|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = a +b y+\sqrt {\operatorname {A0} +\operatorname {B0} y}
\] |
[_quadrature] |
✓ |
78.381 |
|
|
\[
{}y^{\prime } = a x +b \sqrt {y}
\] |
[[_homogeneous, ‘class G‘], _Chini] |
✓ |
4.493 |
|
|
\[
{}y^{\prime }+x^{3} = x \sqrt {x^{4}+4 y}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
3.899 |
|
|
\[
{}y^{\prime }+2 y \left (1-x \sqrt {y}\right ) = 0
\] |
[_Bernoulli] |
✓ |
1.306 |
|
|
\[
{}y^{\prime } = \sqrt {a +b y^{2}}
\] |
[_quadrature] |
✓ |
8.455 |
|
|
\[
{}y^{\prime } = y \sqrt {a +b y}
\] |
[_quadrature] |
✓ |
119.475 |
|
|
\[
{}y^{\prime }+\left (f \left (x \right )-y\right ) g \left (x \right ) \sqrt {\left (y-a \right ) \left (y-b \right )} = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
5.625 |
|
|
\[
{}y^{\prime } = \sqrt {X Y}
\] |
[_quadrature] |
✓ |
0.437 |
|
|
\[
{}y^{\prime } = \cos \left (x \right )^{2} \cos \left (y\right )
\] |
[_separable] |
✓ |
2.479 |
|
|
\[
{}y^{\prime } = \sec \left (x \right )^{2} \cot \left (y\right ) \cos \left (y\right )
\] |
[_separable] |
✓ |
2.897 |
|
|
\[
{}y^{\prime } = a +b \cos \left (A x +B y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
36.640 |
|
|
\[
{}y^{\prime }+f \left (x \right )+g \left (x \right ) \sin \left (a y\right )+h \left (x \right ) \cos \left (a y\right ) = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
6.354 |
|
|
\[
{}y^{\prime } = a +b \cos \left (y\right )
\] |
[_quadrature] |
✓ |
37.933 |
|
|
\[
{}y^{\prime }+x \left (\sin \left (2 y\right )-x^{2} \cos \left (y\right )^{2}\right ) = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
5.098 |
|
|
\[
{}y^{\prime }+\tan \left (x \right ) \sec \left (x \right ) \cos \left (y\right )^{2} = 0
\] |
[_separable] |
✓ |
2.635 |
|
|
\[
{}y^{\prime } = \cot \left (x \right ) \cot \left (y\right )
\] |
[_separable] |
✓ |
1.977 |
|
|
\[
{}y^{\prime }+\cot \left (x \right ) \cot \left (y\right ) = 0
\] |
[_separable] |
✓ |
2.075 |
|
|
\[
{}y^{\prime } = \sin \left (x \right ) \left (\csc \left (y\right )-\cot \left (y\right )\right )
\] |
[_separable] |
✓ |
3.218 |
|
|
\[
{}y^{\prime } = \tan \left (x \right ) \cot \left (y\right )
\] |
[_separable] |
✓ |
1.858 |
|
|
\[
{}y^{\prime }+\tan \left (x \right ) \cot \left (y\right ) = 0
\] |
[_separable] |
✓ |
1.852 |
|
|
\[
{}y^{\prime }+\sin \left (2 x \right ) \csc \left (2 y\right ) = 0
\] |
[_separable] |
✓ |
6.009 |
|
|
\[
{}y^{\prime } = \tan \left (x \right ) \left (\tan \left (y\right )+\sec \left (x \right ) \sec \left (y\right )\right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
7.303 |
|
|
\[
{}y^{\prime } = \cos \left (x \right ) \sec \left (y\right )^{2}
\] |
[_separable] |
✓ |
2.124 |
|
|
\[
{}y^{\prime } = \sec \left (x \right )^{2} \sec \left (y\right )^{3}
\] |
[_separable] |
✓ |
2.095 |
|
|
\[
{}y^{\prime } = a +b \sin \left (y\right )
\] |
[_quadrature] |
✓ |
38.447 |
|
|
\[
{}y^{\prime } = \left (1+\cos \left (x \right ) \sin \left (y\right )\right ) \tan \left (y\right )
\] |
unknown |
✗ |
7.890 |
|
|
\[
{}y^{\prime }+\csc \left (2 x \right ) \sin \left (2 y\right ) = 0
\] |
[_separable] |
✓ |
5.028 |
|
|
\[
{}y^{\prime }+f \left (x \right )+g \left (x \right ) \tan \left (y\right ) = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
3.836 |
|
|
\[
{}y^{\prime } = \sqrt {a +b \cos \left (y\right )}
\] |
[_quadrature] |
✓ |
11.815 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{y}+x
