|
# |
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] |
✗ |
1.342 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x \sin \left (y\right ) \cos \left (y\right ) = x \left (x^{2}+1\right ) \cos \left (y\right )^{2}
\] |
[‘y=_G(x,y’)‘] |
✗ |
17.054 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = 1+x^{2}-y \,\operatorname {arccot}\left (x \right )
\] |
[_linear] |
✓ |
2.141 |
|
|
\[
{}\left (-x^{2}+4\right ) y^{\prime }+4 y = \left (x +2\right ) y^{2}
\] |
[_rational, _Bernoulli] |
✓ |
1.469 |
|
|
\[
{}\left (a^{2}+x^{2}\right ) y^{\prime } = b +x y
\] |
[_linear] |
✓ |
1.147 |
|
|
\[
{}\left (a^{2}+x^{2}\right ) y^{\prime } = \left (b +y\right ) \left (x +\sqrt {a^{2}+x^{2}}\right )
\] |
[_separable] |
✓ |
3.873 |
|
|
\[
{}\left (a^{2}+x^{2}\right ) y^{\prime }+\left (x -y\right ) y = 0
\] |
[_rational, _Bernoulli] |
✓ |
2.286 |
|
|
\[
{}\left (a^{2}+x^{2}\right ) y^{\prime } = a^{2}+3 x y-2 y^{2}
\] |
[_rational, _Riccati] |
✓ |
159.749 |
|
|
\[
{}\left (a^{2}+x^{2}\right ) y^{\prime }+x y+b x y^{2} = 0
\] |
[_separable] |
✓ |
2.472 |
|
|
\[
{}x \left (1-x \right ) y^{\prime } = a +\left (x +1\right ) y
\] |
[_linear] |
✓ |
1.072 |
|
|
\[
{}x \left (1-x \right ) y^{\prime } = 2+2 x y
\] |
[_linear] |
✓ |
1.237 |
|
|
\[
{}x \left (1-x \right ) y^{\prime } = 2 x y-2
\] |
[_linear] |
✓ |
1.242 |
|
|
\[
{}x \left (x +1\right ) y^{\prime } = \left (1-2 x \right ) y
\] |
[_separable] |
✓ |
1.728 |
|
|
\[
{}x \left (1-x \right ) y^{\prime }+\left (2 x +1\right ) y = a
\] |
[_linear] |
✓ |
1.296 |
|
|
\[
{}x \left (1-x \right ) y^{\prime } = a +2 \left (2-x \right ) y
\] |
[_linear] |
✓ |
1.394 |
|
|
\[
{}x \left (1-x \right ) y^{\prime }+2-3 x y+y = 0
\] |
[_linear] |
✓ |
1.302 |
|
|
\[
{}x \left (x +1\right ) y^{\prime } = \left (x +1\right ) \left (x^{2}-1\right )+\left (x^{2}+x -1\right ) y
\] |
[_linear] |
✓ |
1.541 |
|
|
\[
{}\left (x -2\right ) \left (x -3\right ) y^{\prime }+x^{2}-8 y+3 x y = 0
\] |
[_linear] |
✓ |
1.537 |
|
|
\[
{}x \left (x +a \right ) y^{\prime } = \left (b +c y\right ) y
\] |
[_separable] |
✓ |
2.404 |
|
|
\[
{}\left (x +a \right )^{2} y^{\prime } = 2 \left (x +a \right ) \left (b +y\right )
\] |
[_separable] |
✓ |
1.137 |
|
|
\[
{}\left (x -a \right )^{2} y^{\prime }+k \left (x +y-a \right )^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
39.737 |
|
|
\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime }+k y = 0
\] |
[_separable] |
✓ |
2.002 |
|
|
\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime } = \left (x -a \right ) \left (x -b \right )+\left (2 x -a -b \right ) y
\] |
[_linear] |
✓ |
1.514 |
|
|
\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime } = c y^{2}
\] |
[_separable] |
✓ |
1.811 |
|
|
