| # |
ODE |
CAS classification |
Solved |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
\left (x +y\right ) y^{\prime }&=x -y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.239 |
|
| \begin{align*}
\left (x -y\right ) y^{\prime }&=x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.300 |
|
| \begin{align*}
x \left (x +y\right ) y^{\prime }&=y \left (x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
7.293 |
|
| \begin{align*}
\left (x +2 y\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.913 |
|
| \begin{align*}
x \left (x +y\right ) y^{\prime }+y \left (3 x +y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
9.925 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.103 |
|
| \begin{align*}
2 x +3 y+\left (3 x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.365 |
|
| \begin{align*}
4 x -y+\left (6 y-x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.588 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y-1}{x +y+3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.219 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y-x +7}{4 x -3 y-18} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.724 |
|
| \begin{align*}
y^{\prime }&=\frac {x +3 y}{-3 x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.191 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=x -y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.799 |
|
| \begin{align*}
\left (x -y\right ) y^{\prime }&=x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.372 |
|
| \begin{align*}
x \left (x +y\right ) y^{\prime }&=y \left (x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
10.191 |
|
| \begin{align*}
\left (x +2 y\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.303 |
|
| \begin{align*}
x \left (x +y\right ) y^{\prime }+y \left (3 x +y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
14.014 |
|
| \begin{align*}
2 x +3 y+\left (3 x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.176 |
|
| \begin{align*}
4 x -y+\left (6 y-x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.565 |
|
| \begin{align*}
y^{\prime }&=\frac {x +3 y}{-3 x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.828 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x^{2}-1}{3+2 y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.442 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x}{1+2 y} \\
y \left (2\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.790 |
|
| \begin{align*}
y^{\prime }&=\frac {-{\mathrm e}^{x}+3 x^{2}}{-5+2 y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.575 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{-x}-{\mathrm e}^{x}}{3+4 y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.719 |
|
| \begin{align*}
y^{\prime }&=\frac {2-{\mathrm e}^{x}}{3+2 y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.069 |
|
| \begin{align*}
y^{\prime }&=\frac {2 \cos \left (2 x \right )}{3+2 y} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.119 |
|
| \begin{align*}
y^{\prime }&=\frac {4 y-3 x}{2 x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.720 |
|
| \begin{align*}
y^{\prime }&=-\frac {4 x +3 y}{2 x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.233 |
|
| \begin{align*}
y^{\prime }&=\frac {x +3 y}{x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
10.560 |
|
| \begin{align*}
y^{\prime }&=\frac {\cot \left (t \right ) y}{1+y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.263 |
|
| \begin{align*}
3+2 x +\left (-2+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.744 |
|
| \begin{align*}
2 x +4 y+\left (2 x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
17.944 |
|
| \begin{align*}
y^{\prime }&=\frac {-a x -b y}{b x +c y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.671 |
|
| \begin{align*}
y^{\prime }&=\frac {-a x +b y}{b x -c y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
11.770 |
|
| \begin{align*}
2 x -y+\left (-x +2 y\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 3 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.319 |
|
| \begin{align*}
-1+9 x^{2}+y+\left (x -4 y\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
2.759 |
|
| \begin{align*}
3 y x +y^{2}+\left (y x +x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
16.540 |
|
| \begin{align*}
y^{\prime }&=\frac {-1-2 y x -y^{2}}{x^{2}+2 y x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
4.567 |
|
| \begin{align*}
y^{\prime }&=\frac {-1-2 y x}{x^{2}+2 y} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
3.250 |
|
| \begin{align*}
\frac {-x^{2}+x +1}{x^{2}}+\frac {y y^{\prime }}{-2+y}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.872 |
|
| \begin{align*}
x +y+\left (x +2 y\right ) y^{\prime }&=0 \\
y \left (2\right ) &= 3 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.233 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.786 |
|
| \begin{align*}
2 y x +3 y^{2}-\left (x^{2}+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
17.691 |
|
| \begin{align*}
y^{\prime }&=\frac {-3 x^{2} y-y^{2}}{2 x^{3}+3 y x} \\
y \left (1\right ) &= -2 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
212.855 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x^{2}+2 x +1}{-2+y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.895 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+3 x +2}{-2+y} \\
y \left (1\right ) &= 4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.020 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x}{1+2 y} \\
y \left (2\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.618 |
|
| \begin{align*}
y^{\prime }+y&=\frac {2 x \,{\mathrm e}^{-x}}{1+{\mathrm e}^{x} y} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
5.721 |
|
| \begin{align*}
y^{\prime } x -2 y&=\frac {x^{6}}{y+x^{2}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
13.260 |
|
| \begin{align*}
y^{\prime }-2 y&=\frac {x \,{\mathrm e}^{2 x}}{1-y \,{\mathrm e}^{-2 x}} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
5.793 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +3 y}{x -4 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
23.690 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.049 |
|
| \begin{align*}
y^{\prime }&=\frac {x +2 y}{2 x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.253 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{y-2 x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.651 |
|
| \begin{align*}
y y^{\prime } x&=x^{2}-y x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
28.069 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y^{2}-y x +2 x^{2}}{y x +2 x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
51.091 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y x +y^{2}}{y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
27.724 |
|
| \begin{align*}
y^{\prime }&=\frac {-6 x +y-3}{2 x -y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
25.560 |
|
| \begin{align*}
y^{\prime }&=\frac {-x +3 y-14}{x +y-2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
23.460 |
|
| \begin{align*}
2 x \left (y+2 \sqrt {x}\right ) y^{\prime }&=\left (y+\sqrt {x}\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
9.889 |
|
| \begin{align*}
\left (y+{\mathrm e}^{x^{2}}\right ) y^{\prime }&=2 x \left (y^{2}+y \,{\mathrm e}^{x^{2}}+{\mathrm e}^{2 x^{2}}\right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
6.832 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=\frac {3 y^{2} x^{2}+6 y x +2}{x^{2} \left (2 y x +3\right )} \\
y \left (2\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
25.237 |
|
| \begin{align*}
y^{\prime }+\frac {3 y}{x}&=\frac {3 y^{2} x^{4}+10 x^{2} y+6}{x^{3} \left (2 x^{2} y+5\right )} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
16.934 |
|
| \begin{align*}
4 x +7 y+\left (3 x +4 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.004 |
|
| \begin{align*}
2 x +y+\left (2 y+2 x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
21.150 |
|
| \begin{align*}
3 x^{2}+2 y x +4 y^{2}+\left (x^{2}+8 y x +18 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
5.905 |
|
| \begin{align*}
{\mathrm e}^{x} \left (y^{2} x^{2}+2 x y^{2}\right )+6 x +\left (2 x^{2} y \,{\mathrm e}^{x}+2\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
6.729 |
|
| \begin{align*}
4 x^{3} y^{2}-6 x^{2} y-2 x -3+\left (2 x^{4} y-2 x^{3}\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
5.130 |
|
| \begin{align*}
-4 \cos \left (x \right ) y+4 \cos \left (x \right ) \sin \left (x \right )+\sec \left (x \right )^{2}+\left (4 y-4 \sin \left (x \right )\right ) y^{\prime }&=0 \\
y \left (\frac {\pi }{4}\right ) &= 0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.755 |
|
| \begin{align*}
7 x +4 y+\left (4 x +3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.851 |
|
| \begin{align*}
3 x^{2}+2 y+\left (2 y+2 x \right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.431 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=-\frac {2 x y}{x^{2}+2 x^{2} y+1} \\
y \left (1\right ) &= -2 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
10.420 |
|
| \begin{align*}
y^{\prime }-\frac {3 y}{x}&=\frac {2 x^{4} \left (4 x^{3}-3 y\right )}{3 x^{5}+3 x^{3}+2 y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
4.215 |
|
| \begin{align*}
y^{\prime }+2 y x&=-\frac {{\mathrm e}^{-x^{2}} \left (3 x +2 y \,{\mathrm e}^{x^{2}}\right )}{2 x +3 y \,{\mathrm e}^{x^{2}}} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
12.576 |
|
| \begin{align*}
y+\left (2 x +\frac {1}{y}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
12.466 |
|
| \begin{align*}
a y+b x y+\left (c x +d x y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.056 |
|
| \begin{align*}
3 x^{2} y^{3}-y^{2}+y+\left (-y x +2 x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
10.320 |
|
| \begin{align*}
y \left (\cos \left (x \right ) x +2 \sin \left (x \right )\right )+x \left (1+y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.424 |
|
| \begin{align*}
3 y x +2 y^{2}+y+\left (x^{2}+2 y x +x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
5.892 |
|
| \begin{align*}
y^{\prime }&=\frac {3 t^{2}+4 t +2}{-2+2 y} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.770 |
|
| \begin{align*}
y^{\prime }&=\frac {y+t}{t -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.440 |
|
| \begin{align*}
y^{\prime }&=\frac {t +y+1}{t -y+3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.458 |
|
| \begin{align*}
1+t -2 y+\left (4 t -3 y-6\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.092 |
|
| \begin{align*}
t +2 y+3+\left (2 t +4 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.254 |
|
| \begin{align*}
\sec \left (t \right ) \tan \left (t \right )+\sec \left (t \right )^{2} y+\left (\tan \left (t \right )+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
14.914 |
|
| \begin{align*}
\frac {y^{2}}{2}-2 \,{\mathrm e}^{t} y+\left (-{\mathrm e}^{t}+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.503 |
|
| \begin{align*}
3 t^{2}+4 t y+\left (2 y+2 t^{2}\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
1.990 |
|
| \begin{align*}
3 t y+y^{2}+\left (t^{2}+t y\right ) y^{\prime }&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
6.717 |
|
| \begin{align*}
y^{\prime }&=\frac {3 t^{2}+4 t +2}{-2+2 y} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.273 |
|
| \begin{align*}
y^{\prime }&=\frac {y+t}{t -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.071 |
|
| \begin{align*}
y^{\prime }&=\frac {t +y+1}{t -y+3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.963 |
|
| \begin{align*}
1+t -2 y+\left (4 t -3 y-6\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.074 |
|
| \begin{align*}
t +2 y+3+\left (2 t +4 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.720 |
|
| \begin{align*}
\sec \left (t \right ) \tan \left (t \right )+\sec \left (t \right )^{2} y+\left (\tan \left (t \right )+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
13.766 |
|
| \begin{align*}
\frac {y^{2}}{2}-2 \,{\mathrm e}^{t} y+\left (-{\mathrm e}^{t}+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.528 |
|
| \begin{align*}
3 t^{2}+4 t y+\left (2 y+2 t^{2}\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
2.093 |
|
| \begin{align*}
3 t y+y^{2}+\left (t^{2}+t y\right ) y^{\prime }&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
8.036 |
|
| \begin{align*}
y^{\prime } x +y&=x y \left (y^{\prime }-1\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.901 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+x&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.633 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x -y}{x +4 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.592 |
|
| \begin{align*}
x +y y^{\prime }&=2 y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
4.756 |
|
| \begin{align*}
\left (y x -x^{2}\right ) y^{\prime }-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
14.234 |
|
| \begin{align*}
x +y+\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.331 |
|
| \begin{align*}
\left (3 y x -2 x^{2}\right ) y^{\prime }&=2 y^{2}-y x \\
y \left (1\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
30.791 |
|
| \begin{align*}
x +y-\left (x -y+2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.708 |
|
| \begin{align*}
x +\left (x -2 y+2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.601 |
|
| \begin{align*}
2 x -y+1+\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
26.371 |
|
| \begin{align*}
x -y+2+\left (x +y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.503 |
|
| \begin{align*}
x -y+\left (y-x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.630 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y-1}{x -y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
16.203 |
|
| \begin{align*}
x +y+\left (2 x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.866 |
|
| \begin{align*}
x -y+1+\left (x -y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.329 |
|
| \begin{align*}
x +2 y+\left (3 x +6 y+3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.892 |
|
| \begin{align*}
x +2 y+2&=\left (2 x +y-1\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
22.270 |
|
| \begin{align*}
6 x -3 y+6+\left (2 x -y+5\right ) y^{\prime }&=0 \\
y \left (-1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.284 |
|
| \begin{align*}
x +y+4&=\left (2 x +2 y-1\right ) y^{\prime } \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.563 |
|
| \begin{align*}
2 x +3 y-1+\left (2 x +3 y+2\right ) y^{\prime }&=0 \\
y \left (3\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.329 |
|
| \begin{align*}
3 x -y+2+\left (x +2 y+1\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✓ |
✓ |
58.223 |
|
| \begin{align*}
x -2 y+3+\left (1-x +2 y\right ) y^{\prime }&=0 \\
y \left (-4\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.647 |
|
| \begin{align*}
2 x +y+\left (4 x +2 y+1\right ) y^{\prime }&=0 \\
y \left (-\frac {1}{6}\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
✗ |
10.622 |
|
| \begin{align*}
2 x +y+\left (4 x -2 y+1\right ) y^{\prime }&=0 \\
y \left (\frac {1}{2}\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
42.955 |
|
| \begin{align*}
x +y+\left (x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.654 |
|
| \begin{align*}
3 x +y+\left (x +3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.557 |
|
| \begin{align*}
a_{1} x +b_{1} y+c_{1} +\left (b_{1} x +b_{2} y+c_{2} \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
69.728 |
|
| \begin{align*}
x \left (6 y x +5\right )+\left (2 x^{3}+3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
3.288 |
|
| \begin{align*}
\frac {y \left (2+x^{3} y\right )}{x^{3}}&=\frac {\left (1-2 x^{3} y\right ) y^{\prime }}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
9.760 |
|
| \begin{align*}
y^{2} \csc \left (x \right )^{2}+6 y x -2&=\left (2 \cot \left (x \right ) y-3 x^{2}\right ) y^{\prime } \\
\end{align*} |
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
20.132 |
|
| \begin{align*}
y x +\left (y+x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
27.134 |
|
| \begin{align*}
\left (-2 y x +x \right ) y^{\prime }+2 y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.641 |
|
| \begin{align*}
y+x y^{2}+\left (x -x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
36.516 |
|
| \begin{align*}
2 y x +\left (-x^{2}+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.097 |
|
| \begin{align*}
y&=x \left (x^{2} y-1\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
19.554 |
|
| \begin{align*}
\left (2 x +3 x^{2} y\right ) y^{\prime }+y+2 x y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
29.969 |
|
| \begin{align*}
y^{2} x^{2}-y+\left (2 x^{3} y+x \right ) y^{\prime }&=0 \\
y \left (2\right ) &= -2 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
9.183 |
|
| \begin{align*}
y+\left (2 x -3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.784 |
|
| \begin{align*}
