| # |
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] |
✓ |
✓ |
✓ |
✓ |
4.631 |
|
| \begin{align*}
y^{\prime }&=\left (\tan \left (x \right )+y^{3} \sec \left (x \right )\right ) y \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
50.540 |
|
| \begin{align*}
y^{\prime }&=a \,x^{\frac {n}{1-n}}+b y^{n} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Chini] |
✓ |
✓ |
✓ |
✗ |
5.944 |
|
| \begin{align*}
y^{\prime }&=f \left (x \right ) y+g \left (x \right ) y^{k} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.161 |
|
| \begin{align*}
y^{\prime }&=f \left (x \right )+g \left (x \right ) y+h \left (x \right ) y^{n} \\
\end{align*} |
[_Chini] |
✗ |
✗ |
✗ |
✗ |
1.664 |
|
| \begin{align*}
y^{\prime }&=\sqrt {{| y|}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.731 |
|
| \begin{align*}
y^{\prime }&=a +b y+\sqrt {A +B y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
50.867 |
|
| \begin{align*}
y^{\prime }&=a +b y-\sqrt {A +B y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
50.845 |
|
| \begin{align*}
y^{\prime }&=a x +b \sqrt {y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Chini] |
✓ |
✓ |
✓ |
✗ |
6.660 |
|
| \begin{align*}
y^{\prime }+x^{3}&=x \sqrt {x^{4}+4 y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
9.602 |
|
| \begin{align*}
y^{\prime }+2 y \left (1-x \sqrt {y}\right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.261 |
|
| \begin{align*}
y^{\prime }&=\sqrt {a +b y^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.186 |
|
| \begin{align*}
y^{\prime }&=y \sqrt {a +b y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
31.448 |
|
| \begin{align*}
y^{\prime }&=\cos \left (y\right ) \cos \left (x \right )^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
2.812 |
|
| \begin{align*}
y^{\prime }&=\sec \left (x \right )^{2} \cot \left (y\right ) \cos \left (y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.951 |
|
| \begin{align*}
y^{\prime }&=a +b \cos \left (A x +B y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.990 |
|
| \begin{align*}
y^{\prime }&=a +b \cos \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
4.438 |
|
| \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’)‘] |
✓ |
✓ |
✓ |
✗ |
12.677 |
|
| \begin{align*}
y^{\prime }+\tan \left (x \right ) \sec \left (x \right ) \cos \left (y\right )^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
2.500 |
|
| \begin{align*}
y^{\prime }&=\cot \left (x \right ) \cot \left (y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.575 |
|
| \begin{align*}
y^{\prime }+\cot \left (x \right ) \cot \left (y\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.841 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x \right ) \left (\csc \left (y\right )-\cot \left (y\right )\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.407 |
|
| \begin{align*}
y^{\prime }&=\tan \left (x \right ) \cot \left (y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.788 |
|
| \begin{align*}
y^{\prime }+\tan \left (x \right ) \cot \left (y\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.632 |
|
| \begin{align*}
y^{\prime }+\sin \left (2 x \right ) \csc \left (2 y\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
21.654 |
|
| \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’)‘] |
✗ |
✓ |
✓ |
✓ |
7.564 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x \right ) \sec \left (y\right )^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.013 |
|
| \begin{align*}
y^{\prime }&=\sec \left (x \right )^{2} \sec \left (y\right )^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
2.261 |
|
| \begin{align*}
y^{\prime }&=a +b \sin \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
4.645 |
|
| \begin{align*}
y^{\prime }&=a +b \sin \left (A x +B y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.976 |
|
| \begin{align*}
y^{\prime }&=\left (1+\sin \left (y\right ) \cos \left (x \right )\right ) \tan \left (y\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✓ |
✓ |
6.018 |
|
| \begin{align*}
y^{\prime }+\csc \left (2 x \right ) \sin \left (2 y\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.802 |
|
| \begin{align*}
y^{\prime }&=\sqrt {a +b \cos \left (y\right )} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
8.878 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{y}+x \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.643 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x +y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.769 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x} \left (a +b \,{\mathrm e}^{-y}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.809 |
|
| \begin{align*}
y \ln \left (x \right ) \ln \left (y\right )+y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.522 |
|
| \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)]‘]] |
✗ |
✓ |
✓ |
✗ |
5.967 |
|
| \begin{align*}
y^{\prime }&=a f \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.689 |
|
| \begin{align*}
y^{\prime }&=f \left (a +b x +c y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.151 |
|
| \begin{align*}
y^{\prime }&=f \left (x \right ) g \left (y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.483 |
|
| \begin{align*}
y^{\prime }&=\sec \left (x \right )^{2}+y \sec \left (x \right ) \operatorname {Csx} \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.047 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
1.319 |
|
| \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’)‘] |
✗ |
✗ |
✓ |
✗ |
52.014 |
|
| \begin{align*}
2 y^{\prime }+a x&=\sqrt {a^{2} x^{2}-4 b \,x^{2}-4 c y} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
9.323 |
|
| \begin{align*}
2 y^{\prime }+a x&=-\sqrt {a^{2} x^{2}-4 b \,x^{2}-4 c y} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
8.813 |
|
| \begin{align*}
3 y^{\prime }&=x +\sqrt {x^{2}-3 y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
16.386 |
|
| \begin{align*}
3 y^{\prime }&=x -\sqrt {x^{2}-3 y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
88.042 |
|
| \begin{align*}
