| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime } x&=a y+b \left (-x^{2}+1\right ) y^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.788 |
|
| \begin{align*}
y^{\prime } x +2 y&=a \,x^{2 k} y^{k} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
42.584 |
|
| \begin{align*}
y^{\prime } x&=4 y-4 \sqrt {y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
22.216 |
|
| \begin{align*}
y^{\prime } x +2 y&=\sqrt {1+y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
17.252 |
|
| \begin{align*}
y^{\prime } x +2 y&=-\sqrt {1+y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
17.293 |
|
| \begin{align*}
y^{\prime } x&=y+\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
24.539 |
|
| \begin{align*}
y^{\prime } x&=y+\sqrt {x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
77.677 |
|
| \begin{align*}
y^{\prime } x&=y+x \sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
8.467 |
|
| \begin{align*}
y^{\prime } x&=y-x \left (x -y\right ) \sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
✓ |
✓ |
✗ |
17.381 |
|
| \begin{align*}
y^{\prime } x&=y+a \sqrt {y^{2}+b^{2} x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
84.317 |
|
| \begin{align*}
y^{\prime } x&=y+a \sqrt {y^{2}-b^{2} x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
82.416 |
|
| \begin{align*}
y^{\prime } x +\left (\sin \left (y\right )-3 \cos \left (y\right ) x^{2}\right ) \cos \left (y\right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
5.649 |
|
| \begin{align*}
y^{\prime } x +x -y+x \cos \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.521 |
|
| \begin{align*}
y^{\prime } x&=y-x \cos \left (\frac {y}{x}\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
11.585 |
|
| \begin{align*}
y^{\prime } x&=\left (-2 x^{2}+1\right ) \cot \left (y\right )^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.521 |
|
| \begin{align*}
y^{\prime } x&=y-x \cot \left (\frac {y}{x}\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
14.567 |
|
| \begin{align*}
y^{\prime } x +y+2 x \sec \left (y x \right )&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
4.083 |
|
| \begin{align*}
y^{\prime } x -y+x \sec \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.949 |
|
| \begin{align*}
y^{\prime } x&=y+x \sec \left (\frac {y}{x}\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
12.950 |
|
| \begin{align*}
y^{\prime } x&=\sin \left (x -y\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
65.623 |
|
| \begin{align*}
y^{\prime } x&=y+x \sin \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
14.167 |
|
| \begin{align*}
y^{\prime } x +\tan \left (y\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.861 |
|
| \begin{align*}
y^{\prime } x +x +\tan \left (x +y\right )&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
8.498 |
|
| \begin{align*}
y^{\prime } x&=y-x \tan \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
16.312 |
|
| \begin{align*}
y^{\prime } x&=\left (1+y^{2}\right ) \left (x^{2}+\arctan \left (y\right )\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
7.258 |
|
| \begin{align*}
y^{\prime } x&={\mathrm e}^{\frac {y}{x}} x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
14.897 |
|
| \begin{align*}
y^{\prime } x&=x +y+{\mathrm e}^{\frac {y}{x}} x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
17.943 |
|
| \begin{align*}
y^{\prime } x&=\ln \left (y\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.813 |
|
| \begin{align*}
y^{\prime } x&=\left (1+\ln \left (x \right )-\ln \left (y\right )\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
21.501 |
|
| \begin{align*}
y^{\prime } x +\left (1-\ln \left (x \right )-\ln \left (y\right )\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
13.343 |
|
| \begin{align*}
y^{\prime } x&=y-2 x \tanh \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
30.923 |
|
| \begin{align*}
y^{\prime } x +n y&=f \left (x \right ) g \left (x^{n} y\right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
✓ |
✓ |
✗ |
9.754 |
|
| \begin{align*}
y^{\prime } x&=y f \left (x^{m} y^{n}\right ) \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
12.819 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=x^{3} \left (3 x +4\right )+y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.218 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=\left (x +1\right )^{4}+2 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.728 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&={\mathrm e}^{x} \left (x +1\right )^{n +1}+n y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.746 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=a y+b x y^{2} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
20.444 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }+y+\left (x +1\right )^{4} y^{3}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.823 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=\left (1-x y^{3}\right ) y \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.039 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=1+y+\left (x +1\right ) \sqrt {1+y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
13.938 |
|
| \begin{align*}
\left (a +x \right ) y^{\prime }&=b x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.987 |
|
| \begin{align*}
\left (a +x \right ) y^{\prime }&=b x +y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.895 |
|
| \begin{align*}
\left (a +x \right ) y^{\prime }+b \,x^{2}+y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.753 |
|
| \begin{align*}
\left (a +x \right ) y^{\prime }&=2 \left (a +x \right )^{5}+3 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.473 |
|
| \begin{align*}
\left (a +x \right ) y^{\prime }&=b +c y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.106 |
|
| \begin{align*}
\left (a +x \right ) y^{\prime }&=-b -c y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.995 |
|
| \begin{align*}
\left (a +x \right ) y^{\prime }&=b x +c y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
9.776 |
|
| \begin{align*}
\left (a +x \right ) y^{\prime }&=y \left (1-a y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.533 |
|
| \begin{align*}
\left (a -x \right ) y^{\prime }&=y+\left (c x +b \right ) y^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.484 |
|
| \begin{align*}
