|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}2 y^{\prime } x +4 y+a +\sqrt {a^{2}-4 b -4 c y} = 0
\] |
[_separable] |
✓ |
33.053 |
|
|
\[
{}\left (1-2 x \right ) y^{\prime } = 16+32 x -6 y
\] |
[_linear] |
✓ |
8.296 |
|
|
\[
{}\left (2 x +1\right ) y^{\prime } = 4 \,{\mathrm e}^{-y}-2
\] |
[_separable] |
✓ |
7.870 |
|
|
\[
{}2 \left (1-x \right ) y^{\prime } = 4 x \sqrt {1-x}+y
\] |
[_linear] |
✓ |
3.408 |
|
|
\[
{}2 \left (x +1\right ) y^{\prime }+2 y+\left (x +1\right )^{4} y^{3} = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
12.855 |
|
|
\[
{}3 y^{\prime } x = 3 x^{{2}/{3}}+\left (1-3 y\right ) y
\] |
[_rational, _Riccati] |
✓ |
4.161 |
|
|
\[
{}3 y^{\prime } x = \left (2+x y^{3}\right ) y
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
16.071 |
|
|
\[
{}3 y^{\prime } x = \left (1+3 x y^{3} \ln \left (x \right )\right ) y
\] |
[_Bernoulli] |
✓ |
17.623 |
|
|
\[
{}x^{2} y^{\prime } = -y+a
\] |
[_separable] |
✓ |
4.088 |
|
|
\[
{}x^{2} y^{\prime } = a +b x +c \,x^{2}+y x
\] |
[_linear] |
✓ |
2.470 |
|
|
\[
{}x^{2} y^{\prime } = a +b x +c \,x^{2}-y x
\] |
[_linear] |
✓ |
2.224 |
|
|
\[
{}x^{2} y^{\prime }+\left (1-2 x \right ) y = x^{2}
\] |
[_linear] |
✓ |
3.585 |
|
|
\[
{}x^{2} y^{\prime } = a +b x y
\] |
[_linear] |
✓ |
5.301 |
|
|
\[
{}x^{2} y^{\prime } = \left (b x +a \right ) y
\] |
[_separable] |
✓ |
4.939 |
|
|
\[
{}x^{2} y^{\prime }+x \left (x +2\right ) y = x \left (1-{\mathrm e}^{-2 x}\right )-2
\] |
[_linear] |
✓ |
3.246 |
|
|
\[
{}x^{2} y^{\prime }+2 x \left (1-x \right ) y = {\mathrm e}^{x} \left (2 \,{\mathrm e}^{x}-1\right )
\] |
[_linear] |
✓ |
3.441 |
|
|
\[
{}x^{2} y^{\prime }+x^{2}+y x +y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
6.075 |
|
|
\[
{}x^{2} y^{\prime } = \left (1+2 x -y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
13.392 |
|
|
\[
{}x^{2} y^{\prime } = a +b y^{2}
\] |
[_separable] |
✓ |
5.648 |
|
|
\[
{}x^{2} y^{\prime } = \left (x +a y\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
44.988 |
|
|
\[
{}x^{2} y^{\prime } = \left (a x +b y\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
69.681 |
|
|
\[
{}x^{2} y^{\prime }+a \,x^{2}+b x y+c y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
196.333 |
|
|
\[
{}x^{2} y^{\prime } = a +b \,x^{n}+x^{2} y^{2}
\] |
[_rational, _Riccati] |
✓ |
9.651 |
|
|
\[
{}x^{2} y^{\prime }+2+x y \left (4+y x \right ) = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
6.901 |
|
|
\[
{}x^{2} y^{\prime }+2+a x \left (1-y x \right )-x^{2} y^{2} = 0
\] |
[_rational, _Riccati] |
✓ |
4.717 |
|
|
\[
{}x^{2} y^{\prime } = a +b \,x^{2} y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
11.467 |
|
|
\[
{}x^{2} y^{\prime } = a +b \,x^{n}+c \,x^{2} y^{2}
\] |
[_rational, _Riccati] |
✓ |
9.184 |
|
|
\[
{}x^{2} y^{\prime } = a +b x y+c \,x^{2} y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
12.573 |
|
|
\[
{}x^{2} y^{\prime } = a +b x y+c \,x^{4} y^{2}
\] |
[_rational, _Riccati] |
✓ |
8.566 |
|
|
\[
{}x^{2} y^{\prime }+\left (x^{2}+y^{2}-x \right ) y = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
7.049 |
|
|
\[
{}x^{2} y^{\prime } = 2 y \left (x -y^{2}\right )
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
18.630 |
|
|
\[
{}x^{2} y^{\prime } = a \,x^{2} y^{2}-a y^{3}
\] |
[_rational, _Abel] |
✗ |
0.520 |
|
|
\[
{}x^{2} y^{\prime }+a y^{2}+b \,x^{2} y^{3} = 0
\] |
[_rational, _Abel] |
✗ |
0.596 |
|
|
\[
{}x^{2} y^{\prime } = \left (a x +b y^{3}\right ) y
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
20.080 |
|
|
\[
{}x^{2} y^{\prime }+y x +\sqrt {y} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
23.981 |
|
|
\[
