| # |
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] |
✓ |
✓ |
✓ |
✓ |
9.174 |
|
| \begin{align*}
y^{\prime }&=\left (\tan \left (x \right )+y^{3} \sec \left (x \right )\right ) y \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.677 |
|
| \begin{align*}
y^{\prime }&=a \,x^{\frac {n}{1-n}}+b y^{n} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Chini] |
✓ |
✓ |
✓ |
✗ |
12.842 |
|
| \begin{align*}
y^{\prime }&=f \left (x \right ) y+g \left (x \right ) y^{k} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.759 |
|
| \begin{align*}
y^{\prime }&=f \left (x \right )+g \left (x \right ) y+h \left (x \right ) y^{n} \\
\end{align*} |
[_Chini] |
✗ |
✗ |
✗ |
✗ |
6.024 |
|
| \begin{align*}
y^{\prime }&=\sqrt {{| y|}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
13.466 |
|
| \begin{align*}
y^{\prime }&=a +b y+\sqrt {A +B y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
57.720 |
|
| \begin{align*}
y^{\prime }&=a +b y-\sqrt {A +B y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
67.823 |
|
| \begin{align*}
y^{\prime }&=a x +b \sqrt {y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Chini] |
✓ |
✓ |
✓ |
✗ |
12.212 |
|
| \begin{align*}
y^{\prime }+x^{3}&=x \sqrt {x^{4}+4 y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
21.820 |
|
| \begin{align*}
y^{\prime }+2 y \left (1-x \sqrt {y}\right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.279 |
|
| \begin{align*}
y^{\prime }&=\sqrt {a +b y^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.970 |
|
| \begin{align*}
y^{\prime }&=y \sqrt {a +b y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
39.566 |
|
| \begin{align*}
y^{\prime }&=\cos \left (y\right ) \cos \left (x \right )^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
4.028 |
|
| \begin{align*}
y^{\prime }&=\sec \left (x \right )^{2} \cot \left (y\right ) \cos \left (y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.379 |
|
| \begin{align*}
y^{\prime }&=a +b \cos \left (A x +B y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.319 |
|
| \begin{align*}
y^{\prime }&=a +b \cos \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
6.410 |
|
| \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’)‘] |
✓ |
✓ |
✓ |
✗ |
18.645 |
|
| \begin{align*}
y^{\prime }+\tan \left (x \right ) \sec \left (x \right ) \cos \left (y\right )^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
3.676 |
|
| \begin{align*}
y^{\prime }&=\cot \left (x \right ) \cot \left (y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.414 |
|
| \begin{align*}
y^{\prime }+\cot \left (x \right ) \cot \left (y\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.168 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x \right ) \left (\csc \left (y\right )-\cot \left (y\right )\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.980 |
|
| \begin{align*}
y^{\prime }&=\tan \left (x \right ) \cot \left (y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.773 |
|
| \begin{align*}
y^{\prime }+\tan \left (x \right ) \cot \left (y\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.243 |
|
| \begin{align*}
y^{\prime }+\sin \left (2 x \right ) \csc \left (2 y\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.595 |
|
| \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’)‘] |
✗ |
✓ |
✓ |
✓ |
11.130 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x \right ) \sec \left (y\right )^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.215 |
|
| \begin{align*}
y^{\prime }&=\sec \left (x \right )^{2} \sec \left (y\right )^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
3.661 |
|
| \begin{align*}
y^{\prime }&=a +b \sin \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
6.777 |
|
| \begin{align*}
y^{\prime }&=a +b \sin \left (A x +B y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.717 |
|
| \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’)‘] |
✗ |
✗ |
✓ |
✓ |
7.634 |
|
| \begin{align*}
y^{\prime }+\csc \left (2 x \right ) \sin \left (2 y\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.901 |
|
| \begin{align*}
y^{\prime }&=\sqrt {a +b \cos \left (y\right )} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
12.120 |
|
| \begin{align*}
y^{\prime }&=x +{\mathrm e}^{y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.898 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x +y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.028 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x} \left (a +b \,{\mathrm e}^{-y}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.370 |
|
| \begin{align*}
y \ln \left (x \right ) \ln \left (y\right )+y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.680 |
|
| \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)]‘]] |
✗ |
✓ |
✓ |
✗ |
13.417 |
|
| \begin{align*}
y^{\prime }&=a f \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.188 |
|
| \begin{align*}
y^{\prime }&=f \left (a +b x +c y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.177 |
|
| \begin{align*}
y^{\prime }&=f \left (x \right ) g \left (y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.358 |
|
| \begin{align*}
y^{\prime }&=\sec \left (x \right )^{2}+y \sec \left (x \right ) \operatorname {Csx} \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.506 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
2.200 |
|
| \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’)‘] |
✗ |
✗ |
✓ |
✗ |
68.343 |
|
| \begin{align*}
2 y^{\prime }+a x&=\sqrt {a^{2} x^{2}-4 b \,x^{2}-4 c y} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
21.488 |
|
| \begin{align*}
2 y^{\prime }+a x&=-\sqrt {a^{2} x^{2}-4 b \,x^{2}-4 c y} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
15.806 |
|
| \begin{align*}
3 y^{\prime }&=x +\sqrt {x^{2}-3 y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
35.973 |
|
| \begin{align*}
3 y^{\prime }&=x -\sqrt {x^{2}-3 y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
97.709 |
|
| \begin{align*}
x y^{\prime }&=\sqrt {a^{2}-x^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.049 |
