# |
ODE |
CAS classification |
Solved? |
time (sec) |
\[
{}\left (x^{2}+1\right ) y^{\prime } = 1+y^{2}-2 x y \left (1+y^{2}\right )
\] |
[_rational, _Abel] |
✗ |
1.286 |
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x \sin \left (y\right ) \cos \left (y\right ) = x \left (x^{2}+1\right ) \cos \left (y\right )^{2}
\] |
[‘y=_G(x,y’)‘] |
✗ |
16.555 |
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = 1+x^{2}-y \,\operatorname {arccot}\left (x \right )
\] |
[_linear] |
✓ |
1.998 |
|
\[
{}\left (-x^{2}+4\right ) y^{\prime }+4 y = \left (x +2\right ) y^{2}
\] |
[_rational, _Bernoulli] |
✓ |
1.433 |
|
\[
{}\left (a^{2}+x^{2}\right ) y^{\prime } = b +x y
\] |
[_linear] |
✓ |
1.179 |
|
\[
{}\left (a^{2}+x^{2}\right ) y^{\prime } = \left (b +y\right ) \left (x +\sqrt {a^{2}+x^{2}}\right )
\] |
[_separable] |
✓ |
3.706 |
|
\[
{}\left (a^{2}+x^{2}\right ) y^{\prime }+\left (x -y\right ) y = 0
\] |
[_rational, _Bernoulli] |
✓ |
2.369 |
|
\[
{}\left (a^{2}+x^{2}\right ) y^{\prime } = a^{2}+3 x y-2 y^{2}
\] |
[_rational, _Riccati] |
✓ |
160.245 |
|
\[
{}\left (a^{2}+x^{2}\right ) y^{\prime }+x y+b x y^{2} = 0
\] |
[_separable] |
✓ |
2.671 |
|
\[
{}x \left (1-x \right ) y^{\prime } = a +\left (x +1\right ) y
\] |
[_linear] |
✓ |
1.098 |
|
\[
{}x \left (1-x \right ) y^{\prime } = 2+2 x y
\] |
[_linear] |
✓ |
1.107 |
|
\[
{}x \left (1-x \right ) y^{\prime } = 2 x y-2
\] |
[_linear] |
✓ |
1.098 |
|
\[
{}x \left (x +1\right ) y^{\prime } = \left (-2 x +1\right ) y
\] |
[_separable] |
✓ |
1.332 |
|
\[
{}x \left (1-x \right ) y^{\prime }+\left (2 x +1\right ) y = a
\] |
[_linear] |
✓ |
1.270 |
|
\[
{}x \left (1-x \right ) y^{\prime } = a +2 \left (2-x \right ) y
\] |
[_linear] |
✓ |
1.417 |
|
\[
{}x \left (1-x \right ) y^{\prime }+2-3 x y+y = 0
\] |
[_linear] |
✓ |
1.168 |
|
\[
{}x \left (x +1\right ) y^{\prime } = \left (x +1\right ) \left (x^{2}-1\right )+\left (x^{2}+x -1\right ) y
\] |
[_linear] |
✓ |
1.362 |
|
\[
{}\left (-2+x \right ) \left (x -3\right ) y^{\prime }+x^{2}-8 y+3 x y = 0
\] |
[_linear] |
✓ |
1.447 |
|
\[
{}x \left (x +a \right ) y^{\prime } = \left (b +c y\right ) y
\] |
[_separable] |
✓ |
2.566 |
|
\[
{}\left (x +a \right )^{2} y^{\prime } = 2 \left (x +a \right ) \left (b +y\right )
\] |
[_separable] |
✓ |
1.186 |
|
\[
{}\left (x -a \right )^{2} y^{\prime }+k \left (x +y-a \right )^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
42.557 |
|
\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime }+k y = 0
\] |
[_separable] |
✓ |
2.079 |
|
\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime } = \left (x -a \right ) \left (x -b \right )+\left (2 x -a -b \right ) y
\] |
[_linear] |
✓ |
1.554 |
|
\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime } = c y^{2}
\] |