{}x^{2} y^{\prime } = \sec \left (y\right )+3 x \tan \left (y\right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
3.193 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = 1-x^{2}+y
\] |
[_linear] |
✓ |
2.861 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+1 = y x
\] |
[_linear] |
✓ |
2.460 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = 5-y x
\] |
[_linear] |
✓ |
8.915 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+a +y x = 0
\] |
[_linear] |
✓ |
3.218 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+a -y x = 0
\] |
[_linear] |
✓ |
10.748 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+a -y x = 0
\] |
[_linear] |
✓ |
2.872 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }-x +y x = 0
\] |
[_separable] |
✓ |
3.800 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }-x^{2}+y x = 0
\] |
[_linear] |
✓ |
2.319 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+x^{2}+y x = 0
\] |
[_linear] |
✓ |
2.286 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = x \left (x^{2}+1\right )-y x
\] |
[_linear] |
✓ |
14.488 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = x \left (3 x^{2}-y\right )
\] |
[_linear] |
✓ |
14.669 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+2 y x = 0
\] |
[_separable] |
✓ |
4.704 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = 2 x \left (x -y\right )
\] |
[_linear] |
✓ |
2.343 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = 2 x \left (x^{2}+1\right )^{2}+2 y x
\] |
[_linear] |
✓ |
4.123 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+\cos \left (x \right ) = 2 y x
\] |
[_linear] |
✓ |
9.106 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = \tan \left (x \right )-2 y x
\] |
[_linear] |
✓ |
3.250 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = a +4 y x
\] |
[_linear] |
✓ |
3.085 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = \left (2 b x +a \right ) y
\] |
[_separable] |
✓ |
7.573 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = 1+y^{2}
\] |
[_separable] |
✓ |
4.849 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = 1-y^{2}
\] |
[_separable] |
✓ |
5.375 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = 1-\left (2 x -y\right ) y
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
4.598 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = n \left (1-2 y x +y^{2}\right )
\] |
[_rational, _Riccati] |
✗ |
4.707 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x y \left (1-y\right ) = 0
\] |
[_separable] |
✓ |
11.681 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = x y \left (1+a y\right )
\] |
[_separable] |
✓ |
12.197 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = 1+y^{2}-2 x y \left (1+y^{2}\right )
\] |
[_rational, _Abel] |
✗ |
0.829 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x \sin \left (y\right ) \cos \left (y\right ) = x \left (x^{2}+1\right ) \cos \left (y\right )^{2}
\] |
[‘y=_G(x,y’)‘] |
✗ |
5.500 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = 1+x^{2}-y \,\operatorname {arccot}\left (x \right )
\] |
[_linear] |
✓ |
3.727 |
|
|
\[
{}\left (-x^{2}+4\right ) y^{\prime }+4 y = \left (x +2\right ) y^{2}
\] |
[_rational, _Bernoulli] |
✓ |
4.381 |
|
|
\[
{}\left (a^{2}+x^{2}\right ) y^{\prime } = b +y x
\] |
[_linear] |
✓ |
6.819 |
|
|
\[
{}\left (a^{2}+x^{2}\right ) y^{\prime } = \left (b +y\right ) \left (x +\sqrt {a^{2}+x^{2}}\right )
\] |
[_separable] |
✓ |
15.446 |
|
|
\[
{}\left (a^{2}+x^{2}\right ) y^{\prime }+\left (x -y\right ) y = 0
\] |
[_rational, _Bernoulli] |
✓ |
11.569 |
|
|
\[
{}\left (a^{2}+x^{2}\right ) y^{\prime } = a^{2}+3 y x -2 y^{2}
\] |
[_rational, _Riccati] |
✓ |
146.151 |
|
|
\[
