| # |
ODE |
CAS classification |
Solved |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
2.760 |
|
| \begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
40.462 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x -y} \\
y \left (2\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✗ |
✓ |
2.493 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x -y} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.111 |
|
| \begin{align*}
y y^{\prime }&=x -1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.489 |
|
| \begin{align*}
y y^{\prime }&=x -1 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.549 |
|
| \begin{align*}
y^{\prime }&=\ln \left (1+y^{2}\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.431 |
|
| \begin{align*}
y^{\prime }+1&=2 y \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.495 |
|
| \begin{align*}
y^{\prime }&=6 \,{\mathrm e}^{2 x -y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.409 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (a \right ) &= b \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.980 |
|
| \begin{align*}
{y^{\prime }}^{2}&=4 y \\
y \left (a \right ) &= b \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
1.072 |
|
| \begin{align*}
y^{\prime }+y&=2 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.954 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=x -y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.769 |
|
| \begin{align*}
2 x y y^{\prime }&=x^{2}+2 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.049 |
|
| \begin{align*}
x y^{\prime }&=y+2 \sqrt {y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.642 |
|
| \begin{align*}
\left (x -y\right ) y^{\prime }&=x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.465 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
9.817 |
|
| \begin{align*}
\left (x +2 y\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.563 |
|
| \begin{align*}
x y y^{\prime }&=x^{2}+3 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.489 |
|
| \begin{align*}
\left (x^{2}-y^{2}\right ) y^{\prime }&=2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.697 |
|
| \begin{align*}
x y^{\prime }&=y+\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.546 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
15.601 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x +y+1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.969 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.279 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
10.343 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
10.667 |
|
| \begin{align*}
y^{\prime }&=f \left (a x +b y+c \right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.241 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y-1}{x +y+3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.345 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
21.608 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.865 |
|
| \begin{align*}
y^{\prime }+2 y x&=1+x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
2.316 |
|
| \begin{align*}
x^{\prime }&=1-x^{2} \\
x \left (0\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
3.721 |
|
| \begin{align*}
x^{\prime }&=9-4 x^{2} \\
x \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
4.273 |
|
| \begin{align*}
x^{3} y^{\prime }&=x^{2} y-y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
53.204 |
|
| \begin{align*}
2 x^{2} y-x^{3} y^{\prime }&=y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
57.162 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x +y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.250 |
|
| \begin{align*}
y^{\prime }&=-\frac {3 x^{2}+2 y^{2}}{4 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.550 |
|
| \begin{align*}
y^{\prime }&=\frac {x +3 y}{y-3 x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.902 |
|
| \begin{align*}
y^{\prime }+y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.010 |
|
| \begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
2.299 |
|
| \begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
37.945 |
|
| \begin{align*}
y y^{\prime }&=x -1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.602 |
|
| \begin{align*}
y y^{\prime }&=x -1 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.486 |
|
| \begin{align*}
y^{\prime }&=\ln \left (1+y^{2}\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.450 |
|
| \begin{align*}
y^{\prime }+1&=2 y \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.036 |
|
| \begin{align*}
y^{\prime }&=6 \,{\mathrm e}^{2 x -y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.586 |
|
| \begin{align*}
y^{\prime }+y&=2 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.076 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=x -y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.250 |
|
| \begin{align*}
2 x y y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.484 |
|
| \begin{align*}
x y^{\prime }&=y+2 \sqrt {y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.164 |
|
| \begin{align*}
\left (x -y\right ) y^{\prime }&=x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.330 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