[_separable] |
✓ |
1.789 |
|
\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime }+k \left (y-a \right ) \left (y-b \right ) = 0
\] |
[_separable] |
✓ |
3.460 |
|
\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime }+k \left (x +y-a \right ) \left (x +y-b \right )+y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
2.917 |
|
\[
{}2 x^{2} y^{\prime } = y
\] |
[_separable] |
✓ |
1.349 |
|
\[
{}2 x^{2} y^{\prime }+x \cot \left (x \right )-1+2 x^{2} y \cot \left (x \right ) = 0
\] |
[_linear] |
✓ |
1.985 |
|
\[
{}2 x^{2} y^{\prime }+1+2 x y-x^{2} y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.632 |
|
\[
{}2 x^{2} y^{\prime } = 2 x y+\left (1-x \cot \left (x \right )\right ) \left (x^{2}-y^{2}\right )
\] |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
49.634 |
|
\[
{}2 \left (-x^{2}+1\right ) y^{\prime } = \sqrt {-x^{2}+1}+\left (x +1\right ) y
\] |
[_linear] |
✓ |
2.403 |
|
\[
{}x \left (-2 x +1\right ) y^{\prime }+1+\left (1-4 x \right ) y = 0
\] |
[_linear] |
✓ |
1.138 |
|
\[
{}x \left (-2 x +1\right ) y^{\prime } = 4 x -\left (1+4 x \right ) y+y^{2}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
2.392 |
|
\[
{}2 x \left (1-x \right ) y^{\prime }+x +\left (-2 x +1\right ) y = 0
\] |
[_linear] |
✓ |
1.267 |
|
\[
{}2 x \left (1-x \right ) y^{\prime }+x +\left (1-x \right ) y^{2} = 0
\] |
[_rational, _Riccati] |
✓ |
2.185 |
|
\[
{}2 \left (x^{2}+x +1\right ) y^{\prime } = 1+8 x^{2}-\left (2 x +1\right ) y
\] |
[_linear] |
✓ |
3.825 |
|
\[
{}4 \left (x^{2}+1\right ) y^{\prime }-4 x y-x^{2} = 0
\] |
[_linear] |
✓ |
1.172 |
|
\[
{}a \,x^{2} y^{\prime } = x^{2}+a x y+b^{2} y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
23.751 |
|
\[
{}\left (b \,x^{2}+a \right ) y^{\prime } = A +B y^{2}
\] |
[_separable] |
✓ |
2.505 |
|
\[
{}\left (b \,x^{2}+a \right ) y^{\prime } = c x y \ln \left (y\right )
\] |
[_separable] |
✓ |
1.937 |
|
\[
{}x \left (a x +1\right ) y^{\prime }+a -y = 0
\] |
[_separable] |
✓ |
0.990 |
|
\[
{}\left (b x +a \right )^{2} y^{\prime }+c y^{2}+\left (b x +a \right ) y^{3} = 0
\] |
[_rational, _Abel] |
✗ |
1.974 |
|
\[
{}x^{3} y^{\prime } = a +b \,x^{2} y
\] |
[_linear] |
✓ |
1.161 |
|
\[
{}x^{3} y^{\prime } = 3-x^{2}+x^{2} y
\] |
[_linear] |
✓ |
1.018 |
|
\[
{}x^{3} y^{\prime } = x^{4}+y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.158 |
|
\[
{}x^{3} y^{\prime } = y \left (y+x^{2}\right )
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
1.727 |
|
\[
{}x^{3} y^{\prime } = x^{2} \left (y-1\right )+y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
2.105 |
|
\[
{}x^{3} y^{\prime } = \left (x +1\right ) y^{2}
\] |
[_separable] |
✓ |
1.322 |
|
\[
{}x^{3} y^{\prime }+20+x^{2} y \left (1-x^{2} y\right ) = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.899 |