{}\left (a^{2}+x^{2}\right ) y^{\prime }+y x +b x y^{2} = 0
\] |
[_separable] |
✓ |
17.037 |
|
|
\[
{}x \left (1-x \right ) y^{\prime } = a +\left (x +1\right ) y
\] |
[_linear] |
✓ |
4.828 |
|
|
\[
{}x \left (1-x \right ) y^{\prime } = 2+2 y x
\] |
[_linear] |
✓ |
2.997 |
|
|
\[
{}x \left (1-x \right ) y^{\prime } = 2 y x -2
\] |
[_linear] |
✓ |
3.214 |
|
|
\[
{}x \left (x +1\right ) y^{\prime } = \left (1-2 x \right ) y
\] |
[_separable] |
✓ |
5.332 |
|
|
\[
{}x \left (1-x \right ) y^{\prime }+\left (2 x +1\right ) y = a
\] |
[_linear] |
✓ |
1.780 |
|
|
\[
{}x \left (1-x \right ) y^{\prime } = a +2 \left (2-x \right ) y
\] |
[_linear] |
✓ |
1.313 |
|
|
\[
{}x \left (1-x \right ) y^{\prime }+2-3 y x +y = 0
\] |
[_linear] |
✓ |
1.171 |
|
|
\[
{}x \left (x +1\right ) y^{\prime } = \left (x +1\right ) \left (x^{2}-1\right )+\left (x^{2}+x -1\right ) y
\] |
[_linear] |
✓ |
1.062 |
|
|
\[
{}\left (x -2\right ) \left (x -3\right ) y^{\prime }+x^{2}-8 y+3 y x = 0
\] |
[_linear] |
✓ |
1.332 |
|
|
\[
{}x \left (x +a \right ) y^{\prime } = \left (b +c y\right ) y
\] |
[_separable] |
✓ |
3.116 |
|
|
\[
{}\left (x +a \right )^{2} y^{\prime } = 2 \left (x +a \right ) \left (b +y\right )
\] |
[_separable] |
✓ |
1.100 |
|
|
\[
{}\left (x -a \right )^{2} y^{\prime }+k \left (x +y-a \right )^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
44.287 |
|
|
\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime }+k y = 0
\] |
[_separable] |
✓ |
2.333 |
|
|
\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime } = \left (x -a \right ) \left (x -b \right )+\left (2 x -a -b \right ) y
\] |
[_linear] |
✓ |
1.825 |
|
|
\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime } = c y^{2}
\] |
[_separable] |
✓ |
2.165 |
|
|
\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime }+k \left (y-a \right ) \left (y-b \right ) = 0
\] |
[_separable] |
✓ |
36.980 |
|
|
\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime }+k \left (x +y-a \right ) \left (x +y-b \right )+y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
3.437 |
|
|
\[
{}2 x^{2} y^{\prime } = y
\] |
[_separable] |
✓ |
1.054 |
|
|
\[
{}2 x^{2} y^{\prime }+x \cot \left (x \right )-1+2 x^{2} y \cot \left (x \right ) = 0
\] |
[_linear] |
✓ |
2.303 |
|
|
\[
{}2 x^{2} y^{\prime }+1+2 y x -x^{2} y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.501 |
|
|
\[
{}2 x^{2} y^{\prime } = 2 y x +\left (1-x \cot \left (x \right )\right ) \left (x^{2}-y^{2}\right )
\] |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
52.069 |
|
|
\[
{}2 \left (-x^{2}+1\right ) y^{\prime } = \sqrt {-x^{2}+1}+\left (x +1\right ) y
\] |
[_linear] |
✓ |
3.719 |
|
|
\[
{}x \left (1-2 x \right ) y^{\prime }+1+\left (1-4 x \right ) y = 0
\] |
[_linear] |
✓ |
1.211 |
|
|
\[
{}x \left (1-2 x \right ) y^{\prime } = 4 x -\left (1+4 x \right ) y+y^{2}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
2.484 |
|
|
\[
{}2 x \left (1-x \right ) y^{\prime }+x +\left (1-2 x \right ) y = 0
\] |
[_linear] |
✓ |
1.532 |
|
|
\[
{}2 x \left (1-x \right ) y^{\prime }+x +\left (1-x \right ) y^{2} = 0
\] |
[_rational, _Riccati] |
✓ |
2.428 |
|
|
\[
{}2 \left (x^{2}+x +1\right ) y^{\prime } = 1+8 x^{2}-\left (2 x +1\right ) y
\] |
[_linear] |
✓ |
4.170 |
|
|
\[
{}4 \left (x^{2}+1\right ) y^{\prime }-4 y x -x^{2} = 0
\] |
[_linear] |
✓ |
1.513 |
|
|
\[
{}a \,x^{2} y^{\prime } = x^{2}+a x y+b^{2} y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
18.293 |
|
|
\[
{}\left (b \,x^{2}+a \right ) y^{\prime } = A +B y^{2}
\] |
[_separable] |
✓ |
3.212 |
|
|
\[
{}\left (b \,x^{2}+a \right ) y^{\prime } = c x y \ln \left (y\right )
\] |
[_separable] |
✓ |
2.534 |
|