| # |
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] |
✓ |
✓ |
✓ |
✓ |
4.793 |
|
| \begin{align*}
y^{\prime } x +2 y&=a \,x^{2 k} y^{k} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.027 |
|
| \begin{align*}
y^{\prime } x&=4 y-4 \sqrt {y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.976 |
|
| \begin{align*}
y^{\prime } x +2 y&=\sqrt {1+y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.494 |
|
| \begin{align*}
y^{\prime } x +2 y&=-\sqrt {1+y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.484 |
|
| \begin{align*}
y^{\prime } x&=y+\sqrt {y^{2}+x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.534 |
|
| \begin{align*}
y^{\prime } x&=y+\sqrt {x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
17.269 |
|
| \begin{align*}
y^{\prime } x&=y+x \sqrt {y^{2}+x^{2}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
✓ |
✓ |
✗ |
5.414 |
|
| \begin{align*}
y^{\prime } x&=y-x \left (x -y\right ) \sqrt {y^{2}+x^{2}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
✓ |
✓ |
✗ |
7.773 |
|
| \begin{align*}
y^{\prime } x&=y+a \sqrt {y^{2}+b^{2} x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
18.663 |
|
| \begin{align*}
y^{\prime } x&=y+a \sqrt {y^{2}-b^{2} x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
18.906 |
|
| \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’)‘] |
✓ |
✓ |
✓ |
✗ |
3.227 |
|
| \begin{align*}
y^{\prime } x +x -y+x \cos \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.111 |
|
| \begin{align*}
y^{\prime } x&=-x \cos \left (\frac {y}{x}\right )^{2}+y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.297 |
|
| \begin{align*}
y^{\prime } x&=\left (-2 x^{2}+1\right ) \cot \left (y\right )^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.214 |
|
| \begin{align*}
y^{\prime } x&=y-x \cot \left (\frac {y}{x}\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
7.047 |
|
| \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)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.506 |
|
| \begin{align*}
y^{\prime } x -y+x \sec \left (\frac {y}{x}\right )&=0 \\
\end{align*} | [[_homogeneous, ‘class A‘], _dAlembert] | ✓ | ✓ | ✓ | ✓ | 5.007 |
|
| \begin{align*}
y^{\prime } x&=y+x \sec \left (\frac {y}{x}\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
4.289 |
|
| \begin{align*}
y^{\prime } x&=\sin \left (x -y\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
4.167 |
|
| \begin{align*}
y^{\prime } x&=y+x \sin \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.749 |
|
| \begin{align*}
y^{\prime } x +\tan \left (y\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.243 |
|
| \begin{align*}
y^{\prime } x +x +\tan \left (x +y\right )&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.862 |
|
| \begin{align*}
y^{\prime } x&=y-\tan \left (\frac {y}{x}\right ) x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.869 |
|
| \begin{align*}
y^{\prime } x&=\left (1+y^{2}\right ) \left (x^{2}+\arctan \left (y\right )\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
3.928 |
|
| \begin{align*}
y^{\prime } x&={\mathrm e}^{\frac {y}{x}} x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
4.703 |
|
| \begin{align*}
y^{\prime } x&=x +y+{\mathrm e}^{\frac {y}{x}} x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
4.563 |
|
| \begin{align*}
y^{\prime } x&=y \ln \left (y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.200 |
|
| \begin{align*}
y^{\prime } x&=\left (1+\ln \left (x \right )-\ln \left (y\right )\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.859 |
|
| \begin{align*}
y^{\prime } x +\left (1-\ln \left (x \right )-\ln \left (y\right )\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
3.670 |
|
| \begin{align*}
y^{\prime } x&=y-2 x \tanh \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
7.065 |
|
| \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)]‘]] |
✗ |
✓ |
✓ |
✗ |
5.768 |
|
| \begin{align*}
y^{\prime } x&=y f \left (x^{m} y^{n}\right ) \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
5.097 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=x^{3} \left (3 x +4\right )+y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.392 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=\left (x +1\right )^{4}+2 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.358 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&={\mathrm e}^{x} \left (x +1\right )^{n +1}+n y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.020 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=a y+b x y^{2} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.997 |
|
| \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] | ✓ | ✓ | ✓ | ✓ | 5.348 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=\left (1-x y^{3}\right ) y \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.533 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=1+y+\left (x +1\right ) \sqrt {1+y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
46.320 |
|
| \begin{align*}
\left (x +a \right ) y^{\prime }&=b x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.240 |
|
| \begin{align*}
\left (x +a \right ) y^{\prime }&=b x +y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.191 |
|
| \begin{align*}
\left (x +a \right ) y^{\prime }+b \,x^{2}+y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.586 |
|
| \begin{align*}
\left (x +a \right ) y^{\prime }&=2 \left (x +a \right )^{5}+3 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.150 |
|
| \begin{align*}
\left (x +a \right ) y^{\prime }&=b +c y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.539 |
|
| \begin{align*}
\left (x +a \right ) y^{\prime }&=-b -c y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.562 |
|
| \begin{align*}
\left (x +a \right ) y^{\prime }&=b x +c y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.719 |
|
| \begin{align*}
\left (x +a \right ) y^{\prime }&=y \left (1-a y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.418 |
|
| \begin{align*}
\left (a -x \right ) y^{\prime }&=y+\left (c x +b \right ) y^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.451 |
|
| \begin{align*}
