| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y y^{\prime }+x^{3}+y&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
✗ |
11.005 |
|
| \begin{align*}
y y^{\prime }+a y+x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
54.229 |
|
| \begin{align*}
y y^{\prime }+a y+\frac {\left (a^{2}-1\right ) x}{4}+b \,x^{n}&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
✗ |
110.644 |
|
| \begin{align*}
y y^{\prime }+a y+b \,{\mathrm e}^{x}-2 a&=0 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
✗ |
19.380 |
|
| \begin{align*}
y y^{\prime }+4 x \left (x +1\right )+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.849 |
|
| \begin{align*}
y y^{\prime }+a y^{2}-b \cos \left (x +c \right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.052 |
|
| \begin{align*}
y y^{\prime }-\sqrt {a y^{2}+b}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.772 |
|
| \begin{align*}
y y^{\prime }+x y^{2}-4 x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.813 |
|
| \begin{align*}
y y^{\prime }-{\mathrm e}^{\frac {x}{y}} x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.128 |
|
| \begin{align*}
y y^{\prime }+x +f \left (x^{2}+y^{2}\right ) g \left (x \right )&=0 \\
\end{align*} |
[NONE] |
✗ |
✓ |
✓ |
✗ |
6.548 |
|
| \begin{align*}
\left (1+y\right ) y^{\prime }-y-x&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
73.483 |
|
| \begin{align*}
\left (x +y-1\right ) y^{\prime }-y+2 x +3&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
48.674 |
|
| \begin{align*}
\left (y+2 x -2\right ) y^{\prime }-y+x +1&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
44.585 |
|
| \begin{align*}
\left (1-2 x +y\right ) y^{\prime }+y+x&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
44.030 |
|
| \begin{align*}
\left (-x^{2}+y\right ) y^{\prime }-x&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
4.333 |
|
| \begin{align*}
\left (-x^{2}+y\right ) y^{\prime }+4 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
47.250 |
|
| \begin{align*}
2 y y^{\prime }-x y^{2}-x^{3}&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.518 |
|
| \begin{align*}
\left (x +2 y+1\right ) y^{\prime }+1-x -2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.039 |
|
| \begin{align*}
\left (2 y+x +7\right ) y^{\prime }-y+2 x +4&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
22.930 |
|
| \begin{align*}
\left (-x +2 y\right ) y^{\prime }-y-2 x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.258 |
|
| \begin{align*}
\left (2 y-6 x \right ) y^{\prime }-y+3 x +2&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.484 |
|
| \begin{align*}
\left (3+2 x +4 y\right ) y^{\prime }-2 y-x -1&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.996 |
|
| \begin{align*}
\left (4 y-2 x -3\right ) y^{\prime }+2 y-x -1&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.099 |
|
| \begin{align*}
\left (4 y-3 x -5\right ) y^{\prime }-3 y+7 x +2&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.552 |
|
| \begin{align*}
\left (4 y+11 x -11\right ) y^{\prime }-25 y-8 x +62&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
78.243 |
|
| \begin{align*}
\left (12 y-5 x -8\right ) y^{\prime }-5 y+2 x +3&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.026 |
|
| \begin{align*}
a y y^{\prime }+b y^{2}+f \left (x \right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.684 |
|
| \begin{align*}
\left (a y+b x +c \right ) y^{\prime }+\alpha y+\beta x +\gamma &=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
91.673 |
|
| \begin{align*}
y y^{\prime } x +x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.523 |
|
| \begin{align*}
y y^{\prime } x -y^{2}+a \,x^{3} \cos \left (x \right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.530 |
|
| \begin{align*}
y y^{\prime } x -y^{2}+y x +x^{3}-2 x^{2}&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
33.756 |
|
| \begin{align*}
\left (y x +a \right ) y^{\prime }+b y&=0 \\
\end{align*} |
[[_1st_order, _with_exponential_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
14.664 |
|
| \begin{align*}
x \left (4+y\right ) y^{\prime }-y^{2}-2 y-2 x&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
26.679 |
|
| \begin{align*}
x \left (a +y\right ) y^{\prime }+b y+c x&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
23.341 |
|
| \begin{align*}
\left (a +x \left (x +y\right )\right ) y^{\prime }-y \left (x +y\right )-b&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
18.367 |
|
| \begin{align*}
y^{2}-3 y x -2 x^{2}+\left (y x -x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
