|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = a +b y+\sqrt {\operatorname {A0} +\operatorname {B0} y}
\] |
[_quadrature] |
✓ |
5.152 |
|
|
\[
{}y^{\prime } = a x +b \sqrt {y}
\] |
[[_homogeneous, ‘class G‘], _Chini] |
✓ |
3.696 |
|
|
\[
{}y^{\prime }+x^{3} = x \sqrt {x^{4}+4 y}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.760 |
|
|
\[
{}y^{\prime }+2 y \left (1-x \sqrt {y}\right ) = 0
\] |
[_Bernoulli] |
✓ |
1.252 |
|
|
\[
{}y^{\prime } = \sqrt {a +b y^{2}}
\] |
[_quadrature] |
✓ |
1.783 |
|
|
\[
{}y^{\prime } = y \sqrt {a +b y}
\] |
[_quadrature] |
✓ |
8.021 |
|
|
\[
{}y^{\prime }+\left (f \left (x \right )-y\right ) g \left (x \right ) \sqrt {\left (y-a \right ) \left (y-b \right )} = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
5.013 |
|
|
\[
{}y^{\prime } = \sqrt {X Y}
\] |
[_quadrature] |
✓ |
0.443 |
|
|
\[
{}y^{\prime } = \cos \left (x \right )^{2} \cos \left (y\right )
\] |
[_separable] |
✓ |
2.247 |
|
|
\[
{}y^{\prime } = \sec \left (x \right )^{2} \cot \left (y\right ) \cos \left (y\right )
\] |
[_separable] |
✓ |
2.766 |
|
|
\[
{}y^{\prime } = a +b \cos \left (A x +B y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
38.083 |
|
|
\[
{}y^{\prime }+f \left (x \right )+g \left (x \right ) \sin \left (a y\right )+h \left (x \right ) \cos \left (a y\right ) = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
6.034 |
|
|
\[
{}y^{\prime } = a +b \cos \left (y\right )
\] |
[_quadrature] |
✓ |
1.034 |
|
|
\[
{}y^{\prime }+x \left (\sin \left (2 y\right )-x^{2} \cos \left (y\right )^{2}\right ) = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
4.845 |
|
|
\[
{}y^{\prime }+\tan \left (x \right ) \sec \left (x \right ) \cos \left (y\right )^{2} = 0
\] |
[_separable] |
✓ |
2.557 |
|
|
\[
{}y^{\prime } = \cot \left (x \right ) \cot \left (y\right )
\] |
[_separable] |
✓ |
1.865 |
|
|
\[
{}y^{\prime }+\cot \left (x \right ) \cot \left (y\right ) = 0
\] |
[_separable] |
✓ |
1.957 |
|
|
\[
{}y^{\prime } = \sin \left (x \right ) \left (\csc \left (y\right )-\cot \left (y\right )\right )
\] |
[_separable] |
✓ |
3.023 |
|
|
\[
{}y^{\prime } = \tan \left (x \right ) \cot \left (y\right )
\] |
[_separable] |
✓ |
1.802 |
|
|
\[
{}y^{\prime }+\tan \left (x \right ) \cot \left (y\right ) = 0
\] |
[_separable] |
✓ |
1.770 |
|
|
\[
{}y^{\prime }+\sin \left (2 x \right ) \csc \left (2 y\right ) = 0
\] |
[_separable] |
✓ |
5.139 |
|
|
\[
{}y^{\prime } = \tan \left (x \right ) \left (\tan \left (y\right )+\sec \left (x \right ) \sec \left (y\right )\right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
7.764 |
|
|
\[
{}y^{\prime } = \cos \left (x \right ) \sec \left (y\right )^{2}
\] |
[_separable] |
✓ |
1.940 |
|
|
\[
{}y^{\prime } = \sec \left (x \right )^{2} \sec \left (y\right )^{3}
\] |
[_separable] |
✓ |
2.034 |
|
|
\[
{}y^{\prime } = a +b \sin \left (y\right )
\] |
[_quadrature] |
✓ |
1.089 |
|
|
\[
{}y^{\prime } = \left (1+\cos \left (x \right ) \sin \left (y\right )\right ) \tan \left (y\right )
\] |
unknown |
✗ |
7.236 |
|
|
\[
{}y^{\prime }+\csc \left (2 x \right ) \sin \left (2 y\right ) = 0
\] |
[_separable] |
✓ |
4.585 |
|
|
\[
{}y^{\prime }+f \left (x \right )+g \left (x \right ) \tan \left (y\right ) = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
3.540 |
|
|
\[
{}y^{\prime } = \sqrt {a +b \cos \left (y\right )}
\] |
[_quadrature] |
✓ |
2.195 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{y}+x
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