y^{2}+\left (y x +x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
66.076 |
|
| \begin{align*}
2 x +y-\left (x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.040 |
|
| \begin{align*}
x -2 y+1+\left (-2+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.652 |
|
| \begin{align*}
6+2 y&=y y^{\prime } x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.701 |
|
| \begin{align*}
x -3 y&=\left (3 y-x +2\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.812 |
|
| \begin{align*}
y+\left (3 x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
129.655 |
|
| \begin{align*}
\left (3 x +4 y\right ) y^{\prime }+2 x +y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.765 |
|
| \begin{align*}
x +y+\left (2 x +3 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
25.770 |
|
| \begin{align*}
y \left (3 x^{2}+y\right )-x \left (x^{2}-y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
116.655 |
|
| \begin{align*}
x +\left (2 x +3 y+2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.562 |
|
| \begin{align*}
x -2 y+3&=\left (x -2 y+1\right ) y^{\prime } \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.222 |
|
| \begin{align*}
\left (-x +y\right ) y^{\prime }+2 x +3 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.414 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x +2 y+1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.067 |
|
| \begin{align*}
y^{\prime }&=-\frac {x +y}{3 x +3 y-4} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.539 |
|
| \begin{align*}
x \left (1-2 x^{2} y\right ) y^{\prime }+y&=3 y^{2} x^{2} \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
10.787 |
|
| \begin{align*}
\left (5 x +y-7\right ) y^{\prime }&=3 x +3 y+3 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
30.122 |
|
| \begin{align*}
\left (3 x -y\right ) y^{\prime }&=3 y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.532 |
|
| \begin{align*}
2 x \left (2 x +y\right ) y^{\prime }&=y \left (4 x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
16.154 |
|
| \begin{align*}
y^{\prime }&=\frac {1-y^{2}}{2 y x +2} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
4.855 |
|
| \begin{align*}
\left (3 x -y\right ) y^{\prime }&=3 y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.680 |
|
| \begin{align*}
2 x \left (2 x +y\right ) y^{\prime }&=y \left (4 x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
16.817 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x -y}{x +4 y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
33.846 |
|
| \begin{align*}
y^{\prime }&=\frac {x +a y}{a x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
22.074 |
|
| \begin{align*}
y^{\prime }&=\frac {x +\frac {y}{2}}{\frac {x}{2}-y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.530 |
|
| \begin{align*}
y^{\prime }&=\frac {x +2 y-1}{2 x -y+3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
23.263 |
|
| \begin{align*}
5 y x +4 y^{2}+1+\left (x^{2}+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
5.909 |
|
| \begin{align*}
4 x y^{2}+6 y+\left (5 x^{2} y+8 x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
49.459 |
|
| \begin{align*}
5 x +2 y+1+\left (2 x +y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.572 |
|
| \begin{align*}
3 x -y+1-\left (6 x -2 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.361 |
|
| \begin{align*}
x -2 y-3+\left (2 x +y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
23.969 |
|
| \begin{align*}
6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime }&=0 \\
y \left (\frac {1}{2}\right ) &= 3 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.306 |
|
| \begin{align*}
2 x +3 y+1+\left (4 x +6 y+1\right ) y^{\prime }&=0 \\
y \left (-2\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.020 |
|
| \begin{align*}
y y^{\prime } x&=\left (x +1\right ) \left (1+y\right ) \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✗ |
5.946 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x -y}{2 x +y} \\
y \left (2\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
59.876 |
|
| \begin{align*}
3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
131.619 |
|
| \begin{align*}
\left (x +y-1\right ) y^{\prime }&=x -y+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.191 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+4}{x -y-6} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.033 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+4}{x +y-6} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.543 |
|
| \begin{align*}
\left (x +\frac {2}{y}\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
17.878 |
|
| \begin{align*}
y x -1+\left (x^{2}-y x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
2.630 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=-x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.843 |
|
| \begin{align*}
\left (-y x +1\right ) y^{\prime }&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
15.999 |
|
| \begin{align*}
2 x +3 y+1+\left (2 y-3 x +5\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.545 |
|
| \begin{align*}
y^{2}&=\left (x^{3}-y x \right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
17.651 |
|
| \begin{align*}
\left (y x -x^{2}\right ) y^{\prime }&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
52.287 |
|
| \begin{align*}
6 x +4 y+3+\left (3 x +2 y+2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.187 |
|
| \begin{align*}
y^{2}-3 y x -2 x^{2}&=\left (x^{2}-y x \right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
10.135 |
|
| \begin{align*}
x \left (1+y^{2}\right )+\left (1+2 y\right ) {\mathrm e}^{-x} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.740 |
|
| \begin{align*}
x y^{3}+\left (1+y\right ) {\mathrm e}^{-x} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.523 |
|
| \begin{align*}
y^{\prime }+\frac {x}{y}+2&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
3.389 |
|
| \begin{align*}
x^{2}-y x +y^{2}-y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
19.542 |
|
| \begin{align*}
\left (3+2 x +4 y\right ) y^{\prime }&=x +2 y+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.112 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +y-1}{x -y-2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.573 |
|
| \begin{align*}
y+2&=\left (2 x +y-4\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.189 |
|
| \begin{align*}
2 x^{2}-x y^{2}-2 y+3-\left (x^{2} y+2 x \right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
2.764 |
|
| \begin{align*}
x y^{2}+x -2 y+3+\left (x^{2} y-2 y-2 x \right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
3.439 |
|
| \begin{align*}
3 \left (x^{2}-1\right ) y+\left (x^{3}+8 y-3 x \right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.934 |
|
| \begin{align*}
3+y+2 y^{2} \sin \left (x \right )^{2}+\left (x +2 y x -y \sin \left (2 x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
37.401 |
|
| \begin{align*}
y \left (2 x -y+2\right )+2 \left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.570 |
|
| \begin{align*}
4 y x +3 y^{2}-x +x \left (x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
3.667 |
|
| \begin{align*}
x^{2}+2 x +y+\left (3 x^{2} y-x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
2.760 |
|
| \begin{align*}
y \left (x +y\right )+\left (x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.661 |
|
| \begin{align*}
y^{2}-\left (y x +x^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
4.960 |
|
| \begin{align*}
2 y^{2} x^{2}+y+\left (x^{3} y-x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
11.186 |
|
| \begin{align*}
y^{2}+\left (-y+{\mathrm e}^{x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.815 |
|
| \begin{align*}
y^{2} x^{2}-2 y+\left (x^{3} y-x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
10.573 |
|
| \begin{align*}
y^{\prime }&=\frac {4 x^{3} y^{2}}{x^{4} y+2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
15.868 |
|
| \begin{align*}
6 y^{2}-x \left (2 x^{3}+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
22.712 |
|
| \begin{align*}
y y^{\prime }+a x +b y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
51.899 |
|
| \begin{align*}
y y^{\prime }+x \,{\mathrm e}^{-x} \left (1+y\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.685 |
|
| \begin{align*}
\left (1+y\right ) y^{\prime }&=x +y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
26.056 |
|
| \begin{align*}
\left (1+y\right ) y^{\prime }&=x^{2} \left (1-y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.613 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.540 |
|
| \begin{align*}
\left (x -y\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.103 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.007 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=x -y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.236 |
|
| \begin{align*}
\left (x +y+1\right ) y^{\prime }+1+4 x +3 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
22.451 |
|
| \begin{align*}
\left (x +y+2\right ) y^{\prime }&=-x -y+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.079 |
|
| \begin{align*}
\left (3-x -y\right ) y^{\prime }&=1+x -3 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
21.707 |
|
| \begin{align*}
\left (3-x +y\right ) y^{\prime }&=11-4 x +3 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
21.894 |
|
| \begin{align*}
\left (2 x +y\right ) y^{\prime }+x -2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.922 |
|
| \begin{align*}
\left (2 x -y+2\right ) y^{\prime }+3+6 x -3 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.497 |
|
| \begin{align*}
\left (2 x -y+3\right ) y^{\prime }+2&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.111 |
|
| \begin{align*}
\left (5-2 x -y\right ) y^{\prime }+4-x -2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.014 |
|
| \begin{align*}
\left (1-3 x +y\right ) y^{\prime }&=2 x -2 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
133.816 |
|
| \begin{align*}
\left (2-3 x +y\right ) y^{\prime }+5-2 x -3 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.006 |
|
| \begin{align*}
\left (4 x -y\right ) y^{\prime }+2 x -5 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
48.938 |
|
| \begin{align*}
\left (6-4 x -y\right ) y^{\prime }&=2 x -y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
22.523 |
|
| \begin{align*}
\left (1+5 x -y\right ) y^{\prime }+5+x -5 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
13.421 |
|
| \begin{align*}
\left (a +b x +y\right ) y^{\prime }+a -b x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.169 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
2.829 |
|
| \begin{align*}
\left (x^{2}-y\right ) y^{\prime }&=4 y x \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
23.564 |
|
| \begin{align*}
\left (y-\cot \left (x \right ) \csc \left (x \right )\right ) y^{\prime }+\csc \left (x \right ) \left (\cos \left (x \right ) y+1\right ) y&=0 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
39.395 |
|
| \begin{align*}
\left (x -2 y\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.191 |
|
| \begin{align*}
\left (x +2 y\right ) y^{\prime }+2 x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.789 |
|
| \begin{align*}
\left (x -2 y\right ) y^{\prime }+2 x +y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.511 |
|
| \begin{align*}
\left (x -2 y+1\right ) y^{\prime }&=1+2 x -y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.296 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
8.947 |
|
| \begin{align*}
\left (x +2 y+1\right ) y^{\prime }+7+x -4 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
24.802 |
|
| \begin{align*}
2 \left (x +y\right ) y^{\prime }+x^{2}+2 y&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.510 |
|
| \begin{align*}
\left (3+2 x -2 y\right ) y^{\prime }&=1+6 x -2 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.603 |
|
| \begin{align*}
\left (1-4 x -2 y\right ) y^{\prime }+2 x +y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.619 |
|
| \begin{align*}
\left (6 x -2 y\right ) y^{\prime }&=2+3 x -y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.243 |
|
| \begin{align*}
\left (19+9 x +2 y\right ) y^{\prime }+18-2 x -6 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
52.668 |
|
| \begin{align*}
\left (x^{3}+2 y\right ) y^{\prime }&=3 x \left (2-y x \right ) \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
3.885 |
|
| \begin{align*}
\left (\sec \left (x \right ) \tan \left (x \right )-2 y\right ) y^{\prime }+\sec \left (x \right ) \left (1+2 \sin \left (x \right ) y\right ) y&=0 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
38.509 |
|
| \begin{align*}
\left (x \,{\mathrm e}^{-x}-2 y\right ) y^{\prime }&=2 \,{\mathrm e}^{-2 x} x -\left ({\mathrm e}^{-x}+x \,{\mathrm e}^{-x}-2 y\right ) y \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
9.515 |
|
| \begin{align*}
3 \left (2-y\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.787 |
|
| \begin{align*}
\left (x -3 y\right ) y^{\prime }+4+3 x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
50.431 |
|
| \begin{align*}
\left (4-x -3 y\right ) y^{\prime }+3-x -3 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.121 |
|
| \begin{align*}
\left (2 x +3 y+2\right ) y^{\prime }&=1-2 x -3 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.720 |
|
| \begin{align*}
\left (5-2 x -3 y\right ) y^{\prime }+1-2 x -3 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.105 |
|
| \begin{align*}
\left (1+9 x -3 y\right ) y^{\prime }+2+3 x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.658 |
|
| \begin{align*}
\left (x +4 y\right ) y^{\prime }+4 x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.420 |
|
| \begin{align*}
\left (3+2 x +4 y\right ) y^{\prime }&=x +2 y+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.886 |
|
| \begin{align*}
\left (5+2 x -4 y\right ) y^{\prime }&=x -2 y+3 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.354 |
|
| \begin{align*}
\left (5+3 x -4 y\right ) y^{\prime }&=2+7 x -3 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.950 |
|
| \begin{align*}
4 \left (-x -y+1\right ) y^{\prime }+2-x&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
22.727 |
|
| \begin{align*}
\left (11-11 x -4 y\right ) y^{\prime }&=62-8 x -25 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
48.089 |
|
| \begin{align*}
\left (6+3 x +5 y\right ) y^{\prime }&=2+x +7 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
146.750 |
|
| \begin{align*}
\left (7 x +5 y\right ) y^{\prime }+10 x +8 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.187 |
|
| \begin{align*}
\left (5-x +6 y\right ) y^{\prime }&=3-x +4 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
53.854 |
|
| \begin{align*}
3 \left (x +2 y\right ) y^{\prime }&=-2 y-x +1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.559 |
|
| \begin{align*}
3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
69.293 |
|
| \begin{align*}
\left (1+x +9 y\right ) y^{\prime }+1+x +5 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
23.083 |
|
| \begin{align*}
\left (8+5 x -12 y\right ) y^{\prime }&=3+2 x -5 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.618 |
|
| \begin{align*}
\left (140+7 x -16 y\right ) y^{\prime }+25+8 x +y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
27.505 |
|
| \begin{align*}
\left (3+9 x +21 y\right ) y^{\prime }&=45+7 x -5 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
26.972 |
|
| \begin{align*}
\left (a x +b y\right ) y^{\prime }+x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
41.336 |
|
| \begin{align*}
\left (a x +b y\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
15.290 |
|
| \begin{align*}
\left (a x +b y\right ) y^{\prime }+b x +a y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
21.235 |
|
| \begin{align*}
\left (a x +b y\right ) y^{\prime }&=a y+b x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
13.128 |
|
| \begin{align*}
\left (a_{2} +b x +c_{2} y\right ) y^{\prime }+a_{1} +b_{1} x +b y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
73.852 |
|
| \begin{align*}
\left (a_{2} +b_{2} x +c_{2} y\right ) y^{\prime }&=a_{1} +b_{1} x +c_{1} y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
57.579 |
|
| \begin{align*}
y y^{\prime } x&=x^{2}-y x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
27.688 |
|
| \begin{align*}
y y^{\prime } x +2 x^{2}-2 y x -y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
10.817 |
|
| \begin{align*}
\left (y x +1\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
37.917 |
|
| \begin{align*}
x \left (1+y\right ) y^{\prime }-\left (1-x \right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.099 |
|
| \begin{align*}
x \left (1-y\right ) y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.353 |
|
| \begin{align*}
x \left (1-y\right ) y^{\prime }+\left (1-x \right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.198 |
|
| \begin{align*}