14.964 |
|
| \begin{align*}
2 y y^{\prime } x -y^{2}+a x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.304 |
|
| \begin{align*}
2 y y^{\prime } x -y^{2}+a \,x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.490 |
|
| \begin{align*}
2 y y^{\prime } x +2 y^{2}+1&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.780 |
|
| \begin{align*}
x \left (x +2 y-1\right ) y^{\prime }-\left (2 x +y+1\right ) y&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
26.406 |
|
| \begin{align*}
y \left (2 x -y-1\right )+x \left (2 y-x -1\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
26.315 |
|
| \begin{align*}
\left (2 y x +4 x^{3}\right ) y^{\prime }+y^{2}+112 x^{2} y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
15.287 |
|
| \begin{align*}
x \left (2 x +3 y\right ) y^{\prime }+3 \left (x +y\right )^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
16.032 |
|
| \begin{align*}
\left (3 x +2\right ) \left (y-2 x -1\right ) y^{\prime }-y^{2}+y x -7 x^{2}-9 x -3&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
38.228 |
|
| \begin{align*}
\left (3+6 y x +x^{2}\right ) y^{\prime }+2 x +2 y x +3 y^{2}&=0 \\
\end{align*} |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
5.506 |
|
| \begin{align*}
\left (a x y+b \,x^{n}\right ) y^{\prime }+\alpha y^{3}+\beta y^{2}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
16.151 |
|
| \begin{align*}
\left (x^{2} y-1\right ) y^{\prime }+x y^{2}-1&=0 \\
\end{align*} |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
5.129 |
|
| \begin{align*}
\left (x^{2} y-1\right ) y^{\prime }-x y^{2}+1&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✓ |
✗ |
67.051 |
|
| \begin{align*}
\left (x^{2} y-1\right ) y^{\prime }+8 x y^{2}-8&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
76.274 |
|
| \begin{align*}
x \left (y x -2\right ) y^{\prime }+x^{2} y^{3}+x y^{2}-2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
16.352 |
|
| \begin{align*}
x \left (y x -3\right ) y^{\prime }+x y^{2}-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
16.602 |
|
| \begin{align*}
x^{2} \left (-1+y\right ) y^{\prime }+\left (x -1\right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.263 |
|
| \begin{align*}
x \left (y x +x^{4}-1\right ) y^{\prime }-y \left (y x -x^{4}-1\right )&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✓ |
✗ |
35.551 |
|
| \begin{align*}
2 x^{2} y y^{\prime }+y^{2}-2 x^{3}-x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.965 |
|
| \begin{align*}
2 x^{2} y y^{\prime }-y^{2}-x^{2} {\mathrm e}^{x -\frac {1}{x}}&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.543 |
|
| \begin{align*}
\left (x +2 x^{2} y\right ) y^{\prime }-x^{2} y^{3}+2 x y^{2}+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
15.989 |
|
| \begin{align*}
\left (2 x^{2} y-x \right ) y^{\prime }-2 x y^{2}-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
15.877 |
|
| \begin{align*}
\left (2 x^{2} y-x^{3}\right ) y^{\prime }+y^{3}-4 x y^{2}+2 x^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
219.760 |
|
| \begin{align*}
2 x^{3}+y y^{\prime }+3 y^{2} x^{2}+7&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.352 |
|
| \begin{align*}
2 x \left (x^{3} y+1\right ) y^{\prime }+\left (3 x^{3} y-1\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
15.972 |
|
| \begin{align*}
\left (-x +y\right ) \sqrt {x^{2}+1}\, y^{\prime }-a \sqrt {\left (1+y^{2}\right )^{3}}&=0 \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✓ |
✓ |
✗ |
273.131 |
|
| \begin{align*}
y y^{\prime } \sin \left (x \right )^{2}+y^{2} \cos \left (x \right ) \sin \left (x \right )-1&=0 \\
\end{align*} |
[_exact, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.520 |
|
| \begin{align*}
f \left (x \right ) y y^{\prime }+g \left (x \right ) y^{2}+h \left (x \right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.970 |
|
| \begin{align*}
\left (y^{2}-x \right ) y^{\prime }-y+x^{2}&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
3.204 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }+2 x \left (2 x +y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.758 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
21.587 |
|
| \begin{align*}
2 y x +\left (a +x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
3.337 |
|
| \begin{align*}
2 y x +x^{2}+b +\left (a +x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
3.763 |
|
| \begin{align*}
\left (x^{2}+y^{2}+x \right ) y^{\prime }-y&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
3.491 |
|