\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime }+k \left (y-a \right ) \left (y-b \right ) = 0
\] |
[_separable] |
✓ |
3.351 |
|
|
\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime }+k \left (x +y-a \right ) \left (x +y-b \right )+y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
2.960 |
|
|
\[
{}2 x^{2} y^{\prime } = y
\] |
[_separable] |
✓ |
1.712 |
|
|
\[
{}2 x^{2} y^{\prime }+x \cot \left (x \right )-1+2 x^{2} y \cot \left (x \right ) = 0
\] |
[_linear] |
✓ |
2.138 |
|
|
\[
{}2 x^{2} y^{\prime }+1+2 x y-x^{2} y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.787 |
|
|
\[
{}2 x^{2} y^{\prime } = 2 x y+\left (1-x \cot \left (x \right )\right ) \left (x^{2}-y^{2}\right )
\] |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
49.533 |
|
|
\[
{}2 \left (-x^{2}+1\right ) y^{\prime } = \sqrt {-x^{2}+1}+\left (x +1\right ) y
\] |
[_linear] |
✓ |
2.513 |
|
|
\[
{}x \left (1-2 x \right ) y^{\prime }+1+\left (1-4 x \right ) y = 0
\] |
[_linear] |
✓ |
1.262 |
|
|
\[
{}x \left (1-2 x \right ) y^{\prime } = 4 x -\left (1+4 x \right ) y+y^{2}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
2.311 |
|
|
\[
{}2 x \left (1-x \right ) y^{\prime }+x +\left (1-2 x \right ) y = 0
\] |
[_linear] |
✓ |
1.400 |
|
|
\[
{}2 x \left (1-x \right ) y^{\prime }+x +\left (1-x \right ) y^{2} = 0
\] |
[_rational, _Riccati] |
✓ |
2.297 |
|
|
\[
{}2 \left (x^{2}+x +1\right ) y^{\prime } = 1+8 x^{2}-\left (2 x +1\right ) y
\] |
[_linear] |
✓ |
3.986 |
|
|
\[
{}4 \left (x^{2}+1\right ) y^{\prime }-4 x y-x^{2} = 0
\] |
[_linear] |
✓ |
1.339 |
|
|
\[
{}a \,x^{2} y^{\prime } = x^{2}+y a x +b^{2} y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
14.879 |
|
|
\[
{}\left (b \,x^{2}+a \right ) y^{\prime } = A +B y^{2}
\] |
[_separable] |
✓ |
3.584 |
|
|
\[
{}\left (b \,x^{2}+a \right ) y^{\prime } = c x y \ln \left (y\right )
\] |
[_separable] |
✓ |
1.887 |
|
|
\[
{}x \left (a x +1\right ) y^{\prime }+a -y = 0
\] |
[_separable] |
✓ |
0.956 |
|
|
\[
{}\left (b x +a \right )^{2} y^{\prime }+c y^{2}+\left (b x +a \right ) y^{3} = 0
\] |
[_rational, _Abel] |
✗ |
2.069 |
|
|
\[
{}x^{3} y^{\prime } = a +b \,x^{2} y
\] |
[_linear] |
✓ |
1.052 |
|
|
\[
{}x^{3} y^{\prime } = 3-x^{2}+x^{2} y
\] |
[_linear] |
✓ |
1.320 |
|
|
\[
{}x^{3} y^{\prime } = x^{4}+y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.369 |
|
|
\[
{}x^{3} y^{\prime } = y \left (y+x^{2}\right )
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
1.926 |
|
|
\[
{}x^{3} y^{\prime } = x^{2} \left (-1+y\right )+y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
2.010 |
|
|
\[
{}x^{3} y^{\prime } = \left (x +1\right ) y^{2}
\] |
[_separable] |
✓ |
1.513 |
|
|
\[
{}x^{3} y^{\prime }+20+x^{2} y \left (1-x^{2} y\right ) = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.954 |
|
|
\[