1.370 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x +y}
\] |
[_separable] |
✓ |
2.383 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x} \left (a +b \,{\mathrm e}^{-y}\right )
\] |
[_separable] |
✓ |
1.682 |
|
|
\[
{}y \ln \left (x \right ) \ln \left (y\right )+y^{\prime } = 0
\] |
[_separable] |
✓ |
1.467 |
|
|
\[
{}y^{\prime } = x^{m -1} y^{1-n} f \left (a \,x^{m}+b y^{n}\right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
3.276 |
|
|
\[
{}y^{\prime } = a f \left (y\right )
\] |
[_quadrature] |
✓ |
0.602 |
|
|
\[
{}y^{\prime } = f \left (a +b x +c y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.044 |
|
|
\[
{}y^{\prime } = f \left (x \right ) g \left (y\right )
\] |
[_separable] |
✓ |
0.969 |
|
|
\[
{}y^{\prime } = \sec \left (x \right )^{2}+y \sec \left (x \right ) \operatorname {Csx} \left (x \right )
\] |
[_linear] |
✓ |
2.285 |
|
|
\[
{}2 y^{\prime } = 2 \sin \left (y\right )^{2} \tan \left (y\right )-x \sin \left (2 y\right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
57.449 |
|
|
\[
{}2 y^{\prime }+a x = \sqrt {a^{2} x^{2}-4 b \,x^{2}-4 c y}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
5.928 |
|
|
\[
{}3 y^{\prime } = x +\sqrt {x^{2}-3 y}
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
5.350 |
|
|
\[
{}y^{\prime } x = \sqrt {a^{2}-x^{2}}
\] |
[_quadrature] |
✓ |
0.568 |
|
|
\[
{}y^{\prime } x +x +y = 0
\] |
[_linear] |
✓ |
2.375 |
|
|
\[
{}y^{\prime } x +x^{2}-y = 0
\] |
[_linear] |
✓ |
1.550 |
|
|
\[
{}y^{\prime } x = x^{3}-y
\] |
[_linear] |
✓ |
1.561 |
|
|
\[
{}y^{\prime } x = 1+x^{3}+y
\] |
[_linear] |
✓ |
1.308 |
|
|
\[
{}y^{\prime } x = x^{m}+y
\] |
[_linear] |
✓ |
0.676 |
|
|
\[
{}y^{\prime } x = x \sin \left (x \right )-y
\] |
[_linear] |
✓ |
1.333 |
|
|
\[
{}y^{\prime } x = x^{2} \sin \left (x \right )+y
\] |
[_linear] |
✓ |
1.564 |
|
|
\[
{}y^{\prime } x = x^{n} \ln \left (x \right )-y
\] |
[_linear] |
✓ |
1.158 |
|
|
\[
{}y^{\prime } x = \sin \left (x \right )-2 y
\] |
[_linear] |
✓ |
1.418 |
|
|
\[
{}y^{\prime } x = a y
\] |
[_separable] |
✓ |
1.269 |
|
|
\[
{}y^{\prime } x = 1+x +a y
\] |
[_linear] |
✓ |
1.232 |
|
|
\[
{}y^{\prime } x = a x +b y
\] |
[_linear] |
✓ |
1.542 |
|
|
\[
{}y^{\prime } x = a \,x^{2}+b y
\] |
[_linear] |
✓ |
1.106 |
|
|
\[
{}y^{\prime } x = a +b \,x^{n}+c y
\] |
[_linear] |
✓ |
1.115 |
|
|
\[
{}y^{\prime } x +2+\left (3-x \right ) y = 0
\] |
[_linear] |
✓ |
1.264 |
|
|
\[
{}y^{\prime } x +x +\left (a x +2\right ) y = 0
\] |
[_linear] |
✓ |
1.022 |
|
|
\[
{}y^{\prime } x +\left (b x +a \right ) y = 0
\] |
[_separable] |
✓ |
1.024 |
|
|
\[
{}y^{\prime } x = x^{3}+\left (-2 x^{2}+1\right ) y
\] |
[_linear] |
✓ |
1.601 |
|
|
\[
{}y^{\prime } x = a x -\left (-b \,x^{2}+1\right ) y
\] |
[_linear] |
✓ |
1.107 |
|
|
\[
{}y^{\prime } x +x +\left (-a \,x^{2}+2\right ) y = 0
\] |
[_linear] |
✓ |
1.158 |
|
|
\[
{}y^{\prime } x +x^{2}+y^{2} = 0
\] |
[_rational, _Riccati] |
✓ |
1.123 |
|
|
\[
{}y^{\prime } x = x^{2}+y \left (1+y\right )
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
1.692 |
|
|
\[
{}y^{\prime } x -y+y^{2} = x^{{2}/{3}}
\] |
[_rational, _Riccati] |
✓ |
11.882 |
|
|
\[
{}y^{\prime } x = a +b y^{2}
\] |
[_separable] |
✓ |
1.733 |
|
|
\[
{}y^{\prime } x = a \,x^{2}+y+b y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
1.362 |
|
|
\[
{}y^{\prime } x = a \,x^{2 n}+\left (n +b y\right ) y
\] |
[_rational, _Riccati] |
✓ |
2.828 |
|
|
\[
{}y^{\prime } x = a \,x^{n}+b y+c y^{2}