| \begin{align*}
\left (y^{2}-x^{2}\right ) y^{\prime }+2 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.088 |
|
| \begin{align*}
\left (x^{4}+y^{2}\right ) y^{\prime }-4 x^{3} y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
19.109 |
|
| \begin{align*}
\left (y^{2}+4 \sin \left (x \right )\right ) y^{\prime }-\cos \left (x \right )&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
4.418 |
|
| \begin{align*}
\left (x +2 y+y^{2}\right ) y^{\prime }+y \left (1+y\right )+\left (x +y\right )^{2} y^{2}&=0 \\
\end{align*} |
[_rational] |
✗ |
✓ |
✓ |
✗ |
12.166 |
|
| \begin{align*}
\left (x +y\right )^{2} y^{\prime }-a^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
18.448 |
|
| \begin{align*}
x^{2}+2 y x -y^{2}+\left (y^{2}+2 y x -x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
19.044 |
|
| \begin{align*}
\left (-1+3 x +y\right )^{2} y^{\prime }-\left (-1+2 y\right ) \left (4 y+6 x -3\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
✓ |
✗ |
13.780 |
|
| \begin{align*}
3 \left (y^{2}-x^{2}\right ) y^{\prime }+2 y^{3}-6 \left (x +1\right ) x y-3 \,{\mathrm e}^{x}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
4.432 |
|
| \begin{align*}
\left (x^{2}+4 y^{2}\right ) y^{\prime }-y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
14.048 |
|
| \begin{align*}
\left (3 x^{2}+2 y x +4 y^{2}\right ) y^{\prime }+2 x^{2}+6 y x +y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
18.464 |
|
| \begin{align*}
\left (1-3 x +2 y\right )^{2} y^{\prime }-\left (3 y-2 x -4\right )^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
✓ |
✗ |
16.427 |
|
| \begin{align*}
\left (2 y-4 x +1\right )^{2} y^{\prime }-\left (y-2 x \right )^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.442 |
|
| \begin{align*}
\left (1-3 x^{2} y+6 y^{2}\right ) y^{\prime }-3 x y^{2}+x&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✗ |
3.685 |
|
| \begin{align*}
\left (6 y-x \right )^{2} y^{\prime }-6 y^{2}+2 y x +a&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.724 |
|
| \begin{align*}
\left (a y^{2}+2 b x y+c \,x^{2}\right ) y^{\prime }+b y^{2}+2 c x y+d \,x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
129.281 |
|
| \begin{align*}
\left (b \left (\beta y+x \alpha \right )^{2}-\beta \left (a x +b y\right )\right ) y^{\prime }+a \left (\beta y+x \alpha \right )^{2}-\alpha \left (a x +b y\right )&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
6.605 |
|
| \begin{align*}
\left (a y+b x +c \right )^{2} y^{\prime }+\left (\alpha y+\beta x +\gamma \right )^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
✓ |
✗ |
11.659 |
|
| \begin{align*}
x \left (y^{2}-3 x \right ) y^{\prime }+2 y^{3}-5 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
13.980 |
|
| \begin{align*}
x \left (y^{2}+x^{2}-a \right ) y^{\prime }-\left (a +x^{2}+y^{2}\right ) y&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
14.846 |
|
| \begin{align*}
x \left (y^{2}+y x -x^{2}\right ) y^{\prime }-y^{3}+x y^{2}+x^{2} y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
22.275 |
|
| \begin{align*}
x \left (y^{2}+x^{2} y+x^{2}\right ) y^{\prime }-2 y^{3}-2 y^{2} x^{2}+x^{4}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
11.952 |
|
| \begin{align*}
2 x \left (5 x^{2}+y^{2}\right ) y^{\prime }+y^{3}-x^{2} y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
24.638 |
|
| \begin{align*}
3 y^{\prime } y^{2} x +y^{3}-2 x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.703 |
|
| \begin{align*}
\left (3 x y^{2}-x^{2}\right ) y^{\prime }+y^{3}-2 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
✓ |
✗ |
7.888 |
|
| \begin{align*}
6 y^{\prime } y^{2} x +x +2 y^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.248 |
|
| \begin{align*}
\left (x^{2}+6 x y^{2}\right ) y^{\prime }-y \left (3 y^{2}-x \right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
11.437 |
|
| \begin{align*}
\left (y^{2} x^{2}+x \right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
6.513 |
|
| \begin{align*}
\left (y x -1\right )^{2} x y^{\prime }+\left (1+y^{2} x^{2}\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
7.197 |
|
| \begin{align*}
\left (10 x^{3} y^{2}+x^{2} y+2 x \right ) y^{\prime }+5 x^{2} y^{3}+x y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
12.825 |
|
| \begin{align*}
\left (y^{3}-3 x \right ) y^{\prime }-3 y+x^{2}&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
3.417 |
|
| \begin{align*}
\left (y^{3}-x^{3}\right ) y^{\prime }-x^{2} y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.493 |
|