| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x y^{\prime }&=a y+b \left (-x^{2}+1\right ) y^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.095 |
|
| \begin{align*}
x y^{\prime }+2 y&=a \,x^{2 k} y^{k} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.304 |
|
| \begin{align*}
x y^{\prime }&=4 y-4 \sqrt {y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.938 |
|
| \begin{align*}
x y^{\prime }+2 y&=\sqrt {1+y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.559 |
|
| \begin{align*}
x y^{\prime }+2 y&=-\sqrt {1+y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.498 |
|
| \begin{align*}
x y^{\prime }&=y+\sqrt {y^{2}+x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.501 |
|
| \begin{align*}
x y^{\prime }&=y+\sqrt {x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
28.826 |
|
| \begin{align*}
x y^{\prime }&=y+x \sqrt {y^{2}+x^{2}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
3.858 |
|
| \begin{align*}
x y^{\prime }&=y-x \left (x -y\right ) \sqrt {y^{2}+x^{2}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
65.310 |
|
| \begin{align*}
x y^{\prime }&=y+a \sqrt {y^{2}+b^{2} x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
32.025 |
|
| \begin{align*}
x y^{\prime }&=y+a \sqrt {y^{2}-b^{2} x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
32.019 |
|
| \begin{align*}
x y^{\prime }+\left (\sin \left (y\right )-3 \cos \left (y\right ) x^{2}\right ) \cos \left (y\right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
3.164 |
|
| \begin{align*}
x y^{\prime }+x -y+x \cos \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.667 |
|
| \begin{align*}
x y^{\prime }&=-x \cos \left (\frac {y}{x}\right )^{2}+y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.140 |
|
| \begin{align*}
x y^{\prime }&=\left (-2 x^{2}+1\right ) \cot \left (y\right )^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.926 |
|
| \begin{align*}
x y^{\prime }&=y-x \cot \left (\frac {y}{x}\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
10.958 |
|
| \begin{align*}
x y^{\prime }+y+2 x \sec \left (x y\right )&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.473 |
|
| \begin{align*}
x y^{\prime }-y+x \sec \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.941 |
|
| \begin{align*}
x y^{\prime }&=y+x \sec \left (\frac {y}{x}\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
9.122 |
|
| \begin{align*}
x y^{\prime }&=\sin \left (x -y\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
283.430 |
|
| \begin{align*}
x y^{\prime }&=y+x \sin \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.839 |
|
| \begin{align*}
x y^{\prime }+\tan \left (y\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.586 |
|
| \begin{align*}
x y^{\prime }+x +\tan \left (x +y\right )&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.465 |
|
| \begin{align*}
x y^{\prime }&=y-x \tan \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.023 |
|
| \begin{align*}
x y^{\prime }&=\left (1+y^{2}\right ) \left (x^{2}+\arctan \left (y\right )\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
3.633 |
|
| \begin{align*}
x y^{\prime }&={\mathrm e}^{\frac {y}{x}} x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.761 |
|
| \begin{align*}
x y^{\prime }&=x +y+{\mathrm e}^{\frac {y}{x}} x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
6.559 |
|
| \begin{align*}
x y^{\prime }&=\ln \left (y\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.780 |
|
| \begin{align*}
x y^{\prime }&=\left (1+\ln \left (x \right )-\ln \left (y\right )\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.990 |
|
| \begin{align*}
x y^{\prime }+\left (1-\ln \left (x \right )-\ln \left (y\right )\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
4.469 |
|
| \begin{align*}
x y^{\prime }&=y-2 x \tanh \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
27.102 |
|
| \begin{align*}
x y^{\prime }+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)]‘]] |
✗ |
✓ |
✓ |
✗ |
4.730 |
|
| \begin{align*}
x y^{\prime }&=y f \left (x^{m} y^{n}\right ) \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
4.624 |
|
| \begin{align*}
\left (1+x \right ) y^{\prime }&=x^{3} \left (3 x +4\right )+y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.020 |
|
| \begin{align*}
\left (1+x \right ) y^{\prime }&=\left (1+x \right )^{4}+2 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.864 |
|
| \begin{align*}
\left (1+x \right ) y^{\prime }&={\mathrm e}^{x} \left (1+x \right )^{n +1}+n y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.579 |
|
| \begin{align*}
\left (1+x \right ) y^{\prime }&=a y+b x y^{2} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.434 |
|
| \begin{align*}
\left (1+x \right ) y^{\prime }+y+\left (1+x \right )^{4} y^{3}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.289 |
|
| \begin{align*}
\left (1+x \right ) y^{\prime }&=\left (1-x y^{3}\right ) y \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.009 |
|
| \begin{align*}
\left (1+x \right ) y^{\prime }&=1+y+\left (1+x \right ) \sqrt {1+y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
6.375 |
|
| \begin{align*}
\left (x +a \right ) y^{\prime }&=b x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.257 |
|
| \begin{align*}
\left (x +a \right ) y^{\prime }&=b x +y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.194 |
|
| \begin{align*}
\left (x +a \right ) y^{\prime }+b \,x^{2}+y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.230 |
|
| \begin{align*}
\left (x +a \right ) y^{\prime }&=2 \left (x +a \right )^{5}+3 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.327 |
|
| \begin{align*}
\left (x +a \right ) y^{\prime }&=b +c y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.227 |
|
| \begin{align*}
\left (x +a \right ) y^{\prime }&=-b -c y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.941 |
|
| \begin{align*}
\left (x +a \right ) y^{\prime }&=b x +c y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.494 |
|
| \begin{align*}
\left (x +a \right ) y^{\prime }&=y \left (1-a y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.842 |
|
| \begin{align*}
\left (-x +a \right ) y^{\prime }&=y+\left (c x +b \right ) y^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.381 |