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
1.389 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x +y}
\] |
[_separable] |
✓ |
2.665 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x} \left (a +b \,{\mathrm e}^{-y}\right )
\] |
[_separable] |
✓ |
1.875 |
|
|
\[
{}y \ln \left (x \right ) \ln \left (y\right )+y^{\prime } = 0
\] |
[_separable] |
✓ |
1.704 |
|
|
\[
{}y^{\prime } = x^{m -1} y^{1-n} f \left (a \,x^{m}+b y^{n}\right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
3.713 |
|
|
\[
{}y^{\prime } = a f \left (y\right )
\] |
[_quadrature] |
✓ |
1.068 |
|
|
\[
{}y^{\prime } = f \left (a +b x +c y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.138 |
|
|
\[
{}y^{\prime } = f \left (x \right ) g \left (y\right )
\] |
[_separable] |
✓ |
1.063 |
|
|
\[
{}y^{\prime } = \sec \left (x \right )^{2}+y \sec \left (x \right ) \operatorname {Csx} \left (x \right )
\] |
[_linear] |
✓ |
1.448 |
|
|
\[
{}2 y^{\prime } = 2 \sin \left (y\right )^{2} \tan \left (y\right )-x \sin \left (2 y\right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
44.194 |
|
|
\[
{}2 y^{\prime }+a x = \sqrt {a^{2} x^{2}-4 b \,x^{2}-4 c y}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
13.868 |
|
|
\[
{}3 y^{\prime } = x +\sqrt {x^{2}-3 y}
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
8.118 |
|
|
\[
{}x y^{\prime } = \sqrt {a^{2}-x^{2}}
\] |
[_quadrature] |
✓ |
0.500 |
|
|
\[
{}x y^{\prime }+x +y = 0
\] |
[_linear] |
✓ |
2.765 |
|
|
\[
{}x y^{\prime }+x^{2}-y = 0
\] |
[_linear] |
✓ |
1.607 |
|
|
\[
{}x y^{\prime } = x^{3}-y
\] |
[_linear] |
✓ |
1.504 |
|
|
\[
{}x y^{\prime } = 1+x^{3}+y
\] |
[_linear] |
✓ |
1.365 |
|
|
\[
{}x y^{\prime } = x^{m}+y
\] |
[_linear] |
✓ |
0.728 |
|
|
\[
{}x y^{\prime } = x \sin \left (x \right )-y
\] |
[_linear] |
✓ |
1.415 |
|
|
\[
{}x y^{\prime } = x^{2} \sin \left (x \right )+y
\] |
[_linear] |
✓ |
1.572 |
|
|
\[
{}x y^{\prime } = x^{n} \ln \left (x \right )-y
\] |
[_linear] |
✓ |
1.246 |
|
|
\[
{}x y^{\prime } = \sin \left (x \right )-2 y
\] |
[_linear] |
✓ |
1.493 |
|
|
\[
{}x y^{\prime } = a y
\] |
[_separable] |
✓ |
1.204 |
|
|
\[
{}x y^{\prime } = 1+x +a y
\] |
[_linear] |
✓ |
1.595 |
|
|
\[
{}x y^{\prime } = a x +b y
\] |
[_linear] |
✓ |
2.328 |
|
|
\[
{}x y^{\prime } = a \,x^{2}+b y
\] |
[_linear] |
✓ |
1.415 |
|
|
\[
{}x y^{\prime } = a +b \,x^{n}+c y
\] |
[_linear] |
✓ |
1.297 |
|
|
\[
{}x y^{\prime }+2+\left (3-x \right ) y = 0
\] |
[_linear] |
✓ |
1.290 |
|
|
\[
{}x y^{\prime }+x +\left (a x +2\right ) y = 0
\] |
[_linear] |
✓ |
1.078 |
|
|
\[
{}x y^{\prime }+\left (b x +a \right ) y = 0
\] |
[_separable] |
✓ |
1.098 |
|
|
\[
{}x y^{\prime } = x^{3}+\left (-2 x^{2}+1\right ) y
\] |
[_linear] |
✓ |
1.570 |
|
|
\[
{}x y^{\prime } = a x -\left (-b \,x^{2}+1\right ) y
\] |
[_linear] |
✓ |
1.145 |
|
|
\[
{}x y^{\prime }+x +\left (-a \,x^{2}+2\right ) y = 0
\] |
[_linear] |
✓ |
1.188 |
|
|
\[
{}x y^{\prime }+x^{2}+y^{2} = 0
\] |
[_rational, _Riccati] |
✓ |
1.155 |
|
|
\[
{}x y^{\prime } = x^{2}+y \left (y+1\right )
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
1.683 |
|
|
\[
{}x y^{\prime }-y+y^{2} = x^{{2}/{3}}
\] |
[_rational, _Riccati] |
✓ |
11.772 |
|
|
\[
{}x y^{\prime } = a +b y^{2}
\] |
[_separable] |
✓ |
1.477 |
|
|
\[
{}x y^{\prime } = a \,x^{2}+y+b y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
1.372 |
|
|
\[
{}x y^{\prime } = a \,x^{2 n}+\left (n +b y\right ) y
\] |
[_rational, _Riccati] |
✓ |
2.848 |
|
|
\[
{}x y^{\prime } = a \,x^{n}+b y+c y^{2}