11.213 |
|
| \begin{align*}
\left (x +2 y\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.997 |
|
| \begin{align*}
x y y^{\prime }&=x^{2}+3 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.797 |
|
| \begin{align*}
\left (x^{2}-y^{2}\right ) y^{\prime }&=2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
14.133 |
|
| \begin{align*}
x y^{\prime }&=y+\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.413 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
15.720 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x +y+1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.079 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
11.412 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
11.993 |
|
| \begin{align*}
3 x^{2}+2 y^{2}+\left (4 y x +6 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
11.119 |
|
| \begin{align*}
x^{3} y^{\prime }&=x^{2} y-y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
56.396 |
|
| \begin{align*}
2 x^{2} y-x^{3} y^{\prime }&=y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
61.032 |
|
| \begin{align*}
y^{\prime }&=\frac {-3 x^{2}-2 y^{2}}{4 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.707 |
|
| \begin{align*}
y^{\prime }&=\frac {x +3 y}{y-3 x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.753 |
|
| \begin{align*}
y^{\prime }&=1+y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.020 |
|
| \begin{align*}
y^{\prime }&=\frac {1-2 x}{y} \\
y \left (1\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.247 |
|
| \begin{align*}
y^{\prime }&=\frac {b +a y}{d +c y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.951 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+3 y^{2}}{2 x y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.362 |
|
| \begin{align*}
y^{\prime }&=\frac {4 y-3 x}{2 x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.795 |
|
| \begin{align*}
y^{\prime }&=-\frac {4 x +3 y}{2 x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.329 |
|
| \begin{align*}
y^{\prime }&=\frac {x +3 y}{x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
10.436 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}-3 y^{2}}{2 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.683 |
|
| \begin{align*}
y^{\prime }&=\frac {3 y^{2}-x^{2}}{2 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
61.401 |
|
| \begin{align*}
y^{3}+y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.864 |
|
| \begin{align*}
y^{\prime }&=a y+b y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.996 |
|
| \begin{align*}
y^{\prime }&=-1+{\mathrm e}^{y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.703 |
|
| \begin{align*}
y^{\prime }&=-1+{\mathrm e}^{-y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.668 |
|
| \begin{align*}
y^{\prime }&=-\frac {2 \arctan \left (y\right )}{1+y^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.898 |
|
| \begin{align*}
y^{\prime }&=-k \left (-1+y\right )^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.262 |
|
| \begin{align*}
y^{\prime }&=-b \sqrt {y}+a y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.856 |
|
| \begin{align*}
3+2 x +\left (-2+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.824 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
18.016 |
|
| \begin{align*}
y^{\prime }&=\frac {-a x -b y}{b x +c y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.465 |
|
| \begin{align*}
y^{\prime }&=\frac {-a x +b y}{b x -c y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
10.022 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
12.365 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
16.818 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
12.725 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x +y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.029 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.434 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
16.555 |
|
| \begin{align*}
y^{\prime }&=2 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.162 |
|
| \begin{align*}
y^{\prime }&=a y^{\frac {a -1}{a}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.210 |
|
| \begin{align*}
y^{\prime }+a y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.049 |
|
| \begin{align*}
y^{\prime }+3 y&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.823 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +3 y}{x -4 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
21.569 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x +y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.158 |
|
| \begin{align*}
y^{\prime }&=y^{{2}/{5}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
2.977 |
|
| \begin{align*}
x y y^{\prime }&=x^{2}+2 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.547 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.168 |
|
| \begin{align*}
y^{\prime }&=\frac {x +2 y}{2 x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.868 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{y-2 x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.434 |
|
| \begin{align*}