x \left (4+y\right ) y^{\prime }&=2 x +2 y+y^{2} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
18.175 |
|
| \begin{align*}
x \left (a +y\right ) y^{\prime }&=y \left (B x +A \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.288 |
|
| \begin{align*}
x \left (x +y\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
74.647 |
|
| \begin{align*}
x \left (x -y\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
63.694 |
|
| \begin{align*}
x \left (x +y\right ) y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
15.321 |
|
| \begin{align*}
x \left (x -y\right ) y^{\prime }+2 x^{2}+3 y x -y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
18.858 |
|
| \begin{align*}
x \left (2 x +y\right ) y^{\prime }&=x^{2}+y x -y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
46.855 |
|
| \begin{align*}
x \left (4 x -y\right ) y^{\prime }+4 x^{2}-6 y x -y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
89.983 |
|
| \begin{align*}
x \left (x^{3}+y\right ) y^{\prime }&=\left (x^{3}-y\right ) y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
49.335 |
|
| \begin{align*}
x \left (2 x^{3}+y\right ) y^{\prime }&=\left (2 x^{3}-y\right ) y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
44.230 |
|
| \begin{align*}
x \left (2 x^{3}+y\right ) y^{\prime }&=6 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
47.721 |
|
| \begin{align*}
y \left (1-x \right ) y^{\prime }+\left (1-y\right ) x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.465 |
|
| \begin{align*}
\left (3-x +2 y x \right ) y^{\prime }+3 x^{2}-y+y^{2}&=0 \\
\end{align*} |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
5.707 |
|
| \begin{align*}
x \left (x -2 y\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
33.780 |
|
| \begin{align*}
x \left (x +2 y\right ) y^{\prime }+y \left (2 x -y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
38.971 |
|
| \begin{align*}
x \left (x -2 y\right ) y^{\prime }+y \left (2 x -y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
26.325 |
|
| \begin{align*}
2 x \left (2 x^{2}+y\right ) y^{\prime }+\left (12 x^{2}+y\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
17.849 |
|
| \begin{align*}
x \left (2 x +3 y\right ) y^{\prime }&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
51.241 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
21.323 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
5.546 |
|
| \begin{align*}
3 x \left (x +2 y\right ) y^{\prime }+x^{3}+3 y \left (2 x +y\right )&=0 \\
\end{align*} |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
6.874 |
|
| \begin{align*}
x \left (a +b y\right ) y^{\prime }&=c y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.096 |
|
| \begin{align*}
x \left (x -a y\right ) y^{\prime }&=y \left (y-a x \right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
19.641 |
|
| \begin{align*}
\left (1-x^{2} y\right ) y^{\prime }+1-x y^{2}&=0 \\
\end{align*} |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
5.326 |
|
| \begin{align*}
x \left (-y x +1\right ) y^{\prime }+\left (y x +1\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
47.378 |
|
| \begin{align*}
x \left (y x +2\right ) y^{\prime }&=3+2 x^{3}-2 y-x y^{2} \\
\end{align*} |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
5.013 |
|
| \begin{align*}
x \left (2-y x \right ) y^{\prime }+2 y-x y^{2} \left (y x +1\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
32.924 |
|
| \begin{align*}
x \left (3-y x \right ) y^{\prime }&=y \left (y x -1\right ) \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
46.165 |
|
| \begin{align*}
x^{2} \left (1-y\right ) y^{\prime }+\left (1-x \right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.170 |
|
| \begin{align*}
x^{2} \left (1-y\right ) y^{\prime }+\left (x +1\right ) y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.554 |
|
| \begin{align*}
x \left (1-2 y x \right ) y^{\prime }+y \left (2 y x +1\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
44.414 |
|
| \begin{align*}
x \left (2 y x +1\right ) y^{\prime }+\left (2+3 y x \right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
35.431 |
|
| \begin{align*}
x \left (2 y x +1\right ) y^{\prime }+\left (1+2 y x -y^{2} x^{2}\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
35.083 |
|
| \begin{align*}
x^{2} \left (x -2 y\right ) y^{\prime }&=2 x^{3}-4 x y^{2}+y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
91.441 |
|
| \begin{align*}
x^{2} \left (4 x -3 y\right ) y^{\prime }&=\left (6 x^{2}-3 y x +2 y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
18.191 |
|
| \begin{align*}
\left (1-x^{3} y\right ) y^{\prime }&=y^{2} x^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
35.504 |
|
| \begin{align*}
x \left (3-2 x^{2} y\right ) y^{\prime }&=4 x -3 y+3 y^{2} x^{2} \\
\end{align*} |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
6.187 |
|
| \begin{align*}
x \left (3+2 x^{2} y\right ) y^{\prime }+\left (4+3 x^{2} y\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
134.736 |
|
| \begin{align*}
\left (1+y\right ) y^{\prime } \sqrt {x^{2}+1}&=y^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.731 |
|
| \begin{align*}
y^{\prime }&=\frac {-3+x +y}{x -y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
23.675 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +y-1}{4 x +2 y+5} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.250 |
|
| \begin{align*}
x \left (1-y\right ) y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.945 |
|
| \begin{align*}
y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.996 |
|
| \begin{align*}
\left (-x +y\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.908 |
|
| \begin{align*}
\left (7 x +5 y\right ) y^{\prime }+10 x +8 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.166 |
|
| \begin{align*}
2 x -y+1+\left (-1+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
24.128 |
|
| \begin{align*}
3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
78.207 |
|
| \begin{align*}
\left (7 x +5 y\right ) y^{\prime }+10 x +8 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.351 |
|
| \begin{align*}
y^{2}+\left (y x +x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
81.178 |
|
| \begin{align*}
x +y-\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.461 |
|
| \begin{align*}
x +2 y-4-\left (2 x -4 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
24.852 |
|
| \begin{align*}
3 x +2 y+1-\left (3 x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.330 |
|
| \begin{align*}
x +y-1+\left (2 x +2 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.115 |
|
| \begin{align*}
x +y-1-\left (x -y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
24.018 |
|
| \begin{align*}
x +y+\left (2 x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.957 |
|
| \begin{align*}
x +2 y+\left (3 x +6 y+3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.875 |
|
| \begin{align*}
x +2 y+\left (-1+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
20.811 |
|
| \begin{align*}
3 x -2 y+4-\left (2 x +7 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.582 |
|
| \begin{align*}
x +y+\left (3 x +3 y-4\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
✗ |
11.904 |
|
| \begin{align*}
3 x +2 y+3-\left (x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
34.840 |
|
| \begin{align*}
x +y+2-\left (x -y-4\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
23.698 |
|
| \begin{align*}
\left (3 x +2 y+1\right ) y^{\prime }+4 x +3 y+2&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.147 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
26.790 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
6.389 |
|
| \begin{align*}
\left (x^{2} y-1\right ) y^{\prime }+x y^{2}-1&=0 \\
\end{align*} |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
6.129 |
|
| \begin{align*}
y^{2}+12 x^{2} y+\left (2 y x +4 x^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
24.447 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
3.893 |
|
| \begin{align*}
\left (x^{2}-y\right ) y^{\prime }-4 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
38.076 |
|
| \begin{align*}
x \left (1-y\right ) y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.375 |
|
| \begin{align*}
y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.796 |
|
| \begin{align*}
a x y^{\prime }+2 y&=y y^{\prime } x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.119 |
|
| \begin{align*}
\left (y x +x \right ) y^{\prime }+y&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.095 |
|
| \begin{align*}
\left (x -y\right ) y^{\prime }+x +y+1&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
22.910 |
|
| \begin{align*}
y^{2}-y x +\left (y x +x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
22.686 |
|
| \begin{align*}
2 x -y \sin \left (2 x \right )&=\left (\sin \left (x \right )^{2}-2 y\right ) y^{\prime } \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
10.565 |
|
| \begin{align*}
u \left (1-v \right )+v^{2} \left (1-u\right ) u^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.921 |
|
| \begin{align*}
\left (2 x +y\right ) y^{\prime }-x +2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
29.569 |
|
| \begin{align*}
x^{2} y^{\prime }&=\frac {4 x^{2}-x -2}{\left (x +1\right ) \left (1+y\right )} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.800 |
|
| \begin{align*}
\sin \left (x \right ) y^{2}+\left (\frac {1}{x}-\frac {y}{x}\right ) y^{\prime }&=0 \\
y \left (\pi \right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
11.848 |
|
| \begin{align*}
2 x +\frac {y}{x}+\left (y x -1\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
6.072 |
|
| \begin{align*}
\left (x -2 y\right ) y^{\prime }+2 x +y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
27.801 |
|
| \begin{align*}
3 x^{2}+y+\left (x^{2} y-x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
5.861 |
|
| \begin{align*}
2 y^{2}+2 y+4 x^{2}+\left (2 y x +x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
6.702 |
|
| \begin{align*}
2 y^{2}-6 y x +\left (3 y x -4 x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
50.481 |
|
| \begin{align*}
3 y+2 x y^{2}+\left (x +2 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
66.766 |
|
| \begin{align*}
3+y+y x +\left (3+x +y x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
10.566 |
|
| \begin{align*}
\left (t +x+2\right ) x^{\prime }+3 t -x-6&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
52.517 |
|
| \begin{align*}
x +y-1+\left (y-x -5\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
28.188 |
|
| \begin{align*}
-4 x -y-1+\left (x +y+3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
191.014 |
|
| \begin{align*}
2 x -y+\left (4 x +y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
35.677 |
|
| \begin{align*}
y-2 x -1+\left (x +y-4\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
20.092 |
|
| \begin{align*}
2 x -2 y-8+\left (x -3 y-6\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
39.842 |
|
| \begin{align*}
y-x +\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
29.088 |
|
| \begin{align*}
y \left (x -y-2\right )+x \left (-x +y+4\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
31.708 |
|
| \begin{align*}
3 x -y-5+\left (x -y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
98.322 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y-1}{x +y+5} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.857 |
|
| \begin{align*}
x \left (y-3\right ) y^{\prime }&=4 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
16.451 |
|
| \begin{align*}
\left (-x +2 y\right ) y^{\prime }&=2 x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
29.454 |
|
| \begin{align*}
y x +y^{2}+\left (x^{2}-y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
37.742 |
|
| \begin{align*}
y-3 x +\left (3 x +4 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
28.994 |
|
| \begin{align*}
\left (3 x +3 y-4\right ) y^{\prime }&=-x -y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.507 |
|
| \begin{align*}
x -y-1+\left (4 y+x -1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
31.605 |
|
| \begin{align*}
3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
86.527 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+2 y x}{x^{2}+2 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
24.046 |
|
| \begin{align*}
x^{2} y^{\prime }&=y^{2}-y y^{\prime } x \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
30.911 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=y y^{\prime } x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
32.630 |
|
| \begin{align*}
y^{\prime }&=\frac {x -2 y+1}{2 x -4 y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.433 |
|
| \begin{align*}
x y^{2}+y+\left (x^{2} y-x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
71.399 |
|
| \begin{align*}
x +y+1+\left (2 x +2 y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.441 |
|
| \begin{align*}
x +2 y+\left (2 x +3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
33.004 |
|
| \begin{align*}
3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
91.069 |
|
| \begin{align*}
y y^{\prime } x&=\left (1+y\right ) \left (1-x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.010 |
|
| \begin{align*}
y \left (2 y x +1\right )+x \left (-y x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
74.555 |
|
| \begin{align*}
3 x +2 y+1-\left (3 x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.890 |
|
| \begin{align*}
x +y+1-\left (-3+x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
32.575 |
|
| \begin{align*}
y+\left (y x +x -3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
6.259 |
|
| \begin{align*}
\left (2 s-{\mathrm e}^{2 t}\right ) s^{\prime }&=2 s \,{\mathrm e}^{2 t}-2 \cos \left (2 t \right ) \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
13.579 |
|
| \begin{align*}
2 y x +\left (x^{2}-y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.431 |
|
| \begin{align*}
\left (-x +y\right ) y^{\prime }&=x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.655 |
|
| \begin{align*}
\left (-2+2 y\right ) y^{\prime }&=2 x -1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.334 |
|
| \begin{align*}
\left (-y x +1\right ) y^{\prime }&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
26.063 |
|
| \begin{align*}
y \ln \left (x \right ) y^{\prime }&=\frac {\left (1+y\right )^{2}}{x^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.115 |
|
| \begin{align*}
y^{\prime }&=\frac {y x +3 x -y-3}{y x -2 x +4 y-8} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.043 |
|
| \begin{align*}
y^{\prime }&=\frac {y x +2 y-x -2}{y x -3 y+x -3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.886 |
|
| \begin{align*}
\left (-2+2 y\right ) y^{\prime }&=3 x^{2}+4 x +2 \\
y \left (1\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.487 |
|
| \begin{align*}
\left (2 y+2\right ) y^{\prime }-4 x^{3}-6 x&=0 \\
y \left (0\right ) &= -3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.813 |
|
| \begin{align*}
2 x -1+\left (3 y+7\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.049 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x^{2}+4 x +2}{-2+2 y} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.990 |
|
| \begin{align*}
\left (x +2 y\right ) y^{\prime }&=1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.382 |
|
| \begin{align*}
y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.642 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.730 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=y y^{\prime } x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
15.066 |
|
| \begin{align*}
x +y-\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.034 |
|
| \begin{align*}
-y+y^{\prime } x&=y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.970 |
|
| \begin{align*}
y^{2}+\left (x^{2}-y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
58.766 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.742 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y-2}{y-x -4} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.619 |
|
| \begin{align*}
2 x -4 y+6+\left (x +y-2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
22.358 |
|
| \begin{align*}
y^{\prime }&=-\frac {4 x +3 y+15}{2 x +y+7} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
47.695 |
|
| \begin{align*}
y^{\prime }&=\frac {x +3 y-5}{x -y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
20.520 |
|
| \begin{align*}
2 x +y+1-\left (4 x +2 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.572 |
|
| \begin{align*}
x -y-1+\left (y-x +2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.109 |
|
| \begin{align*}
\left (x +4 y\right ) y^{\prime }&=2 x +3 y-5 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
37.015 |
|
| \begin{align*}
y+2&=\left (2 x +y-4\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.326 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x -y+1}{2 x +y+4} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