{}x^{3} y^{\prime }+3+\left (3-2 x \right ) x^{2} y-x^{6} y^{2} = 0
\] |
[_rational, _Riccati] |
✓ |
1.713 |
|
|
\[
{}x^{3} y^{\prime } = \left (2 x^{2}+y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
87.207 |
|
|
\[
{}x^{3} y^{\prime } = \cos \left (y\right ) \left (\cos \left (y\right )-2 x^{2} \sin \left (y\right )\right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
45.719 |
|
|
\[
{}x \left (x^{2}+1\right ) y^{\prime } = a \,x^{2}+y
\] |
[_linear] |
✓ |
1.065 |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime } = a \,x^{2}+y
\] |
[_linear] |
✓ |
1.131 |
|
|
\[
{}x \left (x^{2}+1\right ) y^{\prime } = a \,x^{3}+y
\] |
[_linear] |
✓ |
1.002 |
|
|
\[
{}x \left (x^{2}+1\right ) y^{\prime } = a -x^{2} y
\] |
[_linear] |
✓ |
1.077 |
|
|
\[
{}x \left (x^{2}+1\right ) y^{\prime } = \left (-x^{2}+1\right ) y
\] |
[_separable] |
✓ |
1.763 |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime } = \left (x^{2}-x +1\right ) y
\] |
[_separable] |
✓ |
1.891 |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime } = a \,x^{3}+\left (-2 x^{2}+1\right ) y
\] |
[_linear] |
✓ |
1.096 |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime } = x^{3} \left (-x^{2}+1\right )+\left (-2 x^{2}+1\right ) y
\] |
[_linear] |
✓ |
2.827 |
|
|
\[
{}x \left (x^{2}+1\right ) y^{\prime } = 2-4 x^{2} y
\] |
[_linear] |
✓ |
1.302 |
|
|
\[
{}x \left (x^{2}+1\right ) y^{\prime } = x -\left (5 x^{2}+3\right ) y
\] |
[_linear] |
✓ |
1.347 |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime }+x^{2}+\left (-x^{2}+1\right ) y^{2} = 0
\] |
[_rational, _Riccati] |
✓ |
109.183 |
|
|
\[
{}x^{2} \left (1-x \right ) y^{\prime } = \left (2-x \right ) x y-y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.229 |
|
|
\[
{}2 x^{3} y^{\prime } = \left (x^{2}-y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
87.688 |
|
|
\[
{}2 x^{3} y^{\prime } = \left (3 x^{2}+a y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
12.907 |
|
|
\[
{}6 x^{3} y^{\prime } = 4 x^{2} y+\left (1-3 x \right ) y^{4}
\] |
[_rational, _Bernoulli] |
✓ |
2.086 |
|
|
\[
{}x \left (c \,x^{2}+b x +a \right ) y^{\prime }+x^{2}-\left (c \,x^{2}+b x +a \right ) y = y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
2.634 |
|
|
\[
{}x^{4} y^{\prime } = \left (x^{3}+y\right ) y
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
1.954 |
|
|
\[
{}x^{4} y^{\prime }+a^{2}+x^{4} y^{2} = 0
\] |
[_rational, [_Riccati, _special]] |
✓ |
2.876 |
|
|
\[
{}x^{4} y^{\prime }+x^{3} y+\csc \left (x y\right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
13.240 |
|
|
\[
{}\left (-x^{4}+1\right ) y^{\prime } = 2 x \left (1-y^{2}\right )
\] |
[_separable] |
✓ |
2.567 |
|
|
\[
{}x \left (-x^{3}+1\right ) y^{\prime } = 2 x -\left (-4 x^{3}+1\right ) y
\] |
[_linear] |
✓ |
1.316 |
