|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = 2+2 \sec \left (2 x \right )+2 y \tan \left (2 x \right )
\] |
[_linear] |
✓ |
22.519 |
|
|
\[
{}y^{\prime } = \csc \left (x \right )+3 y \tan \left (x \right )
\] |
[_linear] |
✓ |
4.928 |
|
|
\[
{}y^{\prime } = \left (a +\cos \left (\ln \left (x \right )\right )+\sin \left (\ln \left (x \right )\right )\right ) y
\] |
[_separable] |
✓ |
14.214 |
|
|
\[
{}y^{\prime } = 6 \,{\mathrm e}^{2 x}-y \tanh \left (x \right )
\] |
[_linear] |
✓ |
4.577 |
|
|
\[
{}y^{\prime } = f \left (x \right ) f^{\prime }\left (x \right )+f^{\prime }\left (x \right ) y
\] |
[_linear] |
✓ |
10.483 |
|
|
\[
{}y^{\prime } = f \left (x \right )+g \left (x \right ) y
\] |
[_linear] |
✓ |
3.233 |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
[_Riccati] |
✓ |
2.010 |
|
|
\[
{}y^{\prime }+f \left (x \right )^{2} = f^{\prime }\left (x \right )+y^{2}
\] |
[_Riccati] |
✓ |
2.734 |
|
|
\[
{}y^{\prime }+1-x = y \left (x +y\right )
\] |
[_Riccati] |
✓ |
10.964 |
|
|
\[
{}y^{\prime } = \left (x +y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
2.194 |
|
|
\[
{}y^{\prime } = \left (x -y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
5.769 |
|
|
\[
{}y^{\prime } = 3-3 x +3 y+\left (x -y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
19.809 |
|
|
\[
{}y^{\prime } = 2 x -\left (x^{2}+1\right ) y+y^{2}
\] |
[_Riccati] |
✓ |
11.079 |
|
|
\[
{}y^{\prime } = x \left (x^{3}+2\right )-\left (2 x^{2}-y\right ) y
\] |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
2.008 |
|
|
\[
{}y^{\prime } = 1+x \left (-x^{3}+2\right )+\left (2 x^{2}-y\right ) y
\] |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
5.166 |
|
|
\[
{}y^{\prime } = \cos \left (x \right )-\left (\sin \left (x \right )-y\right ) y
\] |
[_Riccati] |
✓ |
13.834 |
|
|
\[
{}y^{\prime } = \cos \left (2 x \right )+\left (\sin \left (2 x \right )+y\right ) y
\] |
[_Riccati] |
✓ |
29.244 |
|
|
\[
{}y^{\prime } = f \left (x \right )+x f \left (x \right ) y+y^{2}
\] |
[_Riccati] |
✓ |
4.132 |
|
|
\[
{}y^{\prime } = \left (3+x -4 y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
21.865 |
|
|
\[
{}y^{\prime } = \left (1+4 x +9 y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
67.198 |
|
|
\[
{}y^{\prime } = 3 a +3 b x +3 b y^{2}
\] |
[_Riccati] |
✓ |
12.402 |
|
|
\[
{}y^{\prime } = a +b y^{2}
\] |
[_quadrature] |
✓ |
3.592 |
|
|
\[
{}y^{\prime } = a x +b y^{2}
\] |
[[_Riccati, _special]] |
✓ |
2.296 |
|
|
\[
{}y^{\prime } = a +b x +c y^{2}
\] |
[_Riccati] |
✓ |
2.923 |
|
|
\[
{}y^{\prime } = a \,x^{n -1}+b \,x^{2 n}+c y^{2}
\] |
[_Riccati] |
✗ |
225.848 |
|
|
\[
{}y^{\prime } = a \,x^{2}+b y^{2}
\] |
[[_Riccati, _special]] |
✓ |
4.509 |
|
|
\[