60.571 |
|
| \begin{align*}
3+2 x +\left (-2+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.102 |
|
| \begin{align*}
2 x +4 y+\left (2 x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
19.714 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x^{2}+4 x +2}{-2+2 y} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.267 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y-1}{x -y+3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.663 |
|
| \begin{align*}
x +y-\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.654 |
|
| \begin{align*}
x +y y^{\prime }+y-y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.746 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.329 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{y x +x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
63.743 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y+2}{x +y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.616 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +3 y+1}{x -2 y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
29.036 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+1}{2 x +2 y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.040 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{y x -x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
64.017 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y^{2}}{1-x^{2} y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
21.407 |
|
| \begin{align*}
y y^{\prime } x&=-1+y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.312 |
|
| \begin{align*}
\left (1+y\right ) y^{\prime }&=-x^{2}+1 \\
y \left (-1\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.148 |
|
| \begin{align*}
y^{\prime } x +2&=x^{3} \left (-1+y\right ) y^{\prime } \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
7.145 |
|
| \begin{align*}
\left (x +\frac {2}{y}\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
39.212 |
|
| \begin{align*}
x -y-\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.789 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+4}{x -y-6} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
20.609 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+4}{x +y-6} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.121 |
|
| \begin{align*}
2 x -2 y+\left (-1+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.411 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y-1}{x +4 y+2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
231.377 |
|
| \begin{align*}
y^{\prime }&=\frac {y-x y^{2}}{x +x^{2} y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
40.842 |
|
| \begin{align*}
y^{\prime }&=\frac {x +2 y}{2 x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.723 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x -y}{x +4 y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
35.855 |
|
| \begin{align*}
y^{\prime }&=\frac {-y x -1}{4 x^{3} y-2 x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
114.824 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=y y^{\prime } x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
49.042 |
|
| \begin{align*}
2 t +3 x+\left (2+x\right ) x^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.955 |
|
| \begin{align*}
y y^{\prime }-y&=x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
5.487 |
|
| \begin{align*}
y y^{\prime }+a y+x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
23.759 |
|
| \begin{align*}
\left (1+y\right ) y^{\prime }-y-x&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
24.641 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
31.723 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
28.378 |
|
| \begin{align*}
\left (1-2 x +y\right ) y^{\prime }+y+x&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
27.819 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
2.758 |
|
| \begin{align*}
\left (-x^{2}+y\right ) y^{\prime }+4 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
26.074 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
8.271 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
19.539 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
18.193 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
8.709 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
8.380 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
8.520 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
11.618 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
51.026 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
15.569 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
51.482 |
|
| \begin{align*}
x \left (4+y\right ) y^{\prime }-y^{2}-2 y-2 x&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
14.855 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
9.383 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
18.565 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
61.076 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
20.823 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
18.796 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
4.500 |
|
| \begin{align*}
\left (x^{2} y-1\right ) y^{\prime }+x y^{2}-1&=0 \\
\end{align*} |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
4.204 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
26.606 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
41.911 |
|
| \begin{align*}
x^{2} \left (-1+y\right ) y^{\prime }+\left (x -1\right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.952 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
27.969 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
44.565 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
64.902 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
47.934 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{y+\sqrt {x}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
45.460 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{y+2+\sqrt {1+3 x}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
49.017 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}}{y+x^{{3}/{2}}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
67.305 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{{5}/{3}}}{y+x^{{4}/{3}}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
99.128 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y+\sqrt {x^{2}+1}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
91.884 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{b x}}{y \,{\mathrm e}^{-b x}+1} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
10.807 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{x}}{{\mathrm e}^{-x} y+1} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
9.842 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{\frac {2 x}{3}}}{y \,{\mathrm e}^{-\frac {2 x}{3}}+1} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
26.450 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{-x^{2}} x}{y \,{\mathrm e}^{x^{2}}+1} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
10.162 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{3} {\mathrm e}^{-\frac {4 x}{3}}}{y \,{\mathrm e}^{-\frac {2 x}{3}}+1} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
16.500 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{3} {\mathrm e}^{-2 b x}}{y \,{\mathrm e}^{-b x}+1} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
18.539 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{3} {\mathrm e}^{-2 x}}{{\mathrm e}^{-x} y+1} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
14.250 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{3} x \,{\mathrm e}^{2 x^{2}}}{y \,{\mathrm e}^{x^{2}}+1} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
19.528 |
|
| \begin{align*}
y^{\prime }&=\frac {-a b y+b^{2}+a b +b^{2} x -b a \sqrt {x}-a^{2}}{a \left (-a y+b +a +b x -a \sqrt {x}\right )} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
43.937 |
|
| \begin{align*}
y^{\prime }&=-\frac {a b y-b c +b^{2} x +b a \sqrt {x}-a^{2}}{a \left (a y-c +b x +a \sqrt {x}\right )} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
43.479 |
|
| \begin{align*}
y^{\prime }&=\frac {x \left (-1+x -2 y x +2 x^{3}\right )}{x^{2}-y} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
5.305 |
|
| \begin{align*}
y^{\prime }&=\frac {-4 y x +x^{3}+2 x^{2}-4 x -8}{-8 y+2 x^{2}+4 x -8} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.092 |
|
| \begin{align*}
y^{\prime }&=\frac {-4 y x -x^{3}+4 x^{2}-4 x +8}{8 y+2 x^{2}-8 x +8} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.490 |
|
| \begin{align*}
y^{\prime }&=\frac {-8 y x -x^{3}+2 x^{2}-8 x +32}{32 y+4 x^{2}-8 x +32} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.185 |
|
| \begin{align*}
y^{\prime }&=\frac {-4 a x y-a^{2} x^{3}-2 a b \,x^{2}-4 a x +8}{8 y+2 a \,x^{2}+4 b x +8} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
40.258 |
|
| \begin{align*}
y^{\prime }&=\frac {y x +x +y^{2}}{\left (x -1\right ) \left (x +y\right )} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
12.491 |
|
| \begin{align*}
y^{\prime }&=\frac {-4 y x -x^{3}-2 a \,x^{2}-4 x +8}{8 y+2 x^{2}+4 a x +8} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
20.155 |
|
| \begin{align*}
y^{\prime }&=\frac {x \left (-x -1+x^{2}-2 x^{2} y+2 x^{4}\right )}{\left (x^{2}-y\right ) \left (x +1\right )} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
6.454 |
|
| \begin{align*}
y^{\prime }&=-\frac {y \left (y x +1\right )}{x \left (y x +1-y\right )} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
40.257 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (-3 x^{3} y-3+y^{2} x^{7}\right )}{x \left (x^{3} y+1\right )} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
10.776 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (x^{3}+x^{2} y+y^{2}\right )}{x^{2} \left (x -1\right ) \left (x +y\right )} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
38.269 |
|
| \begin{align*}
y^{\prime }&=\frac {14 y x +12+2 x +x^{3} y^{3}+6 y^{2} x^{2}}{x^{2} \left (y x +2+x \right )} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
10.200 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left ({\mathrm e}^{-\frac {x^{2}}{2}} x y+{\mathrm e}^{-\frac {x^{2}}{4}} x +2 y^{2} {\mathrm e}^{-\frac {3 x^{2}}{4}}\right ) {\mathrm e}^{\frac {x^{2}}{4}}}{2 y \,{\mathrm e}^{-\frac {x^{2}}{4}}+2} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
22.989 |
|
| \begin{align*}
y^{\prime }&=\frac {-x +1-2 y+3 x^{2}-2 x^{2} y+2 x^{4}+x^{3}-2 x^{3} y+2 x^{5}}{x^{2}-y} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
6.328 |
|
| \begin{align*}
y^{\prime }&=\frac {-30 x^{3} y+12 x^{6}+70 x^{{7}/{2}}-30 x^{3}-25 \sqrt {x}\, y+50 x -25 \sqrt {x}-25}{5 \left (-5 y+2 x^{3}+10 \sqrt {x}-5\right ) x} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
12.299 |
|
| \begin{align*}
y^{\prime }&=-\frac {y^{2} \left (x^{2} y-2 x -2 y x +y\right )}{2 \left (-2+y x -2 y\right ) x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
15.868 |
|
| \begin{align*}
y^{\prime }&=\frac {-2 y x +2 x^{3}-2 x -y^{3}+3 y^{2} x^{2}-3 x^{4} y+x^{6}}{-y+x^{2}-1} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
9.061 |
|
| \begin{align*}
y^{\prime }&=\frac {-18 y x -6 x^{3}-18 x +27 y^{3}+27 y^{2} x^{2}+9 x^{4} y+x^{6}}{27 y+9 x^{2}+27} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
9.185 |
|
| \begin{align*}
y^{\prime }&=\frac {a^{2} x y+a +a^{2} x +a^{3} x^{3} y^{3}+3 y^{2} a^{2} x^{2}+3 a x y+1}{a^{2} x^{2} \left (a x y+1+a x \right )} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
11.067 |
|
| \begin{align*}
y^{\prime }&=\frac {6 x^{2} y-2 x +1-5 x^{3} y^{2}-2 y x +x^{4} y^{3}}{x^{2} \left (x^{2} y-x +1\right )} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
29.721 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2} \left (-2 y+2 x^{2}+2 x^{2} y+x^{4} y\right )}{x^{3} \left (x^{2}-y+x^{2} y\right )} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
13.829 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (-256 a \,x^{2} y-32 a^{2} x^{6}-256 a \,x^{2}+512 y^{3}+192 x^{4} a y^{2}+24 y a^{2} x^{8}+a^{3} x^{12}\right ) x}{512 y+64 a \,x^{4}+512} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
9.849 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (-108 x^{{3}/{2}} y+18 x^{{9}/{2}}-108 x^{{3}/{2}}-216 y^{3}+108 x^{3} y^{2}-18 x^{6} y+x^{9}\right ) \sqrt {x}}{-216 y+36 x^{3}-216} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
11.013 |
|
| \begin{align*}
y^{\prime }&=\frac {32 y x^{5}+8 x^{3}+32 x^{5}+64 x^{6} y^{3}+48 y^{2} x^{4}+12 x^{2} y+1}{16 x^{6} \left (4 x^{2} y+1+4 x^{2}\right )} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
8.634 |
|
| \begin{align*}
y^{\prime }&=-\frac {-y^{3}-y+2 y^{2} \ln \left (x \right )-\ln \left (x \right )^{2} y^{3}-1+3 y \ln \left (x \right )-3 \ln \left (x \right )^{2} y^{2}+\ln \left (x \right )^{3} y^{3}}{y x} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
17.726 |
|
| \begin{align*}
y^{\prime }&=-\frac {-y^{3}-y+4 y^{2} \ln \left (x \right )-4 \ln \left (x \right )^{2} y^{3}-1+6 y \ln \left (x \right )-12 \ln \left (x \right )^{2} y^{2}+8 \ln \left (x \right )^{3} y^{3}}{y x} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
17.467 |
|
| \begin{align*}
y^{\prime }&=\frac {-8 x^{2} y^{3}+16 x y^{2}+16 x y^{3}-8+12 y x -6 y^{2} x^{2}+x^{3} y^{3}}{16 \left (-2+y x -2 y\right ) x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
17.253 |
|
| \begin{align*}
y^{\prime }&=-\frac {16 x y^{3}-8 y^{3}-8 y+8 x y^{2}-2 x^{2} y^{3}-8+12 y x -6 y^{2} x^{2}+x^{3} y^{3}}{32 y x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
10.837 |
|
| \begin{align*}
y^{\prime }&=\frac {-3 x^{2} y-2 x^{3}-2 x -x y^{2}-y+x^{3} y^{3}+3 y^{2} x^{4}+3 y x^{5}+x^{6}}{x \left (x^{2}+y x +1\right )} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
10.086 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (27 y^{3}+27 \,{\mathrm e}^{3 x^{2}} y+18 \,{\mathrm e}^{3 x^{2}} y^{2}+3 y^{3} {\mathrm e}^{3 x^{2}}+27 \,{\mathrm e}^{\frac {9 x^{2}}{2}}+27 \,{\mathrm e}^{\frac {9 x^{2}}{2}} y+9 \,{\mathrm e}^{\frac {9 x^{2}}{2}} y^{2}+{\mathrm e}^{\frac {9 x^{2}}{2}} y^{3}\right ) {\mathrm e}^{3 x^{2}} x \,{\mathrm e}^{-\frac {9 x^{2}}{2}}}{243 y} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
18.623 |
|
| \begin{align*}
y^{\prime }&=\frac {-2 y-2 \ln \left (2 x +1\right )-2+2 x y^{3}+y^{3}+6 y^{2} \ln \left (2 x +1\right ) x +3 y^{2} \ln \left (2 x +1\right )+6 y \ln \left (2 x +1\right )^{2} x +3 y \ln \left (2 x +1\right )^{2}+2 \ln \left (2 x +1\right )^{3} x +\ln \left (2 x +1\right )^{3}}{\left (2 x +1\right ) \left (y+\ln \left (2 x +1\right )+1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
29.728 |
|
| \begin{align*}
y^{\prime }&=\frac {-32 y x +16 x^{3}+16 x^{2}-32 x -64 y^{3}+48 y^{2} x^{2}+96 x y^{2}-12 x^{4} y-48 x^{3} y-48 x^{2} y+x^{6}+6 x^{5}+12 x^{4}}{-64 y+16 x^{2}+32 x -64} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
9.038 |
|
| \begin{align*}
y^{\prime }&=\frac {x y \ln \left (x \right )+x^{2} \ln \left (x \right )-2 y x -x^{2}-y^{2}-y^{3}+3 x y^{2} \ln \left (x \right )-3 x^{2} \ln \left (x \right )^{2} y+x^{3} \ln \left (x \right )^{3}}{x \left (-y+x \ln \left (x \right )-x \right )} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
8.902 |
|
| \begin{align*}
y^{\prime }&=\frac {-32 y x -72 x^{3}+32 x^{2}-32 x +64 y^{3}+48 y^{2} x^{2}-192 x y^{2}+12 x^{4} y-96 x^{3} y+192 x^{2} y+x^{6}-12 x^{5}+48 x^{4}}{64 y+16 x^{2}-64 x +64} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
9.078 |
|
| \begin{align*}
y^{\prime }&=\frac {-128 y x -24 x^{3}+32 x^{2}-128 x +512 y^{3}+192 y^{2} x^{2}-384 x y^{2}+24 x^{4} y-96 x^{3} y+96 x^{2} y+x^{6}-6 x^{5}+12 x^{4}}{512 y+64 x^{2}-128 x +512} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
8.895 |
|
| \begin{align*}
y^{\prime }&=\frac {-32 a x y-8 a^{2} x^{3}-16 a b \,x^{2}-32 a x +64 y^{3}+48 a \,x^{2} y^{2}+96 b x y^{2}+12 a^{2} x^{4} y+48 y a \,x^{3} b +48 b^{2} x^{2} y+a^{3} x^{6}+6 a^{2} x^{5} b +12 b^{2} x^{4} a +8 b^{3} x^{3}}{64 y+16 a \,x^{2}+32 b x +64} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
8.950 |
|
| \begin{align*}
y^{\prime }&=\frac {-32 y x -8 x^{3}-16 a \,x^{2}-32 x +64 y^{3}+48 y^{2} x^{2}+96 a x y^{2}+12 x^{4} y+48 y a \,x^{3}+48 y a^{2} x^{2}+x^{6}+6 x^{5} a +12 a^{2} x^{4}+8 a^{3} x^{3}}{64 y+16 x^{2}+32 a x +64} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
8.273 |
|
| \begin{align*}
y^{\prime }&=\frac {\left ({\mathrm e}^{-3 x^{2}} x^{6}-6 \,{\mathrm e}^{-2 x^{2}} x^{4} y-4 \,{\mathrm e}^{-2 x^{2}} x^{4}+12 x^{2} {\mathrm e}^{-x^{2}} y^{2}+8 x^{2} {\mathrm e}^{-x^{2}} y+4 x^{2} {\mathrm e}^{-2 x^{2}}+8 x^{2} {\mathrm e}^{-x^{2}}-8 y^{3}-8 y \,{\mathrm e}^{-x^{2}}-8 \,{\mathrm e}^{-x^{2}}\right ) x}{-8 y+4 x^{2} {\mathrm e}^{-x^{2}}-8} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