x y y^{\prime }&=x^{2}-y x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
27.821 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
46.084 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y x +y^{2}}{y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
14.360 |
|
| \begin{align*}
y^{\prime }&=\frac {-6 x +y-3}{2 x -y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
23.878 |
|
| \begin{align*}
y^{\prime }&=\frac {-x +3 y-14}{x +y-2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
21.691 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
14.451 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
21.383 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
16.893 |
|
| \begin{align*}
x^{2}+y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.531 |
|
| \begin{align*}
y^{\prime }+y^{2}+k^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.765 |
|
| \begin{align*}
y^{\prime }+y^{2}+4 y x +4 x^{2}+2&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.225 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{3+t +y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.540 |
|
| \begin{align*}
t y^{\prime }&=y+\sqrt {t^{2}+y^{2}} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.012 |
|
| \begin{align*}
2 t y y^{\prime }&=3 y^{2}-t^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
60.100 |
|
| \begin{align*}
\left (t -\sqrt {y t}\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
18.984 |
|
| \begin{align*}
y^{\prime }&=\frac {t +y}{t -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.958 |
|
| \begin{align*}
{\mathrm e}^{\frac {t}{y}} \left (y-t \right ) y^{\prime }+y \left (1+{\mathrm e}^{\frac {t}{y}}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
15.480 |
|
| \begin{align*}
y^{\prime }&=\frac {t +y+1}{t -y+3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.842 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
30.349 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
7.477 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{\left (y-t \right )^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.238 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{3+t +y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.835 |
|
| \begin{align*}
t y^{\prime }&=y+\sqrt {t^{2}+y^{2}} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.045 |
|
| \begin{align*}
2 t y y^{\prime }&=3 y^{2}-t^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
62.696 |
|
| \begin{align*}
\left (t -\sqrt {y t}\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
22.451 |
|
| \begin{align*}
y^{\prime }&=\frac {t +y}{t -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.175 |
|
| \begin{align*}
{\mathrm e}^{\frac {t}{y}} \left (y-t \right ) y^{\prime }+y \left (1+{\mathrm e}^{\frac {t}{y}}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
15.905 |
|
| \begin{align*}
y^{\prime }&=\frac {t +y+1}{t -y+3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
22.276 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
33.849 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
7.917 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{\left (y-t \right )^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.450 |
|
| \begin{align*}
x^{\prime }&=x^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.142 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.231 |
|
| \begin{align*}
{\mathrm e}^{y} \left (y^{\prime }+1\right )&=1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.040 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+x&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.833 |
|
| \begin{align*}
x y^{\prime }-y&=\sqrt {y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
23.621 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x -y}{x +4 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
28.216 |
|
| \begin{align*}
x y^{\prime }-y&=\sqrt {x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
50.432 |
|
| \begin{align*}
x y^{\prime }-y+\sqrt {y^{2}-x^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
21.832 |
|
| \begin{align*}
x^{2}+y^{2}&=x y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.587 |
|
| \begin{align*}
\left (y x -x^{2}\right ) y^{\prime }-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
76.708 |
|
| \begin{align*}
x y^{\prime }+y&=2 \sqrt {y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
27.920 |
|
| \begin{align*}
x +y+\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
30.026 |
|
| \begin{align*}
y \left (x^{2}-y x +y^{2}\right )+x y^{\prime } \left (x^{2}+y x +y^{2}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
63.104 |
|
| \begin{align*}
x y^{\prime }-y-x \sin \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.714 |
|
| \begin{align*}
\left (\frac {x}{y}+\frac {y}{x}\right ) y^{\prime }+1&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
17.483 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x -k \sqrt {x^{2}+y^{2}}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
92.337 |
|
| \begin{align*}
x +y-\left (x -y+2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
28.958 |
|
| \begin{align*}