x y^{\prime }&=\sqrt {a^{2}-x^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.338 |
|
| \begin{align*}
x y^{\prime }&=-\sqrt {a^{2}-x^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.263 |
|
| \begin{align*}
x y^{\prime }+x +y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.753 |
|
| \begin{align*}
x y^{\prime }+x^{2}-y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.481 |
|
| \begin{align*}
x y^{\prime }&=x^{3}-y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.607 |
|
| \begin{align*}
x y^{\prime }&=1+x^{3}+y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.691 |
|
| \begin{align*}
x y^{\prime }&=x^{m}+y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.202 |
|
| \begin{align*}
x y^{\prime }&=x \sin \left (x \right )-y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.697 |
|
| \begin{align*}
x y^{\prime }&=x^{2} \sin \left (x \right )+y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.270 |
|
| \begin{align*}
x y^{\prime }&=x^{n} \ln \left (x \right )-y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.894 |
|
| \begin{align*}
x y^{\prime }&=\sin \left (x \right )-2 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.894 |
|
| \begin{align*}
x y^{\prime }&=a y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.621 |
|
| \begin{align*}
x y^{\prime }&=-a y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.555 |
|
| \begin{align*}
x y^{\prime }&=1+x +a y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.933 |
|
| \begin{align*}
x y^{\prime }&=a x +b y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.231 |
|
| \begin{align*}
x y^{\prime }&=a \,x^{2}+b y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.889 |
|
| \begin{align*}
x y^{\prime }&=a +b \,x^{n}+c y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
2.735 |
|
| \begin{align*}
x y^{\prime }+2+\left (-x +3\right ) y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.536 |
|
| \begin{align*}
x y^{\prime }+x +\left (a x +2\right ) y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.495 |
|
| \begin{align*}
x y^{\prime }+\left (b x +a \right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.833 |
|
| \begin{align*}
x y^{\prime }&=x^{3}+\left (-2 x^{2}+1\right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.452 |
|
| \begin{align*}
x y^{\prime }&=a x -\left (-b \,x^{2}+1\right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.643 |
|
| \begin{align*}
x y^{\prime }+\left (-a \,x^{2}+2\right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.538 |
|
| \begin{align*}
x y^{\prime }+x^{2}+y^{2}&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
3.274 |
|
| \begin{align*}
x y^{\prime }&=x^{2}+y \left (1+y\right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
1.687 |
|
| \begin{align*}
x y^{\prime }-y+y^{2}&=x^{{2}/{3}} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
48.535 |
|
| \begin{align*}
x y^{\prime }&=a +b y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.716 |
|
| \begin{align*}
x y^{\prime }&=a \,x^{2}+y+b y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
1.497 |
|
| \begin{align*}
x y^{\prime }&=a \,x^{2 n}+\left (n +b y\right ) y \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
3.461 |
|
| \begin{align*}
x y^{\prime }&=a \,x^{n}+b y+c y^{2} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
28.779 |
|
| \begin{align*}
x y^{\prime }&=k +a \,x^{n}+b y+c y^{2} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
9.367 |
|
| \begin{align*}
x y^{\prime }+a +x y^{2}&=0 \\
\end{align*} |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
3.466 |
|
| \begin{align*}
x y^{\prime }+\left (-x y+1\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.444 |
|
| \begin{align*}
x y^{\prime }&=\left (-x y+1\right ) y \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.474 |
|
| \begin{align*}
x y^{\prime }&=\left (x y+1\right ) y \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.740 |
|
| \begin{align*}
x y^{\prime }&=a \,x^{3} \left (-x y+1\right ) y \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.954 |
|
| \begin{align*}
x y^{\prime }&=x^{3}+\left (2 x^{2}+1\right ) y+x y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.299 |
|
| \begin{align*}
x y^{\prime }&=y \left (1+2 x y\right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.338 |
|
| \begin{align*}
x y^{\prime }+b x +\left (2+a x y\right ) y&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
2.603 |
|
| \begin{align*}
x y^{\prime }+a_{0} +a_{1} x +\left (a_{2} +a_{3} x y\right ) y&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
32.190 |
|
| \begin{align*}
x y^{\prime }+a \,x^{2} y^{2}+2 y&=b \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
31.506 |
|
| \begin{align*}
x y^{\prime }+x^{m}+\frac {\left (n -m \right ) y}{2}+x^{n} y^{2}&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
3.486 |
|
| \begin{align*}
x y^{\prime }+\left (a +b \,x^{n} y\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.006 |
|
| \begin{align*}
x y^{\prime }&=a \,x^{m}-b y-c \,x^{n} y^{2} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
1.427 |
|
| \begin{align*}
x y^{\prime }&=2 x -y+a \,x^{n} \left (x -y\right )^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.677 |
|
| \begin{align*}
x y^{\prime }+\left (1-a y \ln \left (x \right )\right ) y&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.978 |
|
| \begin{align*}
x y^{\prime }&=y+\left (x^{2}-y^{2}\right ) f \left (x \right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
3.584 |
|
| \begin{align*}
x y^{\prime }&=y \left (1+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.874 |
|
| \begin{align*}
x y^{\prime }+y \left (1-x y^{2}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.656 |
|
| \begin{align*}
x y^{\prime }+y&=a \left (x^{2}+1\right ) y^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.295 |
|
| \begin{align*}
x y^{\prime }+y&=a \left (-x^{2}+1\right ) y^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.785 |
|
| \begin{align*}
x y^{\prime }&=a y+b \left (x^{2}+1\right ) y^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.166 |
|