17.320 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2} y+x^{4}+2 x^{3}-3 x^{2}+y x +x +y^{3}+3 y^{2} x^{2}-3 x y^{2}+3 x^{4} y-6 x^{3} y+x^{6}-3 x^{5}}{x \left (y+x^{2}-x +1\right )} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
13.075 |
|
| \begin{align*}
y^{\prime }&=\frac {-150 x^{3} y+60 x^{6}+350 x^{{7}/{2}}-150 x^{3}-125 \sqrt {x}\, y+250 x -125 \sqrt {x}-125 y^{3}+150 x^{3} y^{2}+750 y^{2} \sqrt {x}-60 x^{6} y-600 y x^{{7}/{2}}-1500 y x +8 x^{9}+120 x^{{13}/{2}}+600 x^{4}+1000 x^{{3}/{2}}}{25 \left (-5 y+2 x^{3}+10 \sqrt {x}-5\right ) x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
19.244 |
|
| \begin{align*}
y^{\prime }&=\frac {x \left (-x^{2}+2 x^{2} y-2 x^{4}+1\right )}{-x^{2}+y} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.225 |
|
| \begin{align*}
y y^{\prime }-y&=A x +B \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
130.455 |
|
| \begin{align*}
y y^{\prime }&=\frac {y}{\sqrt {a x +b}}+1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
133.141 |
|
| \begin{align*}
y y^{\prime }&=\left (3 a x +b \right ) y-a^{2} x^{3}-a b \,x^{2}+c x \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
84.363 |
|
| \begin{align*}
y y^{\prime }&=\frac {3 y}{\left (a x +b \right )^{{1}/{3}} x^{{5}/{3}}}+\frac {3}{\left (a x +b \right )^{{2}/{3}} x^{{7}/{3}}} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
81.391 |
|
| \begin{align*}
\left (A y+B x +a \right ) y^{\prime }+B y+x k +b&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
222.365 |
|
| \begin{align*}
\left (y+a x +b \right ) y^{\prime }&=\alpha y+\beta x +\gamma \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
✗ |
241.664 |
|
| \begin{align*}
\left (y+A \,x^{n}+a \right ) y^{\prime }+n A \,x^{n -1} y+k \,x^{m}+b&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
83.418 |
|
| \begin{align*}
x \left (2 a y+b x \right ) y^{\prime }&=a \left (2-m \right ) y^{2}+b \left (-m +1\right ) x y+c \,x^{2}+A \,x^{m +2} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
71.921 |
|
| \begin{align*}
\left (x^{2}+y x +a \right ) y^{\prime }&=y^{2}+y x +b \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
71.446 |
|
| \begin{align*}
x \left (2 a x y+b \right ) y^{\prime }&=-a \left (m +3\right ) x y^{2}-b \left (m +2\right ) y+c \,x^{m} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
65.677 |
|
| \begin{align*}
6 x -2 y+1+\left (2 y-2 x -3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.390 |
|
| \begin{align*}
\left (x +y+1\right ) y^{\prime }+1+4 x +3 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.032 |
|
| \begin{align*}
4 x -y+2+\left (x +y+3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.143 |
|
| \begin{align*}
2 x +y-\left (4 x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.049 |
|
| \begin{align*}
2 y+3 x y^{2}+\left (x +2 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
17.309 |
|
| \begin{align*}
y+x y^{2}+\left (x -x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
27.308 |
|
| \begin{align*}
x^{4} y \left (3 y+2 y^{\prime } x \right )+x^{2} \left (4 y+3 y^{\prime } x \right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
57.477 |
|
| \begin{align*}
2 x^{3} y-y^{2}-\left (2 x^{4}+y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
26.029 |
|
| \begin{align*}
x +y-\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.484 |
|
| \begin{align*}
3 x^{2}+6 y x +3 y^{2}+\left (2 x^{2}+3 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
18.418 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }-1&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.341 |
|
| \begin{align*}
x +y y^{\prime }+y-y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.369 |
|
| \begin{align*}
x \left (1-y\right ) y^{\prime }+\left (1-x \right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.555 |
|
| \begin{align*}
\left (-x +y\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.440 |
|
| \begin{align*}
\left (1-x \right ) y-x \left (1+y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.483 |
|
| \begin{align*}
2 x +3 y-1+\left (2 x +3 y-5\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.431 |
|
| \begin{align*}
\left (2 u+1\right ) u^{\prime }-1-t&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.993 |
|
| \begin{align*}
3 x +2 y+\left (2 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.691 |
|
| \begin{align*}
y^{2}+3+\left (2 y x -4\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
3.273 |
|
| \begin{align*}
2 y x +1+\left (x^{2}+4 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
2.928 |
|
| \begin{align*}
6 y x +2 y^{2}-5+\left (3 x^{2}+4 y x -6\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
3.864 |
|
| \begin{align*}
y \sec \left (x \right )^{2}+\sec \left (x \right ) \tan \left (x \right )+\left (\tan \left (x \right )+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
17.794 |
|
| \begin{align*}
\frac {\left (2 s-1\right ) s^{\prime }}{t}+\frac {s-s^{2}}{t^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.793 |
|
| \begin{align*}
2 y x -3+\left (x^{2}+4 y\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
2.479 |
|
| \begin{align*}
{\mathrm e}^{x} y+2 \,{\mathrm e}^{x}+y^{2}+\left ({\mathrm e}^{x}+2 y x \right ) y^{\prime }&=0 \\
y \left (0\right ) &= 6 \\
\end{align*} |
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
4.853 |
|
| \begin{align*}
2 y x +3 y^{2}-\left (x^{2}+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
17.156 |
|
| \begin{align*}
y+2+y \left (x +4\right ) y^{\prime }&=0 \\
y \left (-3\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.769 |
|
| \begin{align*}
3 x^{2}+9 y x +5 y^{2}-\left (6 x^{2}+4 y x \right ) y^{\prime }&=0 \\
y \left (2\right ) &= -6 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
14.191 |
|
| \begin{align*}
x +2 y+\left (2 x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.385 |
|
| \begin{align*}
3 x -y-\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.132 |
|
| \begin{align*}
2 x^{2}+2 y x +y^{2}+\left (x^{2}+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
27.211 |
|
| \begin{align*}
\left (1+y\right ) y^{\prime }+x \left (y^{2}+2 y\right )&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.937 |
|
| \begin{align*}
3 x -5 y+\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
44.013 |
|
| \begin{align*}
y^{\prime }&=\frac {4 x^{3} y^{2}-3 x^{2} y}{x^{3}-2 x^{4} y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
11.042 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x -7 y}{3 y-8 x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
66.588 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x^{2}+y^{2}}{-x^{2}+2 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
51.743 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +7 y}{2 x -2 y} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
25.207 |
|
| \begin{align*}
5 y x +4 y^{2}+1+\left (x^{2}+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
4.156 |
|
| \begin{align*}
\left (x +1\right ) y^{2}+y+\left (2 y x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
4.183 |
|
| \begin{align*}
4 x y^{2}+6 y+\left (5 x^{2} y+8 x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
33.825 |
|
| \begin{align*}
5 x +2 y+1+\left (2 x +y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.908 |
|
| \begin{align*}
3 x -y+1-\left (6 x -2 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.855 |
|
| \begin{align*}
x -2 y-3+\left (2 x +y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.719 |
|
| \begin{align*}
10 x -4 y+12-\left (x +5 y+3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
24.368 |
|
| \begin{align*}
6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime }&=0 \\
y \left (\frac {1}{2}\right ) &= 3 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.556 |
|
| \begin{align*}
2 x +3 y+1+\left (4 x +6 y+1\right ) y^{\prime }&=0 \\
y \left (-2\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.187 |
|
| \begin{align*}
2 y x -\sec \left (x \right )^{2}+\left (x^{2}+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
7.225 |
|
| \begin{align*}
\left (\frac {1}{y}-a \right ) y^{\prime }+\frac {2}{x}-b&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.464 |
|
| \begin{align*}
12 x +6 y-9+\left (5 x +2 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
30.263 |
|
| \begin{align*}
y-y^{\prime } x&=x^{2} y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
16.133 |
|
| \begin{align*}
2 x +2 y-1+\left (x +y-2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.832 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x -4 y-2}{3 x -4 y-3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.958 |
|
| \begin{align*}
y^{\prime }&=\frac {-3+x +y}{y-x +1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.053 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
10.630 |
|
| \begin{align*}
\left (1+u \right ) v+\left (1-v\right ) u v^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.070 |
|
| \begin{align*}
\left (t^{2}+t^{2} x\right ) x^{\prime }+x^{2}+t x^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.013 |
|
| \begin{align*}
y-x +\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.841 |
|
| \begin{align*}
x +y+\left (-x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.422 |
|
| \begin{align*}
\left (7 x +5 y\right ) y^{\prime }+10 x +8 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.921 |
|
| \begin{align*}
3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
66.082 |
|
| \begin{align*}
x +2 y+1-\left (3+2 x +4 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.644 |
|
| \begin{align*}
x^{2}+y+\left (x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
4.218 |
|
| \begin{align*}
y-3 x^{2}-\left (4 y-x \right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
5.468 |
|
| \begin{align*}
\frac {x}{\left (x +y\right )^{2}}+\frac {\left (2 x +y\right ) y^{\prime }}{\left (x +y\right )^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
8.770 |
|
| \begin{align*}
2 x +2 y-1+\left (x +y-2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.244 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x -y}{x +3 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
20.180 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{-x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
20.095 |
|
| \begin{align*}
y^{\prime }&=\frac {x y}{1-y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.084 |
|
| \begin{align*}
y^{\prime }&=-\frac {y \left (2 x +y\right )}{x \left (x +2 y\right )} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
25.492 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{-y x +1} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
44.631 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{-x +y} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
23.092 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{-x +y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
22.352 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{-x +y} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.897 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{-x +y} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
23.282 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{t y+t +y+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.619 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{\left (1+y\right ) \left (-2+t \right )} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.305 |
|
| \begin{align*}
y^{\prime }&=\frac {t}{y-2} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.759 |
|
| \begin{align*}
\left (-2+y\right ) y^{\prime }&=x -3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
19.897 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (3 x -2 y\right )^{2}+1}{3 x -2 y}+\frac {3}{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
29.579 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y}{x +y} \\
y \left (0\right ) &= 3 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
33.134 |
|
| \begin{align*}
\left (-x +y\right ) y^{\prime }&=1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.163 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
20.022 |
|
| \begin{align*}
\left (2 y x +2 x^{2}\right ) y^{\prime }&=x^{2}+2 y x +2 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
67.096 |
|
| \begin{align*}
2 y x +y^{2}+\left (x^{2}+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
37.616 |
|
| \begin{align*}
\frac {2 y}{x}+\left (4 x^{2} y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
141.036 |
|
| \begin{align*}
3 y+3 y^{2}+\left (2 x +4 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
32.188 |
|
| \begin{align*}
4 y x +\left (3 x^{2}+5 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
58.924 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{y x -3 x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
20.022 |
|
| \begin{align*}
y^{\prime }&=\frac {x +2 y}{x +2 y+3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.635 |
|
| \begin{align*}
y^{\prime }&=\frac {x +2 y}{2 x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.495 |
|
| \begin{align*}
1-\left (x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.958 |
|
| \begin{align*}
y y^{\prime } x&=x^{2}+y x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
39.310 |
|
| \begin{align*}
x \left (1-2 y\right )+\left (-x^{2}+y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.273 |
|
| \begin{align*}
2 x -y-y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
21.898 |
|
| \begin{align*}
3 y \left (t^{2}+y\right )+t \left (t^{2}+6 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
29.477 |
|
| \begin{align*}
y \cos \left (t \right )+\left (2 y+\sin \left (t \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.007 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (x -4\right ) y^{3}}{x^{3} \left (-2+y\right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.300 |
|
| \begin{align*}
2 x -3 y+\left (-3 x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
29.253 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{t}}{1+y} \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.651 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+3}{3 x +3 y+1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.409 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y+2}{2 x -2 y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.428 |
|
| \begin{align*}
3 t^{2} y+3 y^{2}-1+\left (t^{3}+6 t y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
8.597 |
|
| \begin{align*}
\frac {2 t^{2} y \cos \left (t^{2}\right )-y \sin \left (t^{2}\right )}{t^{2}}+\frac {\left (2 t y+\sin \left (t^{2}\right )\right ) y^{\prime }}{t}&=0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
12.125 |
|
| \begin{align*}
1+5 t -y-\left (t +2 y\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
27.340 |
|
| \begin{align*}
y+2 t^{2}+\left (t^{2} y-t \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
6.828 |
|
| \begin{align*}
5 t y+4 y^{2}+1+\left (t^{2}+2 t y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
7.615 |
|
| \begin{align*}
\frac {9 t}{5}+2 y+\left (2 t +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
81.079 |
|
| \begin{align*}
2 t +\frac {19 y}{10}+\left (\frac {19 t}{10}+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
58.563 |
|
| \begin{align*}
2 t +\left (y-3 t \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
108.144 |
|
| \begin{align*}
t y-y^{2}+t \left (t -3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
30.070 |
|
| \begin{align*}
t^{2}+t y+y^{2}-t y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
47.624 |
|
| \begin{align*}
y^{\prime }&=\frac {t +4 y}{4 t +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
34.028 |
|
| \begin{align*}
y+\left (y+t \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
39.750 |
|
| \begin{align*}
2 t^{2}-7 t y+5 y^{2}+t y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
97.703 |
|
| \begin{align*}
y^{2}&=\left (t y-4 t^{2}\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
59.402 |
|
| \begin{align*}
1+t -2 y+\left (4 t -3 y-6\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
61.639 |
|
| \begin{align*}
5 t +2 y+1+\left (2 t +y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
28.170 |
|
| \begin{align*}
3 t -y+1-\left (6 t -2 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.483 |
|
| \begin{align*}
2 t +3 y+1+\left (4 t +6 y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.267 |
|
| \begin{align*}
3 t +\left (t -4 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
39.307 |
|
| \begin{align*}
y-t +\left (y+t \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
44.973 |
|
| \begin{align*}
y^{2}+\left (t^{2}+t y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
142.134 |
|
| \begin{align*}
t^{2}-y+\left (y-t \right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
7.425 |
|
| \begin{align*}
