left (12 x^{2}+y\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
10.954 |
|
|
\[
{}2 \left (x +1\right ) y y^{\prime }+2 x -3 x^{2}+y^{2} = 0
\] |
[_exact, _rational, _Bernoulli] |
✓ |
2.552 |
|
|
\[
{}x \left (2 x +3 y\right ) y^{\prime } = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
14.414 |
|
|
\[
{}x \left (2 x +3 y\right ) y^{\prime }+3 \left (x +y\right )^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
22.793 |
|
|
\[
{}\left (3+6 y x +x^{2}\right ) y^{\prime }+2 x +2 y x +3 y^{2} = 0
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.043 |
|
|
\[
{}3 x \left (x +2 y\right ) y^{\prime }+x^{3}+3 y \left (y+2 x \right ) = 0
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.699 |
|
|
\[
{}a x y y^{\prime } = x^{2}+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
22.709 |
|
|
\[
{}a x y y^{\prime }+x^{2}-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
19.437 |
|
|
\[
{}x \left (a +b y\right ) y^{\prime } = c y
\] |
[_separable] |
✓ |
6.082 |
|
|
\[
{}x \left (x -a y\right ) y^{\prime } = y \left (y-a x \right )
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
22.947 |
|
|
\[
{}x \left (x^{n}+a y\right ) y^{\prime }+\left (b +c y\right ) y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
14.276 |
|
|
\[
{}\left (1-x^{2} y\right ) y^{\prime }+1-x y^{2} = 0
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.902 |
|
|
\[
{}\left (1-x^{2} y\right ) y^{\prime }-1+x y^{2} = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
0.952 |
|
|
\[
{}x \left (1-y x \right ) y^{\prime }+\left (y x +1\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.891 |
|
|
\[
{}x \left (2+y x \right ) y^{\prime } = 3+2 x^{3}-2 y-x y^{2}
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.952 |
|
|
\[
{}x \left (2-y x \right ) y^{\prime }+2 y-x y^{2} \left (y x +1\right ) = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
5.747 |
|
|
\[
{}x \left (3-y x \right ) y^{\prime } = y \left (y x -1\right )
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.918 |
|
|
\[
{}x^{2} \left (1-y\right ) y^{\prime }+\left (1-x \right ) y = 0
\] |
[_separable] |
✓ |
4.186 |
|
|
\[
{}x^{2} \left (1-y\right ) y^{\prime }+\left (x +1\right ) y^{2} = 0
\] |
[_separable] |
✓ |
2.558 |
|
|
\[
{}\left (x^{2}+1\right ) y y^{\prime }+x \left (1-y^{2}\right ) = 0
\] |
[_separable] |
✓ |
6.821 |
|
|
\[
{}\left (-x^{2}+1\right ) y y^{\prime }+2 x^{2}+x y^{2} = 0
\] |
[_rational, _Bernoulli] |
✓ |
2.362 |
|
|
\[
{}2 x^{2} y y^{\prime } = x^{2} \left (2 x +1\right )-y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
6.075 |
|
|
\[
{}x \left (1-2 y x \right ) y^{\prime }+y \left (2 y x +1\right ) = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.888 |
|
|
\[
{}x \left (2 y x +1\right ) y^{\prime }+\left (2+3 y x \right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
22.898 |
|
|
\[
{}x \left (2 y x +1\right ) y^{\prime }+\left (1+2 y x -x^{2} y^{2}\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
6.749 |
|
|
\[
{}x^{2} \left (x -2 y\right ) y^{\prime } = 2 x^{3}-4 x y^{2}+y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
88.178 |
|
|
\[
{}2 \left (x +1\right ) x y y^{\prime } = 1+y^{2}
\] |
[_separable] |
✓ |
5.029 |
|
|
\[
{}3 x^{2} y y^{\prime }+1+2 x y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
6.894 |
|
|
\[
{}x^{2} \left (4 x -3 y\right ) y^{\prime } = \left (6 x^{2}-3 y x +2 y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
33.823 |
|
|
\[
{}\left (1-x^{3} y\right ) y^{\prime } = x^{2} y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
7.690 |
|
|
\[
{}2 x^{3} y y^{\prime }+a +3 x^{2} y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
5.109 |
|
|
\[
{}x \left (3-2 x^{2} y\right ) y^{\prime } = 4 x -3 y+3 x^{2} y^{2}
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.786 |
|
|
\[
