| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }+y^{3} \sec \left (x \right ) \tan \left (x \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.470 |
|
| \begin{align*}
y^{\prime }&=\left (\tan \left (x \right )+y^{3} \sec \left (x \right )\right ) y \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.608 |
|
| \begin{align*}
y^{\prime }&=a \,x^{\frac {n}{1-n}}+b y^{n} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Chini] |
✓ |
✓ |
✓ |
✗ |
9.194 |
|
| \begin{align*}
y^{\prime }&=f \left (x \right ) y+g \left (x \right ) y^{k} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.418 |
|
| \begin{align*}
y^{\prime }&=f \left (x \right )+g \left (x \right ) y+h \left (x \right ) y^{n} \\
\end{align*} |
[_Chini] |
✗ |
✗ |
✗ |
✗ |
1.472 |
|
| \begin{align*}
y^{\prime }&=\sqrt {{| y|}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.752 |
|
| \begin{align*}
y^{\prime }&=a +b y+\sqrt {A +B y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
62.179 |
|
| \begin{align*}
y^{\prime }&=a +b y-\sqrt {A +B y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
59.905 |
|
| \begin{align*}
y^{\prime }&=a x +b \sqrt {y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Chini] |
✓ |
✓ |
✓ |
✗ |
8.402 |
|
| \begin{align*}
y^{\prime }+x^{3}&=x \sqrt {x^{4}+4 y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.951 |
|
| \begin{align*}
y^{\prime }+2 y \left (1-x \sqrt {y}\right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.593 |
|
| \begin{align*}
y^{\prime }&=\sqrt {a +b y^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.650 |
|
| \begin{align*}
y^{\prime }&=y \sqrt {a +b y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
29.816 |
|
| \begin{align*}
y^{\prime }&=\cos \left (y\right ) \cos \left (x \right )^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
2.649 |
|
| \begin{align*}
y^{\prime }&=\sec \left (x \right )^{2} \cot \left (y\right ) \cos \left (y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.329 |
|
| \begin{align*}
y^{\prime }&=a +b \cos \left (A x +B y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.465 |
|
| \begin{align*}
y^{\prime }&=a +b \cos \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
18.107 |
|
| \begin{align*}
y^{\prime }+x \left (\sin \left (2 y\right )-x^{2} \cos \left (y\right )^{2}\right )&=0 \\
\end{align*} | [‘y=_G(x,y’)‘] | ✗ | ✓ | ✓ | ✗ | 6.671 |
|
| \begin{align*}
y^{\prime }+\tan \left (x \right ) \sec \left (x \right ) \cos \left (y\right )^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
2.247 |
|
| \begin{align*}
y^{\prime }&=\cot \left (x \right ) \cot \left (y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.948 |
|
| \begin{align*}
y^{\prime }+\cot \left (x \right ) \cot \left (y\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.421 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x \right ) \left (\csc \left (y\right )-\cot \left (y\right )\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.256 |
|
| \begin{align*}
y^{\prime }&=\tan \left (x \right ) \cot \left (y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.643 |
|
| \begin{align*}
y^{\prime }+\tan \left (x \right ) \cot \left (y\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.704 |
|
| \begin{align*}
y^{\prime }+\sin \left (2 x \right ) \csc \left (2 y\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.852 |
|
| \begin{align*}
y^{\prime }&=\tan \left (x \right ) \left (\tan \left (y\right )+\sec \left (x \right ) \sec \left (y\right )\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
✓ |
7.500 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x \right ) \sec \left (y\right )^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.668 |
|
| \begin{align*}
y^{\prime }&=\sec \left (x \right )^{2} \sec \left (y\right )^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
1.838 |
|
| \begin{align*}
y^{\prime }&=a +b \sin \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
15.710 |
|
| \begin{align*}
y^{\prime }&=a +b \sin \left (A x +B y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.506 |
|
| \begin{align*}
y^{\prime }&=\left (1+\cos \left (x \right ) \sin \left (y\right )\right ) \tan \left (y\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✓ |