|
\[
{}x^{3} y^{\prime }+3+\left (3-2 x \right ) x^{2} y-x^{6} y^{2} = 0
\] |
[_rational, _Riccati] |
✓ |
1.753 |
|
\[
{}x^{3} y^{\prime } = \left (2 x^{2}+y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
92.586 |
|
\[
{}x^{3} y^{\prime } = \cos \left (y\right ) \left (\cos \left (y\right )-2 x^{2} \sin \left (y\right )\right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
45.219 |
|
\[
{}x \left (x^{2}+1\right ) y^{\prime } = a \,x^{2}+y
\] |
[_linear] |
✓ |
1.105 |
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime } = a \,x^{2}+y
\] |
[_linear] |
✓ |
1.168 |
|
\[
{}x \left (x^{2}+1\right ) y^{\prime } = a \,x^{3}+y
\] |
[_linear] |
✓ |
1.044 |
|
\[
{}x \left (x^{2}+1\right ) y^{\prime } = a -x^{2} y
\] |
[_linear] |
✓ |
1.114 |
|
\[
{}x \left (x^{2}+1\right ) y^{\prime } = \left (-x^{2}+1\right ) y
\] |
[_separable] |
✓ |
1.382 |
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime } = \left (x^{2}-x +1\right ) y
\] |
[_separable] |
✓ |
1.521 |
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime } = a \,x^{3}+\left (-2 x^{2}+1\right ) y
\] |
[_linear] |
✓ |
1.142 |
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime } = x^{3} \left (-x^{2}+1\right )+\left (-2 x^{2}+1\right ) y
\] |
[_linear] |
✓ |
2.648 |
|
\[
{}x \left (x^{2}+1\right ) y^{\prime } = 2-4 x^{2} y
\] |
[_linear] |
✓ |
1.174 |
|
\[
{}x \left (x^{2}+1\right ) y^{\prime } = x -\left (5 x^{2}+3\right ) y
\] |
[_linear] |
✓ |
1.217 |
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime }+x^{2}+\left (-x^{2}+1\right ) y^{2} = 0
\] |
[_rational, _Riccati] |
✓ |
108.021 |
|
\[
{}x^{2} \left (1-x \right ) y^{\prime } = \left (2-x \right ) x y-y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.034 |
|
\[
{}2 x^{3} y^{\prime } = \left (x^{2}-y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
89.667 |
|
\[
{}2 x^{3} y^{\prime } = \left (3 x^{2}+y^{2} a \right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
14.138 |
|
\[
{}6 x^{3} y^{\prime } = 4 x^{2} y+\left (1-3 x \right ) y^{4}
\] |
[_rational, _Bernoulli] |
✓ |
2.119 |
|
\[
{}x \left (c \,x^{2}+b x +a \right ) y^{\prime }+x^{2}-\left (c \,x^{2}+b x +a \right ) y = y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
2.731 |
|
\[
{}x^{4} y^{\prime } = \left (x^{3}+y\right ) y
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
1.747 |
|
\[
{}x^{4} y^{\prime }+a^{2}+x^{4} y^{2} = 0
\] |
[_rational, [_Riccati, _special]] |
✓ |
2.958 |
|
\[
{}x^{4} y^{\prime }+x^{3} y+\csc \left (x y\right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
12.951 |
|
\[
{}\left (-x^{4}+1\right ) y^{\prime } = 2 x \left (1-y^{2}\right )
\] |
[_separable] |
✓ |
2.381 |
|
\[
{}x \left (-x^{3}+1\right ) y^{\prime } = 2 x -\left (-4 x^{3}+1\right ) y