\] |
[_rational, _Riccati] |
✓ |
2.379 |
|
|
\[
{}x y^{\prime } = k +a \,x^{n}+b y+c y^{2}
\] |
[_rational, _Riccati] |
✓ |
2.458 |
|
|
\[
{}x y^{\prime }+a +x y^{2} = 0
\] |
[_rational, [_Riccati, _special]] |
✓ |
1.087 |
|
|
\[
{}x y^{\prime }+\left (1-x y\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.630 |
|
|
\[
{}x y^{\prime } = \left (1-x y\right ) y
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.498 |
|
|
\[
{}x y^{\prime } = \left (1+x y\right ) y
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.480 |
|
|
\[
{}x y^{\prime } = a \,x^{3} \left (1-x y\right ) y
\] |
[_Bernoulli] |
✓ |
1.319 |
|
|
\[
{}x y^{\prime } = x^{3}+\left (2 x^{2}+1\right ) y+x y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
1.975 |
|
|
\[
{}x y^{\prime } = y \left (2 x y+1\right )
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.384 |
|
|
\[
{}x y^{\prime }+b x +\left (2+y a x \right ) y = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
2.169 |
|
|
\[
{}x y^{\prime }+\operatorname {a0} +\operatorname {a1} x +\left (\operatorname {a2} +\operatorname {a3} x y\right ) y = 0
\] |
[_rational, _Riccati] |
✓ |
6.668 |
|
|
\[
{}x y^{\prime }+a \,x^{2} y^{2}+2 y = b
\] |
[_rational, _Riccati] |
✓ |
1.514 |
|
|
\[
{}x y^{\prime }+x^{m}+\frac {\left (n -m \right ) y}{2}+x^{n} y^{2} = 0
\] |
[_rational, _Riccati] |
✓ |
2.255 |
|
|
\[
{}x y^{\prime }+\left (a +b \,x^{n} y\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.760 |
|
|
\[
{}x y^{\prime } = a \,x^{m}-b y-c \,x^{n} y^{2}
\] |
[_rational, _Riccati] |
✓ |
3.286 |
|
|
\[
{}x y^{\prime } = 2 x -y+a \,x^{n} \left (x -y\right )^{2}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Riccati] |
✓ |
3.069 |
|
|
\[
{}x y^{\prime }+\left (1-a y \ln \left (x \right )\right ) y = 0
\] |
[_Bernoulli] |
✓ |
2.145 |
|
|
\[
{}x y^{\prime } = y+\left (x^{2}-y^{2}\right ) f \left (x \right )
\] |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
2.020 |
|
|
\[
{}x y^{\prime } = y \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
4.719 |
|
|
\[
{}x y^{\prime }+y \left (1-x y^{2}\right ) = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
3.800 |
|
|
\[
{}x y^{\prime }+y = a \left (x^{2}+1\right ) y^{3}
\] |
[_rational, _Bernoulli] |
✓ |
3.021 |
|
|
\[
{}x y^{\prime } = a y+b \left (x^{2}+1\right ) y^{3}
\] |
[_rational, _Bernoulli] |
✓ |
3.674 |
|
|
\[
{}x y^{\prime }+2 y = a \,x^{2 k} y^{k}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
4.405 |
|
|
\[
{}x y^{\prime } = 4 y-4 \sqrt {y}
\] |
[_separable] |
✓ |
3.608 |
|
|
\[
{}x y^{\prime }+2 y = \sqrt {1+y^{2}}
\] |
[_separable] |
✓ |
3.556 |
|
|
\[
{}x y^{\prime } = y+\sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
8.355 |
|
|
\[
{}x y^{\prime } = y+\sqrt {x^{2}-y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
97.385 |
|
|
\[
{}x y^{\prime } = y+x \sqrt {x^{2}+y^{2}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
3.550 |
|
|
\[
{}x y^{\prime } = y-x \left (x -y\right ) \sqrt {x^{2}+y^{2}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
5.274 |
|
|
\[
{}x y^{\prime } = y+a \sqrt {y^{2}+b^{2} x^{2}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
11.652 |
|
|
\[
{}x y^{\prime }+\left (\sin \left (y\right )-3 x^{2} \cos \left (y\right )\right ) \cos \left (y\right ) = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
2.774 |
|
|
\[
{}x y^{\prime }+x -y+x \cos \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.326 |
|