✓ |
6.652 |
|
| \begin{align*}
y^{\prime }+\csc \left (2 x \right ) \sin \left (2 y\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.477 |
|
| \begin{align*}
y^{\prime }&=\sqrt {a +b \cos \left (y\right )} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.635 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{y}+x \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.355 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x +y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.149 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x} \left (a +b \,{\mathrm e}^{-y}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.179 |
|
| \begin{align*}
y \ln \left (x \right ) \ln \left (y\right )+y^{\prime }&=0 \\
\end{align*} | [_separable] | ✓ | ✓ | ✓ | ✓ | 1.780 |
|
| \begin{align*}
y^{\prime }&=x^{m -1} y^{1-n} f \left (a \,x^{m}+b y^{n}\right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
✓ |
✓ |
✗ |
6.424 |
|
| \begin{align*}
y^{\prime }&=a f \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.485 |
|
| \begin{align*}
y^{\prime }&=f \left (a +b x +c y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| \begin{align*}
y^{\prime }&=f \left (x \right ) g \left (y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.404 |
|
| \begin{align*}
y^{\prime }&=\sec \left (x \right )^{2}+y \sec \left (x \right ) \operatorname {Csx} \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.808 |
|
| \begin{align*}
2 y^{\prime }+2 \csc \left (x \right )^{2}&=y \csc \left (x \right ) \sec \left (x \right )-y^{2} \sec \left (x \right )^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
1.714 |
|
| \begin{align*}
2 y^{\prime }&=2 \sin \left (y\right )^{2} \tan \left (y\right )-x \sin \left (2 y\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✓ |
✗ |
65.720 |
|
| \begin{align*}
2 y^{\prime }+a x&=\sqrt {a^{2} x^{2}-4 b \,x^{2}-4 c y} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
44.829 |
|
| \begin{align*}
2 y^{\prime }+a x&=-\sqrt {a^{2} x^{2}-4 b \,x^{2}-4 c y} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
43.662 |
|
| \begin{align*}
3 y^{\prime }&=x +\sqrt {x^{2}-3 y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
7.009 |
|
| \begin{align*}
3 y^{\prime }&=x -\sqrt {x^{2}-3 y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
7.111 |
|
| \begin{align*}
y^{\prime } x&=\sqrt {a^{2}-x^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| \begin{align*}
y^{\prime } x&=-\sqrt {a^{2}-x^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.261 |
|
| \begin{align*}
y^{\prime } x +x +y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.199 |
|
| \begin{align*}
y^{\prime } x +x^{2}-y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.979 |
|
| \begin{align*}
y^{\prime } x&=x^{3}-y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.651 |
|
| \begin{align*}
y^{\prime } x&=1+x^{3}+y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.353 |
|
| \begin{align*}
y^{\prime } x&=x^{m}+y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.570 |
|
| \begin{align*}
y^{\prime } x&=x \sin \left (x \right )-y \\
\end{align*} | [_linear] | ✓ | ✓ | ✓ | ✓ | 1.498 |
|
| \begin{align*}
y^{\prime } x&=x^{2} \sin \left (x \right )+y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.974 |
|
| \begin{align*}
y^{\prime } x&=x^{n} \ln \left (x \right )-y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.536 |
|
| \begin{align*}
y^{\prime } x&=\sin \left (x \right )-2 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.685 |
|
| \begin{align*}
y^{\prime } x&=a y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.877 |
|
| \begin{align*}
y^{\prime } x&=-a y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.826 |
|
| \begin{align*}
y^{\prime } x&=1+x +a y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.104 |
|
| \begin{align*}
y^{\prime } x&=a x +b y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.550 |
|
| \begin{align*}
y^{\prime } x&=a \,x^{2}+b y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.992 |
|
| \begin{align*}
y^{\prime } x&=a +b \,x^{n}+c y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
2.178 |
|
| \begin{align*}
y^{\prime } x +2+\left (-x +3\right ) y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.305 |