2 x -y-2+\left (-x +2 y\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
32.053 |
|
| \begin{align*}
y^{\prime }&=\frac {1+y}{x -y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.902 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.936 |
|
| \begin{align*}
4 x -3 y+\left (-3 x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.592 |
|
| \begin{align*}
y-x +\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.162 |
|
| \begin{align*}
3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
58.819 |
|
| \begin{align*}
x +y-2+\left (x -y+4\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.131 |
|
| \begin{align*}
x +y+\left (x -y-2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.855 |
|
| \begin{align*}
2 x +3 y-5+\left (3 x +2 y-5\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.730 |
|
| \begin{align*}
8 x +4 y+1+\left (4 x +2 y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.316 |
|
| \begin{align*}
x -2 y-1+\left (3 x -6 y+2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.890 |
|
| \begin{align*}
x +y+\left (x +y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.680 |
|
| \begin{align*}
1-x^{2} y+x^{2} \left (-x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
4.637 |
|
| \begin{align*}
x -y x +\left (y+x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.805 |
|
| \begin{align*}
x -y+3+\left (3 x +y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.451 |
|
| \begin{align*}
x -y+2+\left (x -y+3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.190 |
|
| \begin{align*}
\left (x -1\right ) \left (y^{2}-y+1\right )&=\left (-1+y\right ) \left (x^{2}+x +1\right ) y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.941 |
|
| \begin{align*}
\cos \left (x \right ) y+\left (2 y-\sin \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.648 |
|
| \begin{align*}
\left (3 x +3 y+a^{2}\right ) y^{\prime }&=4 x +4 y+b^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.457 |
|
| \begin{align*}
\left (5 x -7 y+1\right ) y^{\prime }+x +y-1&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
120.428 |
|
| \begin{align*}
x +y+1+\left (2 x +2 y-1\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.989 |
|
| \begin{align*}
y^{\prime }&=\frac {7 x^{2}-1}{7+5 y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.914 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x}{1+2 y} \\
y \left (2\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.898 |
|
| \begin{align*}
y^{\prime }&=\frac {-{\mathrm e}^{x}+3 x^{2}}{2 y-11} \\
y \left (0\right ) &= 11 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.181 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{-x}-{\mathrm e}^{x}}{3+4 y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.751 |
|
| \begin{align*}
y^{\prime }&=\frac {6-{\mathrm e}^{x}}{3+2 y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.977 |
|
| \begin{align*}
y^{\prime }&=\frac {2 \cos \left (2 x \right )}{10+2 y} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.935 |
|
| \begin{align*}
y^{\prime }&=\frac {t -y}{2 t +5 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
12.847 |
|
| \begin{align*}
y^{\prime }&=\frac {\cot \left (t \right ) y}{1+y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.795 |
|
| \begin{align*}
3+2 x +\left (-2+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.053 |
|
| \begin{align*}
2 x +4 y+\left (2 x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
15.532 |
|
| \begin{align*}
y^{\prime }&=-\frac {4 x +2 y}{2 x +3 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.428 |
|
| \begin{align*}
y^{\prime }&=-\frac {4 x -2 y}{2 x -3 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
17.629 |
|
| \begin{align*}
2 x -y+\left (-x +2 y\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 3 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.379 |
|
| \begin{align*}
9 x^{2}+y-1-\left (4 y-x \right ) y^{\prime }&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
2.663 |
|
| \begin{align*}
3 y x +y^{2}+\left (y x +x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
14.292 |
|
| \begin{align*}
y y^{\prime } x&=\left (x +y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
13.780 |
|
| \begin{align*}
y^{\prime }&=\frac {4 y-7 x}{5 x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
13.133 |
|
| \begin{align*}
\left (3 x-y \right ) x^{\prime }+9 y -2 x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.409 |
|
| \begin{align*}
x^{\prime }&=\frac {2 x y +x^{2}}{3 y^{2}+2 x y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
9.627 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=y y^{\prime } x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
14.477 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=-x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.457 |
|
| \begin{align*}
3 y-7 x +7&=\left (3 x -7 y-3\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
59.121 |
|
| \begin{align*}
\left (x +2 y+1\right ) y^{\prime }&=3+2 x +4 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.029 |
|
| \begin{align*}
\left (x \left (x +y\right )+a^{2}\right ) y^{\prime }&=y \left (x +y\right )+b^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
11.916 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{y x -x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
16.345 |
|
| \begin{align*}
y y^{\prime } x&=-1+y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.973 |
|
| \begin{align*}
y y^{\prime } x&=\left (x +1\right ) \left (1+y\right ) \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.888 |
|
| \begin{align*}
x -y-\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.045 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+4}{x -y-6} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.793 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+4}{x +y-6} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.042 |
|
| \begin{align*}
2 x -2 y+\left (-1+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.191 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y-1}{x +4 y+2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
220.730 |
|
| \begin{align*}
y^{\prime }&=\frac {y-x y^{2}}{x +x^{2} y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
42.648 |
|
| \begin{align*}
\left (x +\frac {2}{y}\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
43.602 |
|
| \begin{align*}
y x -1+\left (x^{2}-y x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
5.048 |
|
| \begin{align*}
y^{2}+y x +1+\left (x^{2}+y x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
6.060 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=-x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.076 |
|
| \begin{align*}
y^{\prime } x +2&=x^{3} \left (-1+y\right ) y^{\prime } \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
8.760 |
|
| \begin{align*}
\left (-y x +1\right ) y^{\prime }&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
44.826 |
|
| \begin{align*}
2 x +3 y+1+\left (2 y-3 x +5\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.125 |
|
| \begin{align*}
y^{2}&=\left (x^{3}-y x \right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
48.637 |
|
| \begin{align*}
y y^{\prime } x&=x^{2} y^{\prime }+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
63.190 |
|
| \begin{align*}
6 x +4 y+3+\left (3 x +2 y+2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.336 |
|
| \begin{align*}
y^{2}-3 y x -2 x^{2}&=\left (x^{2}-y x \right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
20.027 |
|
| \begin{align*}
y^{\prime }&=\frac {x +2 y+2}{y-2 x} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.230 |
|
| \begin{align*}
y^{\prime }&=\frac {-3 x -2 y-1}{2 x +3 y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.973 |
|
| \begin{align*}
3 y x +y^{2}+\left (3 y x +x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
17.208 |
|
| \begin{align*}
2 t +3 x+\left (3 t -x\right ) x^{\prime }&=t^{2} \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
5.054 |
|
| \begin{align*}
y^{2}&=x \left (-x +y\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
65.573 |
|
| \begin{align*}
2 a x +b y+\left (2 c y+b x +e \right ) y^{\prime }&=g \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
70.427 |
|
| \begin{align*}
x +y y^{\prime }&=m y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
34.361 |
|
| \begin{align*}
y^{\prime }&=1+\frac {2 y}{x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.737 |
|
| \begin{align*}
x \left (x -2 y\right ) y^{\prime }+x^{2}+2 y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
44.479 |
|
| \begin{align*}
\left (x^{2}+2 y x \right ) y^{\prime }-3 x^{2}+2 y x -y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
26.005 |
|
| \begin{align*}
\left (3 x +2 y-7\right ) y^{\prime }&=2 x -3 y+6 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
26.530 |
|
| \begin{align*}
\left (6 x -5 y+4\right ) y^{\prime }&=1+2 x -y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
97.965 |
|
| \begin{align*}
\left (5 x -2 y+7\right ) y^{\prime }&=x -3 y+2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
73.319 |
|
| \begin{align*}
\left (x -3 y+4\right ) y^{\prime }&=5 x -7 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
65.315 |
|
| \begin{align*}
\left (x -3 y+4\right ) y^{\prime }&=2 x -6 y+7 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.254 |
|
| \begin{align*}
\left (5 x -2 y+7\right ) y^{\prime }&=10 x -4 y+6 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.227 |
|
| \begin{align*}
\left (2 x -2 y+5\right ) y^{\prime }&=x -y+3 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.319 |
|
| \begin{align*}
\left (6 x -4 y+1\right ) y^{\prime }&=3 x -2 y+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.906 |
|
| \begin{align*}
y^{2}+\left (y x +x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
85.941 |
|
| \begin{align*}
\left (3 x +4 y\right ) y^{\prime }+y-2 x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
70.476 |
|
| \begin{align*}
3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
74.299 |
|
| \begin{align*}
\left (y-3 x +3\right ) y^{\prime }&=2 y-x -4 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
101.799 |
|
| \begin{align*}
2 a x +b y+g +\left (2 c y+b x +e \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
73.289 |
|
| \begin{align*}
\left (y x +1\right ) y-x \left (-y x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
56.015 |
|
| \begin{align*}
a \left (y^{\prime } x +2 y\right )&=y y^{\prime } x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.903 |
|
| \begin{align*}
x^{2} y-2 x y^{2}-\left (x^{3}-3 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
18.030 |
|
| \begin{align*}
y^{2}+2 x^{2} y+\left (2 x^{3}-y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
53.424 |
|
| \begin{align*}
y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.490 |
|
| \begin{align*}
2 x -y+1+\left (2 y-x -1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.362 |
|
| \begin{align*}
x +y y^{\prime }&=m \left (-y+y^{\prime } x \right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
25.557 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.659 |
|
| \begin{align*}
3 y+2 x +4-\left (4 x +6 y+5\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.546 |
|
| \begin{align*}
2 y^{2} x^{2}+y-\left (x^{3} y-3 x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
76.957 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=y y^{\prime } x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
67.981 |
|
| \begin{align*}
y-x +\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
25.846 |
|
| \begin{align*}
x +y y^{\prime }&=m \left (-y+y^{\prime } x \right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
27.513 |
|
| \begin{align*}
\left ({\mathrm e}^{x}+1\right ) y y^{\prime }&=\left (1+y\right ) {\mathrm e}^{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.845 |
|
| \begin{align*}
y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.760 |
|
| \begin{align*}
\left (x +y-1\right ) y^{\prime }&=x +y+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.158 |
|
| \begin{align*}
\left (2 x +2 y+1\right ) y^{\prime }&=x +y+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.643 |
|
| \begin{align*}
2 x +3 y-1+\left (2 x +3 y-5\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.516 |
|
| \begin{align*}
\left (2 x -2 y+5\right ) y^{\prime }-x +y-3&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.910 |
|
| \begin{align*}
x +y+1-\left (2 x +2 y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.427 |
|
| \begin{align*}
y^{2}&=\left (y x -x^{2}\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
25.478 |
|
| \begin{align*}
\left (6 x -5 y+4\right ) y^{\prime }+y-2 x -1&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
108.243 |
|
| \begin{align*}
\left (x -3 y+4\right ) y^{\prime }+7 y-5 x&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
77.211 |
|
| \begin{align*}
\left (3+2 x +4 y\right ) y^{\prime }&=x +2 y+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.289 |
|
| \begin{align*}
y^{\prime }&=\frac {1+2 x -y}{x +2 y-3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
20.903 |
|
| \begin{align*}
\left (x -y\right ) y^{\prime }&=x +y+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
24.576 |
|
| \begin{align*}
x -y-2-\left (2 x -2 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.530 |
|
| \begin{align*}
y^{2}+\left (x -\frac {1}{y}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
13.164 |
|
| \begin{align*}
1+4 y x +2 y^{2}+\left (1+4 y x +2 x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
7.710 |
|
| \begin{align*}
x^{2} y-2 x y^{2}-\left (x^{3}-3 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
19.858 |
|
| \begin{align*}
y^{2}+2 x^{2} y+\left (2 x^{3}-y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
56.814 |
|
| \begin{align*}
2 y+3 y^{\prime } x +2 x y \left (3 y+4 y^{\prime } x \right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
125.132 |
|
| \begin{align*}
x +y y^{\prime }&=m \left (-y+y^{\prime } x \right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
29.362 |
|
| \begin{align*}
2 y+3 y^{\prime } x +2 x y \left (3 y+4 y^{\prime } x \right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
120.306 |
|
| \begin{align*}
\left (2 x +2 y+3\right ) y^{\prime }&=x +y+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.486 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=y y^{\prime } x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
73.563 |
|
| \begin{align*}
y^{\prime }+\frac {a x +b y+c}{b x +f y+e}&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
89.483 |
|
| \begin{align*}
y-y^{\prime } x&=x +y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.341 |
|
| \begin{align*}
y^{2}+\left (y x +x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
117.299 |
|
| \begin{align*}
y^{\prime }&=\frac {6 x -2 y-7}{2 x +3 y-6} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
47.533 |
|
| \begin{align*}
2 x +y+1+\left (4 x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.422 |
|
| \begin{align*}
x^{2}-y x +y^{2}-y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
41.846 |
|
| \begin{align*}
y^{\prime }&=\frac {x +2 y+1}{2 x +2+y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
54.148 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +y+1}{x +2 y+2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
150.876 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y \left (-1+y\right )}{x \left (2-y\right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
40.477 |
|
| \begin{align*}
x +3 y+\left (3 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.730 |
|
| \begin{align*}
x +y+\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.451 |
|
| \begin{align*}
y-x^{{1}/{3}}+\left (x +y\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
3.175 |
|
| \begin{align*}
x^{\prime }&=\frac {x-t +1}{x-t +2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.106 |
|
| \begin{align*}
x^{\prime }&=\frac {x-t}{x-t +1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.007 |
|
| \begin{align*}
x^{\prime }&=-\frac {x+t +1}{x-t +1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.030 |
|
| \begin{align*}
2 x \left (1+y\right )-y y^{\prime }&=0 \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.350 |
|
| \begin{align*}
2 x -6 y+3-\left (1+x -3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.989 |
|
| \begin{align*}
2 x +y+1+\left (4 x +2 y+3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.105 |
|
| \begin{align*}
2 x +3 y-1+\left (2 x -3 y+2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
23.168 |
|
| \begin{align*}
x +2 y-4-\left (-5+2 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.296 |
|
| \begin{align*}
x +2 y-1+3 \left (x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
7.821 |
|
| \begin{align*}
x -y+\left (x -4 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