\] |
[_linear] |
✓ |
1.214 |
|
\[
{}x \left (-x^{3}+1\right ) y^{\prime } = x^{2}+\left (1-2 x y\right ) y
\] |
[_rational, _Riccati] |
✓ |
1.690 |
|
\[
{}x^{2} \left (-x^{2}+1\right ) y^{\prime } = \left (x -3 x^{3} y\right ) y
\] |
[_rational, _Bernoulli] |
✓ |
1.373 |
|
\[
{}x \left (-2 x^{3}+1\right ) y^{\prime } = 2 \left (-x^{3}+1\right ) y
\] |
[_separable] |
✓ |
1.495 |
|
\[
{}\left (c \,x^{2}+b x +a \right )^{2} \left (y^{\prime }+y^{2}\right )+A = 0
\] |
[_rational, _Riccati] |
✓ |
3.735 |
|
\[
{}x^{5} y^{\prime } = 1-3 x^{4} y
\] |
[_linear] |
✓ |
1.220 |
|
\[
{}x \left (-x^{4}+1\right ) y^{\prime } = 2 x \left (x^{2}-y^{2}\right )+\left (-x^{4}+1\right ) y
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
2.195 |
|
\[
{}x^{7} y^{\prime }+5 x^{3} y^{2}+2 \left (x^{2}+1\right ) y^{3} = 0
\] |
[_rational, _Abel] |
✗ |
1.246 |
|
\[
{}x^{n} y^{\prime } = a +b \,x^{n -1} y
\] |
[_linear] |
✓ |
1.163 |
|
\[
{}x^{n} y^{\prime } = x^{2 n -1}-y^{2}
\] |
[_Riccati] |
✓ |
1.883 |
|
\[
{}x^{n} y^{\prime }+x^{-2+2 n}+y^{2}+\left (1-n \right ) x^{n -1} = 0
\] |
[_Riccati] |
✓ |
9.745 |
|
\[
{}x^{n} y^{\prime } = a^{2} x^{-2+2 n}+b^{2} y^{2}
\] |
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
4.224 |
|
\[
{}x^{n} y^{\prime } = x^{n -1} \left (a \,x^{2 n}+n y-b y^{2}\right )
\] |
[_rational, _Riccati] |
✓ |
2.495 |
|
\[
{}x^{k} y^{\prime } = a \,x^{m}+b y^{n}
\] |
[_Chini] |
✗ |
1.643 |
|
\[
{}y^{\prime } \sqrt {x^{2}+1} = 2 x -y
\] |
[_linear] |
✓ |
1.558 |
|
\[
{}y^{\prime } \sqrt {-x^{2}+1} = 1+y^{2}
\] |
[_separable] |
✓ |
2.983 |
|
\[
{}\left (x -\sqrt {x^{2}+1}\right ) y^{\prime } = y+\sqrt {1+y^{2}}
\] |
[_separable] |
✓ |
2.543 |
|
\[
{}y^{\prime } \sqrt {a^{2}+x^{2}}+x +y = \sqrt {a^{2}+x^{2}}
\] |
[_linear] |
✓ |
1.520 |
|
\[
{}y^{\prime } \sqrt {b^{2}+x^{2}} = \sqrt {y^{2}+a^{2}}
\] |
[_separable] |
✓ |
13.111 |
|
\[
{}y^{\prime } \sqrt {b^{2}-x^{2}} = \sqrt {a^{2}-y^{2}}
\] |
[_separable] |
✓ |
13.316 |
|
\[
{}x y^{\prime } \sqrt {a^{2}+x^{2}} = y \sqrt {b^{2}+y^{2}}
\] |
[_separable] |
✓ |
2.165 |
|
\[
{}x y^{\prime } \sqrt {-a^{2}+x^{2}} = y \sqrt {y^{2}-b^{2}}
\] |
[_separable] |
✓ |
21.060 |
|
\[
{}y^{\prime } \sqrt {X}+\sqrt {Y} = 0
\] |
[_quadrature] |
✓ |
0.406 |
|
\[
{}y^{\prime } \sqrt {X} = \sqrt {Y}
\] |
[_quadrature] |
✓ |
0.408 |
|
\[
{}x^{{3}/{2}} y^{\prime } = a +b \,x^{{3}/{2}} y^{2}
\] |
[_rational, [_Riccati, _special]] |
✓ |
1.779 |
|
\[
{}y^{\prime } \sqrt {x^{3}+1} = \sqrt {y^{3}+1}
\] |
[_separable] |
✓ |
2.131 |
|
\[
{}y^{\prime } \sqrt {x \left (1-x \right ) \left (-a x +1\right )} = \sqrt {y \left (1-y\right ) \left (1-a y\right )}
\] |
[_separable] |
✓ |
3.080 |
|
\[
{}y^{\prime } \sqrt {-x^{4}+1} = \sqrt {1-y^{4}}
\] |
[_separable] |
✓ |
2.706 |
|