|
| \begin{align*}
y^{\prime } x +x +\left (a x +2\right ) y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.335 |
|
| \begin{align*}
y^{\prime } x +\left (b x +a \right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.128 |
|
| \begin{align*}
y^{\prime } x&=x^{3}+\left (-2 x^{2}+1\right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.753 |
|
| \begin{align*}
y^{\prime } x&=a x -\left (-b \,x^{2}+1\right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.473 |
|
| \begin{align*}
y^{\prime } x +\left (-a \,x^{2}+2\right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.833 |
|
| \begin{align*}
y^{\prime } x +x^{2}+y^{2}&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
2.185 |
|
| \begin{align*}
y^{\prime } x&=x^{2}+y \left (1+y\right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
1.198 |
|
| \begin{align*}
y^{\prime } x -y+y^{2}&=x^{{2}/{3}} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
50.119 |
|
| \begin{align*}
y^{\prime } x&=a +b y^{2} \\
\end{align*} | [_separable] | ✓ | ✓ | ✓ | ✓ | 2.344 |
|
| \begin{align*}
y^{\prime } x&=a \,x^{2}+y+b y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
0.803 |
|
| \begin{align*}
y^{\prime } x&=a \,x^{2 n}+\left (n +b y\right ) y \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
2.368 |
|
| \begin{align*}
y^{\prime } x&=a \,x^{n}+b y+c y^{2} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
28.151 |
|
| \begin{align*}
y^{\prime } x&=k +a \,x^{n}+b y+c y^{2} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
7.213 |
|
| \begin{align*}
y^{\prime } x +a +x y^{2}&=0 \\
\end{align*} |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
2.513 |
|
| \begin{align*}
y^{\prime } x +\left (-y x +1\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.999 |
|
| \begin{align*}
y^{\prime } x&=\left (-y x +1\right ) y \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.455 |
|
| \begin{align*}
y^{\prime } x&=\left (y x +1\right ) y \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.495 |
|
| \begin{align*}
y^{\prime } x&=a \,x^{3} \left (-y x +1\right ) y \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.800 |
|
| \begin{align*}
y^{\prime } x&=x^{3}+\left (2 x^{2}+1\right ) y+x y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
2.539 |
|
| \begin{align*}
y^{\prime } x&=y \left (2 y x +1\right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.476 |
|
| \begin{align*}
y^{\prime } x +b x +\left (2+a x y\right ) y&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
2.650 |
|
| \begin{align*}
y^{\prime } x +a_{0} +a_{1} x +\left (a_{2} +a_{3} x y\right ) y&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
33.851 |
|
| \begin{align*}
y^{\prime } x +a \,x^{2} y^{2}+2 y&=b \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
28.418 |
|
| \begin{align*}
y^{\prime } x +x^{m}+\frac {\left (n -m \right ) y}{2}+x^{n} y^{2}&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
2.897 |
|
| \begin{align*}
y^{\prime } x +\left (a +b \,x^{n} y\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.715 |
|
| \begin{align*}
y^{\prime } x&=a \,x^{m}-b y-c \,x^{n} y^{2} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
0.842 |
|
| \begin{align*}
y^{\prime } x&=2 x -y+a \,x^{n} \left (x -y\right )^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.925 |
|
| \begin{align*}
y^{\prime } x +\left (1-a y \ln \left (x \right )\right ) y&=0 \\
\end{align*} | [_Bernoulli] | ✓ | ✓ | ✓ | ✓ | 3.384 |
|
| \begin{align*}
y^{\prime } x&=y+\left (x^{2}-y^{2}\right ) f \left (x \right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
3.040 |
|
| \begin{align*}
y^{\prime } x&=y \left (1+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.606 |
|
| \begin{align*}
y^{\prime } x +y \left (1-x y^{2}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.637 |
|
| \begin{align*}
y^{\prime } x +y&=a \left (x^{2}+1\right ) y^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.020 |
|
| \begin{align*}
y^{\prime } x +y&=a \left (-x^{2}+1\right ) y^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.933 |
|
| \begin{align*}
y^{\prime } x&=a y+b \left (x^{2}+1\right ) y^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.860 |
|