{}y^{\prime } = \operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2}
\] |
[_quadrature] |
✓ |
3.756 |
|
|
\[
{}y^{\prime } = f \left (x \right )+a y+b y^{2}
\] |
[_Riccati] |
✗ |
0.594 |
|
|
\[
{}y^{\prime } = 1+a \left (x -y\right ) y
\] |
[_Riccati] |
✓ |
2.774 |
|
|
\[
{}y^{\prime } = f \left (x \right )+g \left (x \right ) y+a y^{2}
\] |
[_Riccati] |
✗ |
0.798 |
|
|
\[
{}y^{\prime } = x y \left (3+y\right )
\] |
[_separable] |
✓ |
13.559 |
|
|
\[
{}y^{\prime } = 1-x -x^{3}+\left (2 x^{2}+1\right ) y-x y^{2}
\] |
[_Riccati] |
✓ |
6.257 |
|
|
\[
{}y^{\prime } = x \left (2+x^{2} y-y^{2}\right )
\] |
[_Riccati] |
✓ |
10.733 |
|
|
\[
{}y^{\prime } = x +\left (1-2 x \right ) y-\left (1-x \right ) y^{2}
\] |
[_Riccati] |
✓ |
5.753 |
|
|
\[
{}y^{\prime } = a x y^{2}
\] |
[_separable] |
✓ |
13.816 |
|
|
\[
{}y^{\prime } = x^{n} \left (a +b y^{2}\right )
\] |
[_separable] |
✓ |
13.764 |
|
|
\[
{}y^{\prime } = a \,x^{m}+b \,x^{n} y^{2}
\] |
[_Riccati] |
✓ |
6.076 |
|
|
\[
{}y^{\prime } = \left (a +b y \cos \left (k x \right )\right ) y
\] |
[_Bernoulli] |
✓ |
16.068 |
|
|
\[
{}y^{\prime } = \sin \left (x \right ) \left (2 \sec \left (x \right )^{2}-y\right )
\] |
[_linear] |
✓ |
14.747 |
|
|
\[
{}y^{\prime }+4 \csc \left (x \right ) = \left (3-\cot \left (x \right )\right ) y+y^{2} \sin \left (x \right )
\] |
[_Riccati] |
✓ |
23.470 |
|
|
\[
{}y^{\prime } = y \sec \left (x \right )+\left (\sin \left (x \right )-1\right )^{2}
\] |
[_linear] |
✓ |
6.542 |
|
|
\[
{}y^{\prime }+\tan \left (x \right ) \left (1-y^{2}\right ) = 0
\] |
[_separable] |
✓ |
12.138 |
|
|
\[
{}y^{\prime } = f \left (x \right )+g \left (x \right ) y+h \left (x \right ) y^{2}
\] |
[_Riccati] |
✗ |
1.212 |
|
|
\[
{}y^{\prime } = \left (a +b y+c y^{2}\right ) f \left (x \right )
\] |
[_separable] |
✓ |
18.895 |
|
|
\[
{}y^{\prime }+\left (a x +y\right ) y^{2} = 0
\] |
[_Abel] |
✗ |
0.523 |
|
|
\[
{}y^{\prime } = \left (a \,{\mathrm e}^{x}+y\right ) y^{2}
\] |
[_Abel] |
✗ |
0.756 |
|
|
\[
{}y^{\prime }+3 a \left (y+2 x \right ) y^{2} = 0
\] |
[_Abel] |
✗ |
0.515 |
|
|
\[
{}y^{\prime } = y \left (a +b y^{2}\right )
\] |
[_quadrature] |
✓ |
11.074 |
|
|
\[
{}y^{\prime } = \operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2}+\operatorname {a3} y^{3}
\] |
[_quadrature] |
✓ |
1.509 |
|
|
\[
{}y^{\prime } = x y^{3}
\] |
[_separable] |
✓ |
16.944 |
|
|
\[
{}y^{\prime }+y \left (1-x y^{2}\right ) = 0
\] |
[_Bernoulli] |
✓ |
15.030 |
|
|
\[
{}y^{\prime } = \left (a +b x y\right ) y^{2}
\] |
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
18.023 |
|
|
\[
{}y^{\prime }+2 x y \left (1+a x y^{2}\right ) = 0
\] |
[_Bernoulli] |
✓ |
2.495 |
|
|
\[
{}y^{\prime }+\left (\tan \left (x \right )+y^{2} \sec \left (x \right )\right ) y = 0