{}x \left (3+2 x^{2} y\right ) y^{\prime }+\left (4+3 x^{2} y\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
17.260 |
|
|
\[
{}8 x^{3} y y^{\prime }+3 x^{4}-6 x^{2} y^{2}-y^{4} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
23.367 |
|
|
\[
{}x y \left (b \,x^{2}+a \right ) y^{\prime } = A +B y^{2}
\] |
[_separable] |
✓ |
9.248 |
|
|
\[
{}3 x^{4} y y^{\prime } = 1-2 x^{3} y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
8.851 |
|
|
\[
{}x^{7} y y^{\prime } = 2 x^{2}+2+5 x^{3} y
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
0.505 |
|
|
\[
{}y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}} = 0
\] |
[_separable] |
✓ |
6.817 |
|
|
\[
{}\left (1+y\right ) y^{\prime } \sqrt {x^{2}+1} = y^{3}
\] |
[_separable] |
✓ |
7.336 |
|
|
\[
{}\left (\operatorname {g0} \left (x \right )+y \operatorname {g1} \left (x \right )\right ) y^{\prime } = \operatorname {f0} \left (x \right )+\operatorname {f1} \left (x \right ) y+\operatorname {f2} \left (x \right ) y^{2}+\operatorname {f3} \left (x \right ) y^{3}
\] |
[[_Abel, ‘2nd type‘, ‘class C‘]] |
✗ |
4.457 |
|
|
\[
{}y^{2} y^{\prime }+x \left (2-y\right ) = 0
\] |
[_separable] |
✓ |
4.861 |
|
|
\[
{}y^{2} y^{\prime } = x \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
1.603 |
|
|
\[
{}\left (x +y^{2}\right ) y^{\prime }+y = b x +a
\] |
[_exact, _rational] |
✓ |
1.866 |
|
|
\[
{}\left (x -y^{2}\right ) y^{\prime } = x^{2}-y
\] |
[_exact, _rational] |
✓ |
1.518 |
|
|
\[
{}\left (x^{2}+y^{2}\right ) y^{\prime }+y x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
28.065 |
|
|
\[
{}\left (x^{2}+y^{2}\right ) y^{\prime } = y x
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
8.602 |
|
|
\[
{}\left (x^{2}-y^{2}\right ) y^{\prime } = 2 y x
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
15.517 |
|
|
\[
{}\left (x^{2}-y^{2}\right ) y^{\prime }+x \left (x +2 y\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
288.767 |
|
|
\[
{}\left (x^{2}+y^{2}\right ) y^{\prime }+2 x \left (y+2 x \right ) = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
17.722 |
|
|
\[
{}\left (1-x^{2}+y^{2}\right ) y^{\prime } = 1+x^{2}-y^{2}
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
1.536 |
|
|
\[
{}\left (a^{2}+x^{2}+y^{2}\right ) y^{\prime }+2 y x = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.666 |
|
|
\[
{}\left (a^{2}+x^{2}+y^{2}\right ) y^{\prime }+b^{2}+x^{2}+2 y x = 0
\] |
[_exact, _rational] |
✓ |
4.608 |
|
|
\[
{}\left (x +x^{2}+y^{2}\right ) y^{\prime } = y
\] |
[_rational] |
✓ |
2.280 |
|
|
\[
{}\left (3 x^{2}-y^{2}\right ) y^{\prime } = 2 y x
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
13.406 |
|
|
\[
{}\left (x^{4}+y^{2}\right ) y^{\prime } = 4 x^{3} y
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
8.049 |
|
|
\[
{}y \left (1+y\right ) y^{\prime } = \left (x +1\right ) x
\] |
[_separable] |
✓ |
2.684 |
|
|
\[
{}\left (x +2 y+y^{2}\right ) y^{\prime }+y \left (1+y\right )+\left (x +y\right )^{2} y^{2} = 0
\] |
[_rational] |
✗ |
1.470 |
|
|
\[
{}\left (x^{2}+2 y+y^{2}\right ) y^{\prime }+2 x = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.698 |
|
|
\[
{}\left (x^{3}+2 y-y^{2}\right ) y^{\prime }+3 x^{2} y = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.648 |
|
|
\[
{}\left (1+y+y x +y^{2}\right ) y^{\prime }+1+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
5.317 |
|
|
\[
{}\left (x +y\right )^{2} y^{\prime } = a^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
19.681 |
|
|
\[
{}\left (x -y\right )^{2} y^{\prime } = a^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
11.515 |
|
|
\[
{}\left (x^{2}+2 y x -y^{2}\right ) y^{\prime }+x^{2}-2 y x +y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
16.454 |
|
|
\[
{}\left (x +y\right )^{2} y^{\prime } = x^{2}-2 y x +5 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
23.621 |
|
|
\[
{}\left (a +b +x +y\right )^{2} y^{\prime } = 2 \left (a +y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