42.954 |
|
| \begin{align*}
x^{2}-y x +y^{2}-y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
10.075 |
|
| \begin{align*}
y+x y^{2}+\left (x -x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
27.155 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+3 x +y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.167 |
|
| \begin{align*}
3 x \left (y x -2\right )+\left (x^{3}+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
2.638 |
|
| \begin{align*}
3 x^{2}+4 y x +\left (2 x^{2}+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
2.678 |
|
| \begin{align*}
x +y-\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.504 |
|
| \begin{align*}
y^{\prime }+\frac {y \left (x +y\right )}{x +2 y-1}&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.179 |
|
| \begin{align*}
2 x^{2}+y+\left (x^{2} y-x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
2.769 |
|
| \begin{align*}
4 y x +3 y^{2}-x +x \left (x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
4.130 |
|
| \begin{align*}
\left (x^{3}-y\right ) y-x \left (x^{3}+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
27.293 |
|
| \begin{align*}
y^{\prime }&=\frac {x -2 y}{2 x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.414 |
|
| \begin{align*}
y^{\prime } \left (x +\frac {x^{2}}{y}\right )&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
14.365 |
|
| \begin{align*}
2 x -y+\left (-x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.589 |
|
| \begin{align*}
2 y-1+\left (3 x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.095 |
|
| \begin{align*}
y^{2}+\left (3 y x -1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
31.666 |
|
| \begin{align*}
6 y^{2}-x \left (2 x^{3}+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
28.641 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+1}{x +2 y+3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
35.876 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+1}{x +y+2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.461 |
|
| \begin{align*}
x +2 y+3+\left (2 x +4 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.317 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +y}{y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.792 |
|
| \begin{align*}
2 x +y-3+\left (x +y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.419 |
|
| \begin{align*}
x -2 y+1+\left (4 x -3 y-6\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
22.144 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
56.039 |
|
| \begin{align*}
a x -b y+\left (b x -a y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
10.627 |
|
| \begin{align*}
4 x -2 y+3+\left (5 y-2 x +7\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.842 |
|
| \begin{align*}
-y+y^{\prime } x&=x^{2} y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
13.374 |
|
| \begin{align*}
3 y+2 y^{\prime } x +4 x y^{2}+3 x^{2} y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
32.316 |
|
| \begin{align*}
2-x -y+\left (x +y+3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.968 |
|
| \begin{align*}
4 x +3 y+2+\left (5 x +4 y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
20.193 |
|
| \begin{align*}
x -y-3+\left (3 x -3 y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.198 |
|
| \begin{align*}
2 x -y-1+\left (3 x +2 y-5\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
23.695 |
|
| \begin{align*}
2 x -y+1+\left (x -2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
75.381 |
|
| \begin{align*}
3 x +3 y-2+\left (2 x +2 y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.904 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=x^{2} y y^{\prime }-x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.970 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=y y^{\prime } x \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
11.439 |
|
| \begin{align*}
3 x^{2} y+\left (x^{3}+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.919 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2} y-y}{1+y} \\
y \left (3\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.753 |
|
| \begin{align*}
2 y x +x +\left (y+x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.754 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.841 |
|
| \begin{align*}
y+\left (2 x -3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.275 |
|
| \begin{align*}
y^{\prime }&=\frac {-x +3}{y+5} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.559 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{-x +y} \\
y \left (-2\right ) &= 3 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.842 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (-1+y\right ) \left (3+y\right )}{\left (-2+y\right ) \left (x +3\right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.609 |
|
| \begin{align*}
x +2+\left (2 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
20.787 |
|
| \begin{align*}
y&=\left (2 x +3 y\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
34.943 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +5 y}{2 x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
114.398 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +3 y+1}{3 x -2 y-5} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.270 |
|
| \begin{align*}
\left (3 x -y-9\right ) y^{\prime }&=10-2 x +2 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
143.949 |
|
| \begin{align*}
2 x +3 y+4&=\left (4 x +6 y+1\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.986 |
|
| \begin{align*}
2 x +2 y+1+\left (x +y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.511 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (y x +1\right )}{x \left (-y x +1\right )} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
36.844 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y}{x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.028 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
16.653 |
|
| \begin{align*}
y^{\prime }&=\frac {x -\cos \left (x \right ) y}{y+\sin \left (x \right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
5.869 |
|
| \begin{align*}
{\mathrm e}^{-x} y-\sin \left (x \right )-\left ({\mathrm e}^{-x}+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
27.003 |
|
| \begin{align*}
x^{2}+\frac {y}{x}+\left (\ln \left (x \right )+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
4.918 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (y-{\mathrm e}^{x}\right )}{{\mathrm e}^{x}-2 y x} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
5.286 |
|
| \begin{align*}
y^{\prime }&=\frac {y-2 x}{-x +2 y} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.754 |
|
| \begin{align*}
\left (x^{2}+2 \,{\mathrm e}^{2 x} y\right ) y^{\prime }+2 y x +2 y^{2} {\mathrm e}^{2 x}&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
9.390 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.619 |
|
| \begin{align*}
x y^{2}+2 y+\left (3 x^{2} y-4 x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
83.142 |
|
| \begin{align*}
y^{2}+y x +1+\left (x^{2}+y x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
5.744 |
|
| \begin{align*}
2 y^{2}+4 x^{2} y+\left (4 y x +3 x^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
62.352 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x -3 y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.517 |
|
| \begin{align*}
y^{2}+\left (-x^{3}+y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
38.432 |
|
| \begin{align*}
y+\left (2 x^{2} y-x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
18.846 |
|
| \begin{align*}
x^{3}+y+\left (x^{2} y-x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
7.309 |
|
| \begin{align*}
\left (3-x^{2} y\right ) y^{\prime }&=x y^{2}+4 \\
\end{align*} |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
5.274 |
|
| \begin{align*}
r^{2} \sin \left (t \right )&=\left (2 r \cos \left (t \right )+10\right ) r^{\prime } \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
6.786 |
|
| \begin{align*}
x^{2}+y^{2}+\left (2 y x -3\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
4.739 |
|
| \begin{align*}
y^{\prime }&=\frac {x +2 y}{y-2 x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.292 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.922 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (x +y\right )}{x \left (x -y\right )} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
13.886 |
|
| \begin{align*}
-y+y^{\prime } x&=x^{2} y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
18.766 |
|
| \begin{align*}
y^{2}&=\left (x^{2}+2 y x \right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
55.155 |
|
| \begin{align*}
s^{\prime }&=\frac {1}{s+t +1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.940 |
|
| \begin{align*}
y^{\prime }&=\frac {x +3 y}{x -3 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
21.571 |
|
| \begin{align*}
3 y^{2}+4 y x +\left (x^{2}+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
23.004 |
|
| \begin{align*}
y^{\prime }&=\frac {2}{x +2 y-3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.904 |
|
| \begin{align*}
\left (y+2\right ) x +y \left (2+x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.332 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y}{x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
22.311 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y+1}{x +y+1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.622 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y}{x +y} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
21.925 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y}{x +y} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.977 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (b_{2} x +b_{1} \right )}{x \left (a_{1} +a_{2} y\right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.177 |
|
| \begin{align*}
y y^{\prime }-7 y&=6 x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
17.444 |
|
| \begin{align*}
x +y y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.607 |
|
| \begin{align*}
x -y+\left (y-x +2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.946 |
|
| \begin{align*}
x +y+\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.933 |
|
| \begin{align*}
y^{\prime }&=\frac {y-x +1}{3-x +y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.770 |
|
| \begin{align*}
3 x^{2} y+y^{2}-\left (-x^{3}-2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
19.686 |
|
| \begin{align*}
x -y+\left (y-x +2\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.747 |
|
| \begin{align*}
x +y+\left (x -y\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
22.383 |
|
| \begin{align*}
y^{\prime }&=\frac {y-x +1}{3-x +y} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.592 |
|
| \begin{align*}
y-\left (x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.625 |
|
| \begin{align*}
3 y+\left (7 x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
20.124 |
|
| \begin{align*}
x -y+\left (2 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
20.615 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y}{x +y+2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.155 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +y-4}{x -y+1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
35.094 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x -2 y+7}{2 x +3 y+9} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
31.540 |
|
| \begin{align*}
y^{\prime }&=\frac {5 x -y-2}{x +y+4} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.032 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y+5}{2 x -y-3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
67.040 |
|
| \begin{align*}
y^{\prime }&=\frac {y-x +1}{3 x -y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
26.813 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x -y+1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
22.589 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x}{x -y+1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
18.146 |
|
| \begin{align*}
y^{\prime }&=-\frac {x +2 y}{y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
11.902 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +y-4}{x -y+1} \\
y \left (2\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
44.472 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=x -y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
26.361 |
|
| \begin{align*}
\left (x +y+1\right ) y^{\prime }&=x +y+2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.814 |
|
| \begin{align*}
y+x y^{2}-\left (x +2 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
147.763 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x -y}{x +2 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
23.852 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x^{2}+2 y^{2}-3 y x}{y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
112.899 |
|
| \begin{align*}
y^{\prime }&=\frac {4 x -3 y-17}{3 x +y-3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
33.433 |
|
| \begin{align*}
2 x +2 y-3+\left (1-2 y+2 x \right ) y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.314 |
|
| \begin{align*}
3 x -2 y+2 y^{2}+\left (2 y x -x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
5.658 |
|
| \begin{align*}
20 y-20 x y^{2}+\left (5 x -8 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
38.072 |
|
| \begin{align*}
x y^{2}+\left (3-2 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
46.194 |
|
| \begin{align*}
y+2 x^{3}+\left (2 x -\frac {x^{4}}{y}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
39.924 |
|
| \begin{align*}
x -y+1+\left (2 y-2 x +3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.567 |
|
| \begin{align*}
\left (x +2 y+2\right ) y^{\prime }&=3 x -y-1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
20.012 |
|
| \begin{align*}
1+\left (1-3 x +y\right ) y^{\prime }&=0 \\
y \left (4\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
27.573 |
|
| \begin{align*}
2 x y^{2}+\left (1-x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
51.044 |
|
| \begin{align*}
x y^{3}+\left (1+y\right ) {\mathrm e}^{-x} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.542 |
|
| \begin{align*}
y^{\prime } x +y+x y \left (1+y^{\prime }\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.292 |
|
| \begin{align*}
\left (2 x +y\right ) y^{\prime }+x -2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.382 |
|
| \begin{align*}
\left (x -y\right ) \left (4 x +y\right )+x \left (5 x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
139.168 |
|
| \begin{align*}
5 v-u +\left (3 v-7 u \right ) v^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
101.697 |
|
| \begin{align*}
v^{2}+x \left (x +v\right ) v^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
100.387 |
|
| \begin{align*}
x -y+\left (3 x +y\right ) y^{\prime }&=0 \\
y \left (2\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
18.622 |
|
| \begin{align*}
y \left (2 x^{2}-y x +y^{2}\right )-x^{2} \left (2 x -y\right ) y^{\prime }&=0 \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
34.388 |
|
| \begin{align*}
y \left (9 x -2 y\right )-x \left (6 x -y\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
54.937 |
|
| \begin{align*}
x +y+\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.771 |
|
| \begin{align*}
2 y x -3 x^{2}+\left (y+x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
2.265 |
|
| \begin{align*}
y^{2}-2 y x +6 x -\left (x^{2}-2 y x +2\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
2.875 |
|
| \begin{align*}
2 x -3 y+\left (-3 x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.424 |
|
| \begin{align*}
x y^{2}+y-x +x \left (y x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
4.562 |
|
| \begin{align*}
3 \left (x^{2}-1\right ) y+\left (x^{3}+8 y-3 x \right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.273 |
|
| \begin{align*}
y \left (y+x^{2}\right )+x \left (x^{2}-2 y\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
5.807 |
|
| \begin{align*}
y-2+\left (3 x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
105.805 |
|
| \begin{align*}
y^{2}-x \left (2 x +3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
55.976 |
|
| \begin{align*}
x -y-\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.312 |
|
| \begin{align*}
x y \left (1-y^{\prime }\right )&=x^{2} y^{\prime }+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
8.770 |
|
| \begin{align*}
x -y+\left (3 x +y\right ) y^{\prime }&=0 \\
y \left (2\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
5.954 |
|
| \begin{align*}
y^{2}-\left (y x +2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
28.026 |
|
| \begin{align*}
3 x -2 y+1+\left (3 x -2 y+3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.496 |
|
| \begin{align*}
y x +\left (x^{2}-3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
18.815 |
|
| \begin{align*}