2 y^{\prime } x&=2 x^{3}-y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
11.957 |
|
| \begin{align*}
2 y^{\prime } x +1&=4 i x y+y^{2} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
57.595 |
|
| \begin{align*}
2 y^{\prime } x&=y \left (1+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.633 |
|
| \begin{align*}
2 y^{\prime } x +y \left (1+y^{2}\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.075 |
|
| \begin{align*}
2 y^{\prime } x&=\left (1+x -6 y^{2}\right ) y \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.016 |
|
| \begin{align*}
2 y^{\prime } x +4 y+a +\sqrt {a^{2}-4 b -4 c y}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.408 |
|
| \begin{align*}
2 y^{\prime } x +4 y+a -\sqrt {a^{2}-4 b -4 c y}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.236 |
|
| \begin{align*}
\left (1-2 x \right ) y^{\prime }&=16+32 x -6 y \\
\end{align*} | [_linear] | ✓ | ✓ | ✓ | ✓ | 3.803 |
|
| \begin{align*}
\left (2 x +1\right ) y^{\prime }&=4 \,{\mathrm e}^{-y}-2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.266 |
|
| \begin{align*}
2 \left (1-x \right ) y^{\prime }&=4 x \sqrt {1-x}+y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.142 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
5.968 |
|
| \begin{align*}
3 y^{\prime } x&=3 x^{{2}/{3}}+\left (1-3 y\right ) y \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
3.288 |
|
| \begin{align*}
3 y^{\prime } x&=\left (2+x y^{3}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.251 |
|
| \begin{align*}
3 y^{\prime } x&=\left (3 y^{3} \ln \left (x \right ) x +1\right ) y \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.720 |
|
| \begin{align*}
x^{2} y^{\prime }&=-y+a \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.497 |
|
| \begin{align*}
x^{2} y^{\prime }&=a +b x +c \,x^{2}+y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.940 |
|
| \begin{align*}
x^{2} y^{\prime }&=a +b x +c \,x^{2}-y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.960 |
|
| \begin{align*}
x^{2} y^{\prime }+\left (1-2 x \right ) y&=x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.849 |
|
| \begin{align*}
x^{2} y^{\prime }&=a +b x y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.970 |
|
| \begin{align*}
x^{2} y^{\prime }&=\left (b x +a \right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.904 |
|
| \begin{align*}
x^{2} y^{\prime }+x \left (2+x \right ) y&=x \left (1-{\mathrm e}^{-2 x}\right )-2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.286 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
3.442 |
|
| \begin{align*}
x^{2} y^{\prime }+x^{2}+y x +y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.111 |
|
| \begin{align*}
x^{2} y^{\prime }&=\left (1+2 x -y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.839 |
|
| \begin{align*}
x^{2} y^{\prime }&=a +b y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.404 |
|
| \begin{align*}
x^{2} y^{\prime }&=\left (x +a y\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.850 |
|
| \begin{align*}
x^{2} y^{\prime }&=\left (a x +b y\right ) y \\
\end{align*} | [[_homogeneous, ‘class A‘], _rational, _Bernoulli] | ✓ | ✓ | ✓ | ✓ | 42.598 |
|
| \begin{align*}
x^{2} y^{\prime }+a \,x^{2}+b x y+c y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
62.256 |
|
| \begin{align*}
x^{2} y^{\prime }&=a +b \,x^{n}+y^{2} x^{2} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
0.389 |
|
| \begin{align*}
x^{2} y^{\prime }+2+x y \left (4+y x \right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.807 |
|
| \begin{align*}
x^{2} y^{\prime }+2+a x \left (-y x +1\right )-y^{2} x^{2}&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
3.713 |
|
| \begin{align*}
x^{2} y^{\prime }&=a +b \,x^{2} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
6.015 |
|
| \begin{align*}
x^{2} y^{\prime }&=a +b \,x^{n}+c \,x^{2} y^{2} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
88.596 |
|
| \begin{align*}
x^{2} y^{\prime }&=a +b x y+c \,x^{2} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.303 |
|
| \begin{align*}
x^{2} y^{\prime }&=a +b x y+c \,x^{4} y^{2} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
1.259 |
|
| \begin{align*}
x^{2} y^{\prime }+\left (x^{2}+y^{2}-x \right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.621 |
|
| \begin{align*}
x^{2} y^{\prime }&=2 y \left (x -y^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.618 |
|
| \begin{align*}
x^{2} y^{\prime }&=a \,x^{2} y^{2}-a y^{3} \\
\end{align*} |
[_rational, _Abel] |
✗ |
✓ |
✓ |
✗ |
2.274 |
|
| \begin{align*}
x^{2} y^{\prime }+a y^{2}+b \,x^{2} y^{3}&=0 \\
\end{align*} |
[_rational, _Abel] |
✗ |
✓ |
✓ |
✗ |
3.131 |
|
| \begin{align*}
x^{2} y^{\prime }&=\left (a x +y^{3} b \right ) y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.315 |
|
| \begin{align*}
x^{2} y^{\prime }+y x +\sqrt {y}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.095 |
|
| \begin{align*}
x^{2} y^{\prime }&=\sec \left (y\right )+3 x \tan \left (y\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
✗ |
19.966 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=1-x^{2}+y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.516 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+1&=y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.307 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-1&=y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.297 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=5-y x \\
\end{align*} | [_linear] | ✓ | ✓ | ✓ | ✓ | 4.532 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+a +y x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.369 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }-a +y x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.342 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+a -y x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.098 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }-a -y x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.029 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+a -y x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.364 |
|