11.173 |
|
|
\[
{}\left (2 x^{2}+4 y x -y^{2}\right ) y^{\prime } = x^{2}-4 y x -2 y^{2}
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
19.269 |
|
|
\[
{}\left (3 x +y\right )^{2} y^{\prime } = 4 \left (3 x +2 y\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
36.358 |
|
|
\[
{}\left (1-3 x -y\right )^{2} y^{\prime } = \left (1-2 y\right ) \left (3-6 x -4 y\right )
\] |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
7.243 |
|
|
\[
{}\left (\cot \left (x \right )-2 y^{2}\right ) y^{\prime } = y^{3} \csc \left (x \right ) \sec \left (x \right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
89.675 |
|
|
\[
{}3 y^{2} y^{\prime } = 1+x +a y^{3}
\] |
[_rational, _Bernoulli] |
✓ |
3.547 |
|
|
\[
{}\left (x^{2}-3 y^{2}\right ) y^{\prime }+1+2 y x = 0
\] |
[_exact, _rational] |
✓ |
1.530 |
|
|
\[
{}\left (2 x^{2}+3 y^{2}\right ) y^{\prime }+x \left (3 x +y\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
17.757 |
|
|
\[
{}3 \left (x^{2}-y^{2}\right ) y^{\prime }+3 \,{\mathrm e}^{x}+6 x y \left (x +1\right )-2 y^{3} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
3.187 |
|
|
\[
{}\left (3 x^{2}+2 y x +4 y^{2}\right ) y^{\prime }+2 x^{2}+6 y x +y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
23.220 |
|
|
\[
{}\left (1-3 x +2 y\right )^{2} y^{\prime } = \left (4+2 x -3 y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
47.427 |
|
|
\[
{}\left (1-3 x^{2} y+6 y^{2}\right ) y^{\prime }+x^{2}-3 x y^{2} = 0
\] |
[_exact, _rational] |
✓ |
5.496 |
|
|
\[
{}\left (x -6 y\right )^{2} y^{\prime }+a +2 y x -6 y^{2} = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
3.576 |
|
|
\[
{}\left (x^{2}+a y^{2}\right ) y^{\prime } = y x
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
9.675 |
|
|
\[
{}\left (x^{2}+y x +a y^{2}\right ) y^{\prime } = a \,x^{2}+y x +y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
53.491 |
|
|
\[
{}\left (a \,x^{2}+2 y x -a y^{2}\right ) y^{\prime }+x^{2}-2 a x y-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
33.819 |
|
|
\[
{}\left (a \,x^{2}+2 b x y+c y^{2}\right ) y^{\prime }+k \,x^{2}+2 a x y+b y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
812.516 |
|
|
\[
{}x \left (1-y^{2}\right ) y^{\prime } = \left (x^{2}+1\right ) y
\] |
[_separable] |
✓ |
2.999 |
|
|
\[
{}x \left (3 x -y^{2}\right ) y^{\prime }+\left (5 x -2 y^{2}\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
23.054 |
|
|
\[
{}x \left (x^{2}+y^{2}\right ) y^{\prime } = \left (x^{2}+x^{4}+y^{2}\right ) y
\] |
[[_homogeneous, ‘class D‘], _rational] |
✓ |
3.256 |
|
|
\[
{}x \left (1-x^{2}+y^{2}\right ) y^{\prime }+\left (1+x^{2}-y^{2}\right ) y = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
11.141 |
|
|
\[
{}x \left (a -x^{2}-y^{2}\right ) y^{\prime }+\left (a +x^{2}+y^{2}\right ) y = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
12.996 |
|
|
\[
{}x \left (2 x^{2}+y^{2}\right ) y^{\prime } = \left (2 x^{2}+3 y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
63.655 |
|
|
\[
{}\left (x \left (a -x^{2}-y^{2}\right )+y\right ) y^{\prime }+x -\left (a -x^{2}-y^{2}\right ) y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
6.052 |
|
|
\[
{}x \left (a +y\right )^{2} y^{\prime } = b y^{2}
\] |
[_separable] |
✓ |
8.224 |
|
|
\[
{}x \left (x^{2}-y x +y^{2}\right ) y^{\prime }+\left (x^{2}+y x +y^{2}\right ) y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
134.362 |
|
|
\[
{}x \left (x^{2}-y x -y^{2}\right ) y^{\prime } = \left (x^{2}+y x -y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
124.980 |
|
|
\[
{}x \left (x^{2}+a x y+y^{2}\right ) y^{\prime } = \left (x^{2}+b x y+y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
350.796 |
|
|
\[
{}x \left (x^{2}-2 y^{2}\right ) y^{\prime } = \left (2 x^{2}-y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
92.563 |
|