\] |
[_Bernoulli] |
✓ |
14.170 |
|
|
\[
{}y^{\prime }+y^{3} \sec \left (x \right ) \tan \left (x \right ) = 0
\] |
[_separable] |
✓ |
5.586 |
|
|
\[
{}y^{\prime } = \operatorname {f0} \left (x \right )+\operatorname {f1} \left (x \right ) y+\operatorname {f2} \left (x \right ) y^{2}+\operatorname {f3} \left (x \right ) y^{3}
\] |
[_Abel] |
✗ |
13.404 |
|
|
\[
{}y^{\prime } = a \,x^{\frac {n}{-n +1}}+b y^{n}
\] |
[[_homogeneous, ‘class G‘], _Chini] |
✓ |
8.132 |
|
|
\[
{}y^{\prime } = f \left (x \right ) y+g \left (x \right ) y^{k}
\] |
[_Bernoulli] |
✓ |
13.414 |
|
|
\[
{}y^{\prime } = f \left (x \right )+g \left (x \right ) y+h \left (x \right ) y^{n}
\] |
[_Chini] |
✗ |
6.286 |
|
|
\[
{}y^{\prime } = \sqrt {{| y|}}
\] |
[_quadrature] |
✓ |
19.313 |
|
|
\[
{}y^{\prime } = a +b y+\sqrt {\operatorname {A0} +\operatorname {B0} y}
\] |
[_quadrature] |
✓ |
20.490 |
|
|
\[
{}y^{\prime } = a x +b \sqrt {y}
\] |
[[_homogeneous, ‘class G‘], _Chini] |
✓ |
49.561 |
|
|
\[
{}y^{\prime }+x^{3} = x \sqrt {x^{4}+4 y}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
22.698 |
|
|
\[
{}y^{\prime }+2 y \left (1-x \sqrt {y}\right ) = 0
\] |
[_Bernoulli] |
✓ |
10.804 |
|
|
\[
{}y^{\prime } = \sqrt {a +b y^{2}}
\] |
[_quadrature] |
✓ |
2.793 |
|
|
\[
{}y^{\prime } = y \sqrt {a +b y}
\] |
[_quadrature] |
✓ |
25.668 |
|
|
\[
{}y^{\prime }+\left (f \left (x \right )-y\right ) g \left (x \right ) \sqrt {\left (y-a \right ) \left (y-b \right )} = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
15.477 |
|
|
\[
{}y^{\prime } = \sqrt {X Y}
\] |
[_quadrature] |
✓ |
1.246 |
|
|
\[
{}y^{\prime } = \cos \left (x \right )^{2} \cos \left (y\right )
\] |
[_separable] |
✓ |
5.066 |
|
|
\[
{}y^{\prime } = \sec \left (x \right )^{2} \cot \left (y\right ) \cos \left (y\right )
\] |
[_separable] |
✓ |
6.770 |
|
|
\[
{}y^{\prime } = a +b \cos \left (A x +B y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
52.403 |
|
|
\[
{}y^{\prime }+f \left (x \right )+g \left (x \right ) \sin \left (a y\right )+h \left (x \right ) \cos \left (a y\right ) = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
15.351 |
|
|
\[
{}y^{\prime } = a +b \cos \left (y\right )
\] |
[_quadrature] |
✓ |
1.777 |
|
|
\[
{}y^{\prime }+x \left (\sin \left (2 y\right )-x^{2} \cos \left (y\right )^{2}\right ) = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
2.337 |
|
|
\[
{}y^{\prime }+\tan \left (x \right ) \sec \left (x \right ) \cos \left (y\right )^{2} = 0
\] |
[_separable] |
✓ |
6.685 |
|
|
\[
{}y^{\prime } = \cot \left (x \right ) \cot \left (y\right )
\] |
[_separable] |
✓ |
12.309 |
|
|
\[
{}y^{\prime }+\cot \left (x \right ) \cot \left (y\right ) = 0
\] |
[_separable] |