|
|
\[
{}x \left (-x^{3}+1\right ) y^{\prime } = x^{2}+\left (1-2 x y\right ) y
\] |
[_rational, _Riccati] |
✓ |
1.727 |
|
|
\[
{}x^{2} \left (-x^{2}+1\right ) y^{\prime } = \left (x -3 x^{3} y\right ) y
\] |
[_rational, _Bernoulli] |
✓ |
1.424 |
|
|
\[
{}x \left (-2 x^{3}+1\right ) y^{\prime } = 2 \left (-x^{3}+1\right ) y
\] |
[_separable] |
✓ |
1.869 |
|
|
\[
{}\left (c \,x^{2}+b x +a \right )^{2} \left (y^{\prime }+y^{2}\right )+A = 0
\] |
[_rational, _Riccati] |
✓ |
3.579 |
|
|
\[
{}x^{5} y^{\prime } = 1-3 x^{4} y
\] |
[_linear] |
✓ |
1.434 |
|
|
\[
{}x \left (-x^{4}+1\right ) y^{\prime } = 2 x \left (x^{2}-y^{2}\right )+\left (-x^{4}+1\right ) y
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
2.322 |
|
|
\[
{}x^{7} y^{\prime }+5 x^{3} y^{2}+2 \left (x^{2}+1\right ) y^{3} = 0
\] |
[_rational, _Abel] |
✗ |
1.225 |
|
|
\[
{}x^{n} y^{\prime } = a +b \,x^{n -1} y
\] |
[_linear] |
✓ |
1.072 |
|
|
\[
{}x^{n} y^{\prime } = x^{2 n -1}-y^{2}
\] |
[_Riccati] |
✓ |
1.845 |
|
|
\[
{}x^{n} y^{\prime }+x^{2 n -2}+y^{2}+\left (1-n \right ) x^{n -1} = 0
\] |
[_Riccati] |
✓ |
9.482 |
|
|
\[
{}x^{n} y^{\prime } = a^{2} x^{2 n -2}+b^{2} y^{2}
\] |
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
2.624 |
|
|
\[
{}x^{n} y^{\prime } = x^{n -1} \left (a \,x^{2 n}+n y-b y^{2}\right )
\] |
[_rational, _Riccati] |
✓ |
3.396 |
|
|
\[
{}x^{k} y^{\prime } = a \,x^{m}+b y^{n}
\] |
[_Chini] |
✗ |
1.640 |
|
|
\[
{}y^{\prime } \sqrt {x^{2}+1} = 2 x -y
\] |
[_linear] |
✓ |
1.714 |
|
|
\[
{}y^{\prime } \sqrt {-x^{2}+1} = 1+y^{2}
\] |
[_separable] |
✓ |
3.041 |
|
|
\[
{}\left (x -\sqrt {x^{2}+1}\right ) y^{\prime } = y+\sqrt {1+y^{2}}
\] |
[_separable] |
✓ |
2.595 |
|
|
\[
{}y^{\prime } \sqrt {a^{2}+x^{2}}+x +y = \sqrt {a^{2}+x^{2}}
\] |
[_linear] |
✓ |
1.490 |
|
|
\[
{}y^{\prime } \sqrt {b^{2}+x^{2}} = \sqrt {y^{2}+a^{2}}
\] |
[_separable] |
✓ |
11.514 |
|
|
\[
{}y^{\prime } \sqrt {b^{2}-x^{2}} = \sqrt {a^{2}-y^{2}}
\] |
[_separable] |
✓ |
12.679 |
|
|
\[
{}x y^{\prime } \sqrt {a^{2}+x^{2}} = y \sqrt {b^{2}+y^{2}}
\] |
[_separable] |
✓ |
2.121 |
|
|
\[
{}x y^{\prime } \sqrt {-a^{2}+x^{2}} = y \sqrt {y^{2}-b^{2}}
\] |
[_separable] |
✓ |
16.789 |
|
|
\[
{}y^{\prime } \sqrt {X}+\sqrt {Y} = 0
\] |
[_quadrature] |
✓ |
0.407 |
|
|
\[
{}y^{\prime } \sqrt {X} = \sqrt {Y}
\] |
[_quadrature] |
✓ |
0.510 |
|
|
\[
{}x^{{3}/{2}} y^{\prime } = a +b \,x^{{3}/{2}} y^{2}
\] |
[_rational, [_Riccati, _special]] |
✓ |
1.735 |
|
|
\[
{}y^{\prime } \sqrt {x^{3}+1} = \sqrt {1+y^{3}}
\] |
[_separable] |
✓ |
2.185 |
|
|
\[
{}y^{\prime } \sqrt {x \left (1-x \right ) \left (-a x +1\right )} = \sqrt {y \left (1-y\right ) \left (1-a y\right )}
\] |
[_separable] |
✓ |
3.023 |
|
|
\[
{}y^{\prime } \sqrt {-x^{4}+1} = \sqrt {1-y^{4}}
\] |
[_separable] |
✓ |
2.744 |
|