|
| \begin{align*}
2 x y^{\prime }&=2 x^{3}-y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
20.349 |
|
| \begin{align*}
2 x y^{\prime }+1&=4 i x y+y^{2} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
37.878 |
|
| \begin{align*}
2 x y^{\prime }&=y \left (1+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.720 |
|
| \begin{align*}
2 x y^{\prime }+y \left (1+y^{2}\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.685 |
|
| \begin{align*}
2 x y^{\prime }&=\left (1+x -6 y^{2}\right ) y \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.852 |
|
| \begin{align*}
2 x y^{\prime }+4 y+a +\sqrt {a^{2}-4 b -4 c y}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.679 |
|
| \begin{align*}
2 x y^{\prime }+4 y+a -\sqrt {a^{2}-4 b -4 c y}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.212 |
|
| \begin{align*}
\left (1-2 x \right ) y^{\prime }&=16+32 x -6 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.500 |
|
| \begin{align*}
\left (2 x +1\right ) y^{\prime }&=4 \,{\mathrm e}^{-y}-2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.965 |
|
| \begin{align*}
2 \left (1-x \right ) y^{\prime }&=4 x \sqrt {1-x}+y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.400 |
|
| \begin{align*}
2 \left (1+x \right ) y^{\prime }+2 y+\left (1+x \right )^{4} y^{3}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.477 |
|
| \begin{align*}
3 x y^{\prime }&=3 x^{{2}/{3}}+\left (1-3 y\right ) y \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
3.037 |
|
| \begin{align*}
3 x y^{\prime }&=\left (2+x y^{3}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.016 |
|
| \begin{align*}
3 x y^{\prime }&=\left (3 y^{3} \ln \left (x \right ) x +1\right ) y \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.691 |
|
| \begin{align*}
x^{2} y^{\prime }&=-y+a \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.384 |
|
| \begin{align*}
x^{2} y^{\prime }&=a +b x +c \,x^{2}+x y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.020 |
|
| \begin{align*}
x^{2} y^{\prime }&=a +b x +c \,x^{2}-x y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.002 |
|
| \begin{align*}
x^{2} y^{\prime }+\left (1-2 x \right ) y&=x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.486 |
|
| \begin{align*}
x^{2} y^{\prime }&=a +b x y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.380 |
|
| \begin{align*}
x^{2} y^{\prime }&=\left (b x +a \right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.631 |
|
| \begin{align*}
x^{2} y^{\prime }+x \left (x +2\right ) y&=x \left (1-{\mathrm e}^{-2 x}\right )-2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.398 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
2.589 |
|
| \begin{align*}
x^{2} y^{\prime }+x^{2}+x y+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.347 |
|
| \begin{align*}
x^{2} y^{\prime }&=\left (1+2 x -y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.235 |
|
| \begin{align*}
x^{2} y^{\prime }&=a +b y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.615 |
|
| \begin{align*}
x^{2} y^{\prime }&=\left (x +a y\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.980 |
|
| \begin{align*}
x^{2} y^{\prime }&=\left (a x +b y\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
42.329 |
|
| \begin{align*}
x^{2} y^{\prime }+a \,x^{2}+b x y+c y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
19.484 |
|
| \begin{align*}
x^{2} y^{\prime }&=a +b \,x^{n}+x^{2} y^{2} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
0.537 |
|
| \begin{align*}
x^{2} y^{\prime }+2+x y \left (4+x y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.885 |
|
| \begin{align*}
x^{2} y^{\prime }+2+a x \left (-x y+1\right )-x^{2} y^{2}&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
2.805 |
|
| \begin{align*}
x^{2} y^{\prime }&=a +b \,x^{2} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
4.382 |
|
| \begin{align*}
x^{2} y^{\prime }&=a +b \,x^{n}+c \,x^{2} y^{2} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
88.869 |
|
| \begin{align*}
x^{2} y^{\prime }&=a +b x y+c \,x^{2} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.730 |
|
| \begin{align*}
x^{2} y^{\prime }&=a +b x y+c \,x^{4} y^{2} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
1.736 |
|
| \begin{align*}
x^{2} y^{\prime }+\left (x^{2}+y^{2}-x \right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.908 |
|
| \begin{align*}
x^{2} y^{\prime }&=2 y \left (x -y^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.115 |
|
| \begin{align*}
x^{2} y^{\prime }&=a \,x^{2} y^{2}-a y^{3} \\
\end{align*} |
[_rational, _Abel] |
✗ |
✓ |
✓ |
✗ |
2.392 |
|
| \begin{align*}
x^{2} y^{\prime }+a y^{2}+b \,x^{2} y^{3}&=0 \\
\end{align*} |
[_rational, _Abel] |
✗ |
✓ |
✓ |
✗ |
3.280 |
|
| \begin{align*}
x^{2} y^{\prime }&=\left (a x +y^{3} b \right ) y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.275 |
|
| \begin{align*}
x^{2} y^{\prime }+x y+\sqrt {y}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.361 |
|
| \begin{align*}
x^{2} y^{\prime }&=\sec \left (y\right )+3 x \tan \left (y\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
✗ |
15.930 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=1-x^{2}+y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.894 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+1&=x y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.766 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-1&=x y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.751 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=5-x y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.200 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+a +x y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.652 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }-a +x y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.589 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+a -x y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.047 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }-a -x y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.934 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+a -x y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.737 |
|