x +\left (x -2 y+2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
27.839 |
|
| \begin{align*}
2 x -y+1+\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
52.507 |
|
| \begin{align*}
x -y+2+\left (x +y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
30.137 |
|
| \begin{align*}
x -y+\left (y-x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.119 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y-1}{x -y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
30.608 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
16.269 |
|
| \begin{align*}
x -y+1+\left (x -y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.102 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
16.675 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
45.651 |
|
| \begin{align*}
3 x -y+1+\left (x -3 y-5\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
59.984 |
|
| \begin{align*}
3 x +2 y+3-\left (x +2 y-1\right ) y^{\prime }&=0 \\
y \left (-2\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
134.010 |
|
| \begin{align*}
x +y+\left (x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
36.081 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
31.681 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
99.769 |
|
| \begin{align*}
2 y x -\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
96.760 |
|
| \begin{align*}
\frac {x^{2}+3 y^{2}}{x \left (3 x^{2}+4 y^{2}\right )}+\frac {\left (2 x^{2}+y^{2}\right ) y^{\prime }}{y \left (3 x^{2}+4 y^{2}\right )}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
33.514 |
|
| \begin{align*}
\frac {x^{2}-y^{2}}{x \left (2 x^{2}+y^{2}\right )}+\frac {\left (x^{2}+2 y^{2}\right ) y^{\prime }}{y \left (2 x^{2}+y^{2}\right )}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
73.228 |
|
| \begin{align*}
y+\left (2 x -3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
28.053 |
|
| \begin{align*}
x y y^{\prime }&=x^{2}-y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
25.618 |
|
| \begin{align*}
y^{2}+\left (y x +x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
45.951 |
|
| \begin{align*}
2 x +y-\left (x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.779 |
|
| \begin{align*}
x -2 y+1+\left (-2+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.241 |
|
| \begin{align*}
x -3 y&=\left (3 y-x +2\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.342 |
|
| \begin{align*}
y+\left (3 x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.785 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
7.800 |
|
| \begin{align*}
x y^{\prime }-y-\sqrt {x^{2}+y^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.563 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
16.566 |
|
| \begin{align*}
1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.171 |
|
| \begin{align*}
y \sqrt {x^{2}+y^{2}}+y x&=x^{2} y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
21.096 |
|
| \begin{align*}
y^{\prime }-y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.888 |
|
| \begin{align*}
x \left (-1+{y^{\prime }}^{2}\right )&=2 y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.110 |
|
| \begin{align*}
\left (1-y^{2}\right ) {y^{\prime }}^{2}&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
11.325 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+2 y^{2}&=x^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.028 |
|
| \begin{align*}
y&=y^{\prime } x \left (y^{\prime }+1\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.254 |
|
| \begin{align*}
y&=x +3 \ln \left (y^{\prime }\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.897 |
|
| \begin{align*}
y {y^{\prime }}^{2}-2 x y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.799 |
|
| \begin{align*}
{y^{\prime }}^{2}+y^{2}&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.898 |
|
| \begin{align*}
x \left (-1+{y^{\prime }}^{2}\right )&=2 y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.188 |
|
| \begin{align*}
4 x -2 y y^{\prime }+{y^{\prime }}^{2} x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.739 |
|
| \begin{align*}
y {y^{\prime }}^{2}&=3 x y^{\prime }+y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
27.290 |
|
| \begin{align*}
8 x +1&=y {y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
42.984 |
|
| \begin{align*}
y {y^{\prime }}^{2}+2 y^{\prime }+1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
4.214 |
|
| \begin{align*}
\left (1+{y^{\prime }}^{2}\right ) x&=\left (x +y\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.868 |
|
| \begin{align*}
2 x y^{\prime }+y&={y^{\prime }}^{2} x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.171 |
|
| \begin{align*}
x&=y-{y^{\prime }}^{3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.951 |
|
| \begin{align*}
x +2 y y^{\prime }&={y^{\prime }}^{2} x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.103 |
|
| \begin{align*}
4 x -2 y y^{\prime }+{y^{\prime }}^{2} x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.336 |
|
| \begin{align*}
x {y^{\prime }}^{3}&=y y^{\prime }+1 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
104.724 |
|
| \begin{align*}
y \left (1+{y^{\prime }}^{2}\right )&=2 x y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.850 |