x +2 y-1+\left (2 x +4 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.717 |
|
| \begin{align*}
6 y^{2}-x \left (2 x^{3}+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
21.404 |
|
| \begin{align*}
y+x \left (3 y x -2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
31.527 |
|
| \begin{align*}
x +2 y-1-\left (x +2 y-5\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.112 |
|
| \begin{align*}
12 x +4 y-8-\left (3 x +y\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.624 |
|
| \begin{align*}
y-2-\left (x -y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.315 |
|
| \begin{align*}
x -4 y-9+\left (4 x +y-2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.094 |
|
| \begin{align*}
2 x -y+\left (-6+4 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
15.088 |
|
| \begin{align*}
x -4 y-3-\left (x -6 y-5\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
32.703 |
|
| \begin{align*}
2 x +3 y-5+\left (3 x -y-2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.763 |
|
| \begin{align*}
\left (2 x -y+3\right ) y^{\prime }+2&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.407 |
|
| \begin{align*}
x +y-1+\left (2 x +2 y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.566 |
|
| \begin{align*}
3 x +2 y+7+\left (2 x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.681 |
|
| \begin{align*}
x -2+4 \left (x +y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
14.028 |
|
| \begin{align*}
x -3 y+2+3 \left (x +3 y-4\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.685 |
|
| \begin{align*}
6 x -3 y+2-\left (2 x -y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.195 |
|
| \begin{align*}
9 x -4 y+4-\left (1+2 x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.079 |
|
| \begin{align*}
x +3 y-4+\left (x +4 y-5\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.573 |
|
| \begin{align*}
x +2 y-1-\left (-5+2 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.185 |
|
| \begin{align*}
x -1-\left (3 x -2 y-5\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
27.502 |
|
| \begin{align*}
x +y-4-\left (3 x -y-4\right ) y^{\prime }&=0 \\
y \left (4\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
16.581 |
|
| \begin{align*}
x +y-4-\left (3 x -y-4\right ) y^{\prime }&=0 \\
y \left (3\right ) &= 7 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
12.957 |
|
| \begin{align*}
x^{2}+y^{2}+1+x \left (x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
52.195 |
|
| \begin{align*}
2 y \left (x^{2}-y+x \right )+\left (x^{2}-2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
3.396 |
|
| \begin{align*}
y x +1+x \left (x +4 y-2\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
2.799 |
|
| \begin{align*}
2 y^{2}+3 y x -2 y+6 x +x \left (x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
3.256 |
|
| \begin{align*}
y \left (y+2 x -2\right )-2 \left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.655 |
|
| \begin{align*}
4 y^{2}+10 y x -4 y+8+x \left (2 x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
3.428 |
|
| \begin{align*}
y \left (8 x -9 y\right )+2 x \left (x -3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
11.727 |
|
| \begin{align*}
y \left (2 x^{2}-y x +1\right )+\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
4.568 |
|
| \begin{align*}
y^{2}-3 y-x +\left (2 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.137 |
|
| \begin{align*}
x +3 y-5-\left (x -y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.214 |
|
| \begin{align*}
x -2 y+3+2 \left (x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.908 |
|
| \begin{align*}
2 x +y-4+\left (x -3 y+12\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.471 |
|
| \begin{align*}
a_{1} x +k y+c_{1} +\left (x k +b_{2} y+c_{2} \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
60.862 |
|
| \begin{align*}
\left (x +2 y+1\right ) y^{\prime }+7+x -4 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
16.873 |
|
| \begin{align*}
3 x +y-2+\left (3 x +y+4\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.538 |
|
| \begin{align*}
6 y x -3 y^{2}+2 y+2 \left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.810 |
|
| \begin{align*}
x +y-2-\left (x -4 y-2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.550 |
|
| \begin{align*}
2 x +4 y-1-\left (x +2 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.118 |
|
| \begin{align*}
\left (x -1\right ) y-\left (x^{2}-2 x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.112 |
|
| \begin{align*}
1+\left (x +y\right )^{2}+\left (1+x \left (x +y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
7.059 |
|
| \begin{align*}
2 x -3 y+1-\left (3 x +2 y-4\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.526 |
|
| \begin{align*}
4 x +3 y-7+\left (4 x +3 y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.970 |
|
| \begin{align*}
x +4 y+3-\left (2 x -y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.641 |
|
| \begin{align*}
3 x -3 y-2-\left (x -y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.948 |
|
| \begin{align*}
x -6 y+2+2 \left (x +2 y+2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
16.074 |
|
| \begin{align*}
x -y-1-2 \left (-2+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.392 |
|
| \begin{align*}
x -3 y+3+\left (3 x +y+9\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
14.225 |
|
| \begin{align*}
y^{\prime }&=\frac {t y}{1+y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.677 |
|
| \begin{align*}
y+1+\left (y-1\right ) \left (t^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.169 |
|
| \begin{align*}
y^{\prime }&=\frac {4 t -3 y}{t -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
11.048 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+2 t y}{t^{2}+t y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
14.526 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{2 t -2 y+1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.563 |
|
| \begin{align*}
y-t +\left (t +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.102 |
|
| \begin{align*}
3 y-5 t +2 y y^{\prime }-y^{\prime } t&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
20.600 |
|
| \begin{align*}
2 t y+2 t^{3}+\left (t^{2}-y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.046 |
|
| \begin{align*}
a t +b y-\left (c t +d y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
22.208 |
|
| \begin{align*}
y^{\prime }&=\frac {t -y}{y+t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.075 |
|
| \begin{align*}
y^{\prime }&=\frac {t -y}{y+t} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.279 |
|
| \begin{align*}
y^{\prime }&=\frac {t -y}{y+t} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.733 |
|
| \begin{align*}
y^{\prime }&=\frac {c t -a y}{A t +b y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
61.499 |
|
| \begin{align*}
y^{\prime }&=\frac {4 t -y}{t -6 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.290 |
|
| \begin{align*}
\left (-x +y\right ) y^{\prime }&=y-x +8 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.655 |
|
| \begin{align*}
2 y x +\left (x^{2}-y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.226 |
|
| \begin{align*}
\left (-x +y\right ) y^{\prime }&=x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.053 |
|
| \begin{align*}
\left (-2+2 y\right ) y^{\prime }&=2 x -1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✓ |
11.106 |
|
| \begin{align*}
\left (y x +1\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
37.675 |
|
| \begin{align*}
x^{2} \left (1-y\right ) y^{\prime }+\left (1-x \right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.163 |
|
| \begin{align*}
2 x y \left (4-y^{2}\right )+\left (-1+y\right ) \left (x^{2}+2\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
12.540 |
|
| \begin{align*}
y x -x +\left (y x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.964 |
|
| \begin{align*}
y^{2}+6 x^{2} y+\left (2 y x +2 x^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
17.711 |
|
| \begin{align*}
x \left (-y x +1\right ) y^{\prime }+\left (y x +1\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
43.327 |
|
| \begin{align*}
y^{\prime } x +2&=x^{3} \left (-1+y\right ) y^{\prime } \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
6.857 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y-1}{3-x +y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.101 |
|
| \begin{align*}
3 x +2 y+1-\left (3 x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.387 |
|
| \begin{align*}
2 x +3 y+\left (y+2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
20.691 |
|
| \begin{align*}
2 x +y-\left (4 x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.845 |
|
| \begin{align*}
3 x -2 y+4-\left (2 x +7 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.674 |
|
| \begin{align*}
y^{2}+\left (y x +x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
78.510 |
|
| \begin{align*}
3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
69.837 |
|
| \begin{align*}
y^{\prime } x +y&=y y^{\prime } x -y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.725 |
|
| \begin{align*}
x -2 y+1&=\left (x -2 y\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.673 |
|
| \begin{align*}
x -y+\left (y-x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.660 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y-2}{y-x -4} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.524 |
|
| \begin{align*}
2 x -1-\frac {y}{x^{2}}-\left (2 y-\frac {1}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
5.000 |
|
| \begin{align*}
y^{2}+\frac {y}{\cos \left (x \right )^{2}}+\left (2 y x +\tan \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
23.996 |
|
| \begin{align*}
\left (y x +1\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
42.775 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.017 |
|
| \begin{align*}
x +y-\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.921 |
|
| \begin{align*}
y^{\prime }&=\frac {1+y}{x -y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
20.332 |
|
| \begin{align*}
x y^{2}-y^{2}+x -1+\left (x^{2} y-2 y x +x^{2}+2 y-2 x +2\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.013 |
|
| \begin{align*}
4 x -3 y+\left (-3 x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
29.069 |
|
| \begin{align*}
2 x +2 y-1+\left (x +y-2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.025 |
|
| \begin{align*}
3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
73.375 |
|
| \begin{align*}
4 x y^{2}+\left (3 x^{2} y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
35.742 |
|
| \begin{align*}
\cos \left (x \right ) y+\left (2 y-\sin \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.345 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x^{2}}{1+x^{3}+y} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
4.060 |
|
| \begin{align*}
1-x^{2} y+x^{2} \left (-x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
6.015 |
|
| \begin{align*}
x +y y^{\prime }+x^{2} y^{\prime }-y x&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.266 |
|
| \begin{align*}
x -y+3+\left (3 x +y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
31.412 |
|
| \begin{align*}
\left (x -1\right ) \left (y^{2}-y+1\right )&=\left (1+y\right ) \left (x^{2}+x +1\right ) y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.388 |
|
| \begin{align*}
\cos \left (x \right ) y+\left (2 y-\sin \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.599 |
|
| \begin{align*}
\left (3 x +3 y+a^{2}\right ) y^{\prime }&=4 x +4 y+b^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.559 |
|
| \begin{align*}
2 y^{2}-9 y x +\left (3 y x -6 x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
28.154 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
23.931 |
|
| \begin{align*}
\left (x -2 y\right ) y^{\prime }&=2 x -y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
30.428 |
|
| \begin{align*}
y^{\prime }&=\frac {y-3}{x +y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
29.206 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x -y-9}{x +y+1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
33.928 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y+x +7}{-2 x +y-9} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
21.910 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x -5 y-9}{-4 x +y+9} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
74.826 |
|
| \begin{align*}
1+y^{\prime }&=2 \left (-x +y\right ) \left (y^{\prime }-1\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.035 |
|
| \begin{align*}
y^{\prime }&=\frac {-3 x +y}{x +3 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.618 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
22.742 |
|
| \begin{align*}
\left (x +2 y\right ) y^{\prime }&=1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.076 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
21.966 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=y y^{\prime } x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
33.108 |
|
| \begin{align*}
2 x -4 y+1+\left (-3+x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
42.763 |
|
| \begin{align*}
2 x +y+1-\left (4 x +2 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.882 |
|
| \begin{align*}
x -y-1+\left (y-x +2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.388 |
|
| \begin{align*}
\left (x +4 y\right ) y^{\prime }&=2 x +3 y-5 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
53.820 |
|
| \begin{align*}
y+2&=\left (2 x +y-4\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
37.319 |
|
| \begin{align*}
y+x \left (2 y x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
68.333 |
|
| \begin{align*}
2 y+\left (x^{2} y+1\right ) x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
37.594 |
|
| \begin{align*}
x&=\left (x^{2}-2 y+1\right ) y^{\prime } \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
5.165 |
|
| \begin{align*}
\frac {3 x^{2}+y^{2}}{y^{2}}-\frac {\left (2 x^{3}+5 y\right ) y^{\prime }}{y^{3}}&=0 \\
\end{align*} |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
12.095 |
|
| \begin{align*}
y^{2}-\left (y x +x^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
17.069 |
|
| \begin{align*}
y \left (x +y\right )+\left (y x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
10.000 |
|
| \begin{align*}
x^{2}+2 x +y&=\left (x -3 x^{2} y\right ) y^{\prime } \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
7.263 |
|
| \begin{align*}
y^{2}+\left (-y+{\mathrm e}^{x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.079 |
|
| \begin{align*}
x^{2} y \left (y^{\prime } x +y\right )&=y^{\prime } x +2 y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
38.474 |
|
| \begin{align*}
x^{2}-y^{2}+y+x \left (-1+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
13.332 |
|
| \begin{align*}
2 y^{2} x^{2}+y+\left (x^{3} y-x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
41.189 |
|
| \begin{align*}
y^{\prime }&=\frac {y+2}{x +y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
31.428 |
|
| \begin{align*}
y^{\prime }&=\frac {x +2 y-4}{x -y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
50.688 |
|
| \begin{align*}
x -\frac {y}{y^{\prime }}&=\frac {2}{y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
90.806 |
|
| \begin{align*}
\frac {1}{x}&=\left (\frac {1}{y}-2 x \right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
46.026 |
|
| \begin{align*}
\frac {y-y^{\prime } x}{x +y y^{\prime }}&=2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.766 |
|
| \begin{align*}
\left (y+\sin \left (x \right )\right ) y^{\prime }+\cos \left (x \right ) y-x^{2}&=0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
10.555 |
|
| \begin{align*}
\left (\cos \left (x \right )-x \sin \left (x \right )\right ) y+\left (\cos \left (x \right ) x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
13.055 |
|
| \begin{align*}
1-x^{2} y+x^{2} \left (-x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
8.422 |
|
| \begin{align*}
y y^{\prime }&=4 x +3 y-2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
36.697 |
|
| \begin{align*}
2 x +3 y-1+\left (4 x +6 y-5\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.928 |
|
| \begin{align*}
y y^{\prime }+y x&=x^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
64.536 |
|
| \begin{align*}
\left (2 x +y+5\right ) y^{\prime }&=3 x +6 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
259.418 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x^{2}}{1+x^{3}+y} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
5.473 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (1+y\right )^{2}}{x \left (1+y\right )-x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
13.092 |
|
| \begin{align*}
2 y^{\prime } x +1&=y+\frac {x^{2}}{-1+y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
28.036 |
|
| \begin{align*}
\left (x +y\right ) \left (-y x +1\right )+\left (x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
11.715 |
|