|
| \begin{align*}
x y^{\prime }&=-\sqrt {a^{2}-x^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.895 |
|
| \begin{align*}
x y^{\prime }+x +y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.625 |
|
| \begin{align*}
x y^{\prime }+x^{2}-y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.071 |
|
| \begin{align*}
x y^{\prime }&=x^{3}-y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.066 |
|
| \begin{align*}
x y^{\prime }&=1+x^{3}+y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.300 |
|
| \begin{align*}
x y^{\prime }&=x^{m}+y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.307 |
|
| \begin{align*}
x y^{\prime }&=x \sin \left (x \right )-y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.692 |
|
| \begin{align*}
x y^{\prime }&=x^{2} \sin \left (x \right )+y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.224 |
|
| \begin{align*}
x y^{\prime }&=x^{n} \ln \left (x \right )-y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.857 |
|
| \begin{align*}
x y^{\prime }&=\sin \left (x \right )-2 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.276 |
|
| \begin{align*}
x y^{\prime }&=a y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.353 |
|
| \begin{align*}
x y^{\prime }&=-a y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.484 |
|
| \begin{align*}
x y^{\prime }&=1+x +a y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.378 |
|
| \begin{align*}
x y^{\prime }&=a x +b y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
10.760 |
|
| \begin{align*}
x y^{\prime }&=a \,x^{2}+b y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.083 |
|
| \begin{align*}
x y^{\prime }&=a +b \,x^{n}+c y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
6.365 |
|
| \begin{align*}
x y^{\prime }+2+\left (-x +3\right ) y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.764 |
|
| \begin{align*}
x y^{\prime }+x +\left (a x +2\right ) y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.711 |
|
| \begin{align*}
x y^{\prime }+\left (b x +a \right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.244 |
|
| \begin{align*}
x y^{\prime }&=x^{3}+\left (-2 x^{2}+1\right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.111 |
|
| \begin{align*}
x y^{\prime }&=a x -\left (-b \,x^{2}+1\right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.031 |
|
| \begin{align*}
x y^{\prime }+\left (-a \,x^{2}+2\right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.134 |
|
| \begin{align*}
x y^{\prime }+x^{2}+y^{2}&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
7.986 |
|
| \begin{align*}
x y^{\prime }&=x^{2}+y \left (y+1\right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.934 |
|
| \begin{align*}
x y^{\prime }-y+y^{2}&=x^{{2}/{3}} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
53.305 |
|
| \begin{align*}
x y^{\prime }&=a +b y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.079 |
|
| \begin{align*}
x y^{\prime }&=a \,x^{2}+y+b y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
2.787 |
|
| \begin{align*}
x y^{\prime }&=a \,x^{2 n}+\left (n +b y\right ) y \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
6.352 |
|
| \begin{align*}
x y^{\prime }&=a \,x^{n}+b y+c y^{2} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
33.205 |
|
| \begin{align*}
x y^{\prime }&=k +a \,x^{n}+b y+c y^{2} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
16.161 |
|
| \begin{align*}
x y^{\prime }+a +x y^{2}&=0 \\
\end{align*} |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
6.516 |
|
| \begin{align*}
x y^{\prime }+\left (-y x +1\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.570 |
|
| \begin{align*}
x y^{\prime }&=\left (-y x +1\right ) y \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.580 |
|
| \begin{align*}
x y^{\prime }&=\left (y x +1\right ) y \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.031 |
|
| \begin{align*}
x y^{\prime }&=a \,x^{3} \left (-y x +1\right ) y \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.187 |
|
| \begin{align*}
x y^{\prime }&=x^{3}+\left (2 x^{2}+1\right ) y+x y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.405 |
|
| \begin{align*}
x y^{\prime }&=y \left (1+2 y x \right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.776 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
4.398 |
|
| \begin{align*}
x y^{\prime }+a_{0} +a_{1} x +\left (a_{2} +a_{3} x y\right ) y&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
35.074 |
|
| \begin{align*}
x y^{\prime }+a \,x^{2} y^{2}+2 y&=b \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
33.003 |
|
| \begin{align*}
x y^{\prime }+x^{m}+\frac {\left (n -m \right ) y}{2}+x^{n} y^{2}&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
6.603 |
|
| \begin{align*}
x y^{\prime }+\left (a +b \,x^{n} y\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.353 |
|
| \begin{align*}
x y^{\prime }&=a \,x^{m}-b y-c \,x^{n} y^{2} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
2.826 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
10.126 |
|
| \begin{align*}
x y^{\prime }+\left (1-a y \ln \left (x \right )\right ) y&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.358 |
|
| \begin{align*}
x y^{\prime }&=y+\left (x^{2}-y^{2}\right ) f \left (x \right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
6.819 |
|
| \begin{align*}
x y^{\prime }&=y \left (1+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.938 |
|
| \begin{align*}
x y^{\prime }+y \left (1-x y^{2}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
19.365 |
|
| \begin{align*}
x y^{\prime }+y&=a \left (x^{2}+1\right ) y^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.107 |
|
| \begin{align*}
x y^{\prime }+y&=a \left (-x^{2}+1\right ) y^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.107 |
|
| \begin{align*}
x y^{\prime }&=a y+b \left (x^{2}+1\right ) y^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
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✓ |
✓ |
✓ |
11.597 |
|