|
| \begin{align*}
2 x +{y^{\prime }}^{2} x&=2 y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.586 |
|
| \begin{align*}
x&=y y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.918 |
|
| \begin{align*}
4 {y^{\prime }}^{2} x +2 x y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.719 |
|
| \begin{align*}
y&=y^{\prime } x \left (y^{\prime }+1\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.455 |
|
| \begin{align*}
2 x {y^{\prime }}^{3}+1&=y {y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
7.263 |
|
| \begin{align*}
3 {y^{\prime }}^{4} x&=y {y^{\prime }}^{3}+1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
4.083 |
|
| \begin{align*}
2 {y^{\prime }}^{5}+2 x y^{\prime }&=y \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.585 |
|
| \begin{align*}
y^{\prime }&=2 y-4 \\
y \left (0\right ) &= 5 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.474 |
|
| \begin{align*}
y^{\prime }&=-y^{3} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
8.155 |
|
| \begin{align*}
y^{\prime }&=-1+y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.706 |
|
| \begin{align*}
y^{\prime }&=1-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| \begin{align*}
y^{\prime }&=y^{3}-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
9.735 |
|
| \begin{align*}
y^{\prime }&=1-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.560 |
|
| \begin{align*}
y^{\prime }&=-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.112 |
|
| \begin{align*}
y^{\prime }&=y \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.222 |
|
| \begin{align*}
y^{\prime }&=2 y \\
y \left (\ln \left (3\right )\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.678 |
|
| \begin{align*}
\left (-x +y\right ) y^{\prime }+2 x +3 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.445 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x +2 y+1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.693 |
|
| \begin{align*}
y^{\prime }&=-\frac {x +y}{3 x +3 y-4} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.353 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
28.006 |
|
| \begin{align*}
{\mathrm e}^{x +y} y^{\prime }-1&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.357 |
|
| \begin{align*}
\left (3 x -y\right ) y^{\prime }&=3 y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.626 |
|
| \begin{align*}
x y^{\prime }&=\sqrt {16 x^{2}-y^{2}}+y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
29.000 |
|
| \begin{align*}
x y^{\prime }-y&=\sqrt {9 x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.997 |
|
| \begin{align*}
x \left (x^{2}-y^{2}\right )-x \left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
9.711 |
|
| \begin{align*}
x y^{\prime }+y \ln \left (x \right )&=\ln \left (y\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.879 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
14.490 |
|
| \begin{align*}
x y^{\prime }&=x \tan \left (\frac {y}{x}\right )+y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.890 |
|
| \begin{align*}
y^{\prime }&=-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.285 |
|
| \begin{align*}
{\mathrm e}^{x +y} y^{\prime }-1&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.372 |
|
| \begin{align*}
y^{\prime }&=\frac {2 \sqrt {-1+y}}{3} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.411 |
|
| \begin{align*}
m v^{\prime }&=m g -k v^{2} \\
v \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
4.395 |
|
| \begin{align*}
\left (3 x -y\right ) y^{\prime }&=3 y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.703 |
|
| \begin{align*}
x y^{\prime }&=\sqrt {16 x^{2}-y^{2}}+y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
30.557 |
|
| \begin{align*}
x y^{\prime }-y&=\sqrt {9 x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.388 |
|
| \begin{align*}
x y^{\prime }+y \ln \left (x \right )&=\ln \left (y\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.302 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
13.434 |
|
| \begin{align*}
x y^{\prime }&=x \tan \left (\frac {y}{x}\right )+y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.047 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
19.844 |
|
| \begin{align*}
x y^{\prime }-y&=\sqrt {4 x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
38.632 |
|
| \begin{align*}
y^{\prime }&=\frac {x +a y}{a x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
20.522 |
|
| \begin{align*}
y^{\prime }&=\left (4 x +y+2\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
8.557 |
|
| \begin{align*}
y^{\prime }&=\sin \left (3 x -3 y+1\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.730 |
|
| \begin{align*}
y^{\prime }&=\frac {x +2 y-1}{2 x -y+3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
20.117 |
|
| \begin{align*}
\frac {y^{\prime }}{y}-\frac {2 \ln \left (y\right )}{x}&=\frac {1-2 \ln \left (x \right )}{x} \\
y \left (1\right ) &= {\mathrm e} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.300 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
15.175 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
12.212 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