2 y^{\prime } x&=2 x^{3}-y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
35.504 |
|
| \begin{align*}
2 y^{\prime } x +1&=4 i x y+y^{2} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
65.672 |
|
| \begin{align*}
2 y^{\prime } x&=y \left (1+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.605 |
|
| \begin{align*}
2 y^{\prime } x +y \left (1+y^{2}\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
37.198 |
|
| \begin{align*}
2 y^{\prime } x&=\left (1+x -6 y^{2}\right ) y \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.820 |
|
| \begin{align*}
2 y^{\prime } x +4 y+a +\sqrt {a^{2}-4 b -4 c y}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
16.602 |
|
| \begin{align*}
2 y^{\prime } x +4 y+a -\sqrt {a^{2}-4 b -4 c y}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
19.879 |
|
| \begin{align*}
\left (1-2 x \right ) y^{\prime }&=16+32 x -6 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
9.201 |
|
| \begin{align*}
\left (2 x +1\right ) y^{\prime }&=4 \,{\mathrm e}^{-y}-2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.571 |
|
| \begin{align*}
2 \left (1-x \right ) y^{\prime }&=4 x \sqrt {1-x}+y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.460 |
|
| \begin{align*}
2 \left (x +1\right ) y^{\prime }+2 y+\left (x +1\right )^{4} y^{3}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.806 |
|
| \begin{align*}
3 y^{\prime } x&=3 x^{{2}/{3}}+\left (1-3 y\right ) y \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
6.994 |
|
| \begin{align*}
3 y^{\prime } x&=\left (2+x y^{3}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
16.038 |
|
| \begin{align*}
3 y^{\prime } x&=\left (3 \ln \left (x \right ) y^{3} x +1\right ) y \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.061 |
|
| \begin{align*}
x^{2} y^{\prime }&=-y+a \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.287 |
|
| \begin{align*}
x^{2} y^{\prime }&=a +b x +c \,x^{2}+y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.664 |
|
| \begin{align*}
x^{2} y^{\prime }&=a +b x +c \,x^{2}-y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.314 |
|
| \begin{align*}
x^{2} y^{\prime }+\left (1-2 x \right ) y&=x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.913 |
|
| \begin{align*}
x^{2} y^{\prime }&=a +b x y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
9.427 |
|
| \begin{align*}
x^{2} y^{\prime }&=\left (b x +a \right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.984 |
|
| \begin{align*}
x^{2} y^{\prime }+x \left (2+x \right ) y&=x \left (1-{\mathrm e}^{-2 x}\right )-2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.344 |
|
| \begin{align*}
x^{2} y^{\prime }+2 x \left (1-x \right ) y&={\mathrm e}^{x} \left (2 \,{\mathrm e}^{x}-1\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.466 |
|
| \begin{align*}
x^{2} y^{\prime }+x^{2}+y x +y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
11.471 |
|
| \begin{align*}
x^{2} y^{\prime }&=\left (1+2 x -y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
17.848 |
|
| \begin{align*}
x^{2} y^{\prime }&=a +b y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.113 |
|
| \begin{align*}
x^{2} y^{\prime }&=\left (x +a y\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
16.942 |
|
| \begin{align*}
x^{2} y^{\prime }&=\left (a x +b y\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
79.053 |
|
| \begin{align*}
x^{2} y^{\prime }+a \,x^{2}+b x y+c y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
81.831 |
|
| \begin{align*}
x^{2} y^{\prime }&=a +b \,x^{n}+y^{2} x^{2} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
1.117 |
|
| \begin{align*}
x^{2} y^{\prime }+2+x y \left (4+y x \right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
13.174 |
|
| \begin{align*}
x^{2} y^{\prime }+2+a x \left (-y x +1\right )-y^{2} x^{2}&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
6.020 |
|
| \begin{align*}
x^{2} y^{\prime }&=a +b \,x^{2} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
11.178 |
|
| \begin{align*}
x^{2} y^{\prime }&=a +b \,x^{n}+c \,x^{2} y^{2} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
111.825 |
|
| \begin{align*}
x^{2} y^{\prime }&=a +b x y+c \,x^{2} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
12.025 |
|
| \begin{align*}
x^{2} y^{\prime }&=a +b x y+c \,x^{4} y^{2} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
4.369 |
|
| \begin{align*}
x^{2} y^{\prime }+\left (x^{2}+y^{2}-x \right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.965 |
|
| \begin{align*}
x^{2} y^{\prime }&=2 y \left (x -y^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
24.437 |
|
| \begin{align*}
x^{2} y^{\prime }&=a \,x^{2} y^{2}-a y^{3} \\
\end{align*} |
[_rational, _Abel] |
✗ |
✓ |
✓ |
✗ |
13.001 |
|
| \begin{align*}
x^{2} y^{\prime }+a y^{2}+b \,x^{2} y^{3}&=0 \\
\end{align*} |
[_rational, _Abel] |
✗ |
✓ |
✓ |
✗ |
14.943 |
|
| \begin{align*}
x^{2} y^{\prime }&=\left (a x +y^{3} b \right ) y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
16.117 |
|
| \begin{align*}
x^{2} y^{\prime }+y x +\sqrt {y}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
25.489 |
|
| \begin{align*}
x^{2} y^{\prime }&=\sec \left (y\right )+3 x \tan \left (y\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
✗ |
34.371 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=1-x^{2}+y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.727 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+1&=y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.503 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-1&=y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.493 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=5-y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
14.318 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+a +y x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.530 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }-a +y x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.222 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+a -y x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
15.115 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }-a -y x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
15.012 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+a -y x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.606 |
|