\] |
[_rational, _Riccati] |
✓ |
2.060 |
|
|
\[
{}y^{\prime } x = k +a \,x^{n}+b y+c y^{2}
\] |
[_rational, _Riccati] |
✓ |
2.434 |
|
|
\[
{}y^{\prime } x +a +x y^{2} = 0
\] |
[_rational, [_Riccati, _special]] |
✓ |
0.977 |
|
|
\[
{}y^{\prime } x +\left (1-x y\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.594 |
|
|
\[
{}y^{\prime } x = \left (1-x y\right ) y
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.144 |
|
|
\[
{}y^{\prime } x = \left (1+x y\right ) y
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.195 |
|
|
\[
{}y^{\prime } x = a \,x^{3} \left (1-x y\right ) y
\] |
[_Bernoulli] |
✓ |
1.289 |
|
|
\[
{}y^{\prime } x = x^{3}+\left (2 x^{2}+1\right ) y+x y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
2.131 |
|
|
\[
{}y^{\prime } x = y \left (1+2 x y\right )
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.087 |
|
|
\[
{}y^{\prime } x +b x +\left (2+y a x \right ) y = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
2.421 |
|
|
\[
{}y^{\prime } x +\operatorname {a0} +\operatorname {a1} x +\left (\operatorname {a2} +\operatorname {a3} x y\right ) y = 0
\] |
[_rational, _Riccati] |
✓ |
5.947 |
|
|
\[
{}y^{\prime } x +a \,x^{2} y^{2}+2 y = b
\] |
[_rational, _Riccati] |
✓ |
1.412 |
|
|
\[
{}y^{\prime } x +x^{m}+\frac {\left (n -m \right ) y}{2}+x^{n} y^{2} = 0
\] |
[_rational, _Riccati] |
✓ |
2.240 |
|
|
\[
{}y^{\prime } x +\left (a +b \,x^{n} y\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.611 |
|
|
\[
{}y^{\prime } x = a \,x^{m}-b y-c \,x^{n} y^{2}
\] |
[_rational, _Riccati] |
✓ |
2.731 |
|
|
\[
{}y^{\prime } x = 2 x -y+a \,x^{n} \left (x -y\right )^{2}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Riccati] |
✓ |
2.812 |
|
|
\[
{}y^{\prime } x +\left (1-a y \ln \left (x \right )\right ) y = 0
\] |
[_Bernoulli] |
✓ |
1.817 |
|
|
\[
{}y^{\prime } x = y+\left (x^{2}-y^{2}\right ) f \left (x \right )
\] |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
2.200 |
|
|
\[
{}y^{\prime } x = y \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
3.619 |
|
|
\[
{}y^{\prime } x +y \left (1-x y^{2}\right ) = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.986 |
|
|
\[
{}y^{\prime } x +y = a \left (x^{2}+1\right ) y^{3}
\] |
[_rational, _Bernoulli] |
✓ |
2.341 |
|
|
\[
{}y^{\prime } x = a y+b \left (x^{2}+1\right ) y^{3}
\] |
[_rational, _Bernoulli] |
✓ |
3.280 |
|
|
\[
{}y^{\prime } x +2 y = a \,x^{2 k} y^{k}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
3.783 |
|
|
\[
{}y^{\prime } x = 4 y-4 \sqrt {y}
\] |
[_separable] |
✓ |
3.944 |
|
|
\[
{}y^{\prime } x +2 y = \sqrt {1+y^{2}}
\] |
[_separable] |
✓ |
3.069 |
|
|
\[
{}y^{\prime } x = y+\sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
6.587 |
|
|
\[
{}y^{\prime } x = y+\sqrt {x^{2}-y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
60.303 |
|
|
\[
{}y^{\prime } x = y+x \sqrt {x^{2}+y^{2}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
4.279 |
|
|
\[
{}y^{\prime } x = y-x \left (x -y\right ) \sqrt {x^{2}+y^{2}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
5.326 |
|
|
\[
{}y^{\prime } x = y+a \sqrt {y^{2}+b^{2} x^{2}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
11.811 |
|
|
\[
{}y^{\prime } x +\left (\sin \left (y\right )-3 x^{2} \cos \left (y\right )\right ) \cos \left (y\right ) = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
2.544 |
|
|
\[
{}y^{\prime } x +x -y+x \cos \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.372 |
|