✓ |
3.921 |
|
|
\[
{}y^{\prime } = \sin \left (x \right ) \left (\csc \left (y\right )-\cot \left (y\right )\right )
\] |
[_separable] |
✓ |
15.895 |
|
|
\[
{}y^{\prime } = \tan \left (x \right ) \cot \left (y\right )
\] |
[_separable] |
✓ |
4.027 |
|
|
\[
{}y^{\prime }+\tan \left (x \right ) \cot \left (y\right ) = 0
\] |
[_separable] |
✓ |
3.489 |
|
|
\[
{}y^{\prime }+\sin \left (2 x \right ) \csc \left (2 y\right ) = 0
\] |
[_separable] |
✓ |
62.507 |
|
|
\[
{}y^{\prime } = \tan \left (x \right ) \left (\tan \left (y\right )+\sec \left (x \right ) \sec \left (y\right )\right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
4.300 |
|
|
\[
{}y^{\prime } = \cos \left (x \right ) \sec \left (y\right )^{2}
\] |
[_separable] |
✓ |
14.066 |
|
|
\[
{}y^{\prime } = \sec \left (x \right )^{2} \sec \left (y\right )^{3}
\] |
[_separable] |
✓ |
13.908 |
|
|
\[
{}y^{\prime } = a +b \sin \left (y\right )
\] |
[_quadrature] |
✓ |
2.069 |
|
|
\[
{}y^{\prime } = \left (1+\cos \left (x \right ) \sin \left (y\right )\right ) \tan \left (y\right )
\] |
unknown |
✗ |
8.109 |
|
|
\[
{}y^{\prime }+\csc \left (2 x \right ) \sin \left (2 y\right ) = 0
\] |
[_separable] |
✓ |
32.871 |
|
|
\[
{}y^{\prime }+f \left (x \right )+g \left (x \right ) \tan \left (y\right ) = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
3.967 |
|
|
\[
{}y^{\prime } = \sqrt {a +b \cos \left (y\right )}
\] |
[_quadrature] |
✓ |
8.102 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{y}+x
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
2.412 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x +y}
\] |
[_separable] |
✓ |
8.086 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x} \left (a +b \,{\mathrm e}^{-y}\right )
\] |
[_separable] |
✓ |
15.269 |
|
|
\[
{}y^{\prime }+y \ln \left (x \right ) \ln \left (y\right ) = 0
\] |
[_separable] |
✓ |
15.189 |
|
|
\[
{}y^{\prime } = x^{m -1} y^{-n +1} f \left (a \,x^{m}+b y^{n}\right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
2.008 |
|
|
\[
{}y^{\prime } = a f \left (y\right )
\] |
[_quadrature] |
✓ |
0.665 |
|
|
\[
{}y^{\prime } = f \left (a +b x +c y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
16.474 |
|
|
\[
{}y^{\prime } = f \left (x \right ) g \left (y\right )
\] |
[_separable] |
✓ |
3.342 |
|
|
\[
{}y^{\prime } = \sec \left (x \right )^{2}+y \sec \left (x \right ) \operatorname {Csx} \left (x \right )
\] |
[_linear] |
✓ |
13.478 |
|
|
\[
{}2 y^{\prime } = 2 \sin \left (y\right )^{2} \tan \left (y\right )-x \sin \left (2 y\right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
112.213 |
|
|
\[
{}2 y^{\prime }+a x = \sqrt {a^{2} x^{2}-4 b \,x^{2}-4 c y}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
75.711 |
|