20.860 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
17.695 |
|
| \begin{align*}
y&=y^{\prime }+\frac {{y^{\prime }}^{2}}{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.571 |
|
| \begin{align*}
-x +y&={y^{\prime }}^{2} \left (1-\frac {2 y^{\prime }}{3}\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.177 |
|
| \begin{align*}
y^{\prime }+y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.526 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x -2 y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.306 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x -y+1}{-x +3 y+5} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
45.636 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x -y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.295 |
|
| \begin{align*}
\left (x +y-1\right ) y^{\prime }&=x -y+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.694 |
|
| \begin{align*}
x y y^{\prime }&=2 x^{2}-y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.926 |
|
| \begin{align*}
x^{2}-y^{2}+x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.314 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x -y+1\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.147 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+4}{x -y-6} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
23.691 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+4}{x +y-6} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.762 |
|
| \begin{align*}
\left (3 x^{2}-y^{2}\right ) y^{\prime }-2 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
15.815 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=-x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.873 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
25.625 |
|
| \begin{align*}
x y^{\prime }&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
29.806 |
|
| \begin{align*}
\left (y x -x^{2}\right ) y^{\prime }&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
28.250 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
14.415 |
|
| \begin{align*}
y^{\prime } \ln \left (x -y\right )&=1+\ln \left (x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.550 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
28.266 |
|
| \begin{align*}
x +y+\left (x -y\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.306 |
|
| \begin{align*}
x \cos \left (\frac {y}{x}\right )^{2}-y+x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
10.148 |
|
| \begin{align*}
x y^{\prime }&=y \left (1+\ln \left (y\right )-\ln \left (x \right )\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
17.197 |
|
| \begin{align*}
y x +\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
16.812 |
|
| \begin{align*}
\left (1-{\mathrm e}^{-\frac {y}{x}}\right ) y^{\prime }+1-\frac {y}{x}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
30.165 |
|
| \begin{align*}
x^{2}-y x +y^{2}-x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
38.327 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
15.072 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +y-1}{x -y-2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
40.511 |
|
| \begin{align*}
y+2&=\left (2 x +y-4\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
31.347 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x -y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
6.302 |
|
| \begin{align*}
y^{\prime }&=\left (x +1\right )^{2}+\left (4 y+1\right )^{2}+8 y x +1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
25.869 |
|
| \begin{align*}
2 y x +\left (x^{2}+2 y x +y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
38.996 |
|
| \begin{align*}
x -\sqrt {x^{2}+y^{2}}+\left (y-\sqrt {x^{2}+y^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
71.989 |
|
| \begin{align*}
x y^{\prime } \left (y^{\prime }+2\right )&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.801 |
|
| \begin{align*}
x y^{\prime }+y&=4 \sqrt {y^{\prime }} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
36.950 |
|
| \begin{align*}
2 \sqrt {y x}-y-x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
24.336 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{\frac {x y^{\prime }}{y}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
16.973 |
|
| \begin{align*}
x y^{\prime }-y&=x \tan \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
14.982 |
|
| \begin{align*}
4 x -2 y y^{\prime }+{y^{\prime }}^{2} x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.669 |
|
| \begin{align*}
x y^{\prime }&=y+\sqrt {x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
43.130 |
|
| \begin{align*}
\left (y^{\prime }+1\right ) \ln \left (\frac {x +y}{x +3}\right )&=\frac {x +y}{x +3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
21.946 |
|
| \begin{align*}
2 {y^{\prime }}^{3}-3 {y^{\prime }}^{2}+x&=y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
1.307 |
|
| \begin{align*}
y^{\prime }&=3 y-3 x +3+\left (x -y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.749 |
|
| \begin{align*}
y^{\prime }&=\left (3+x -4 y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
14.872 |
|
| \begin{align*}
y^{\prime }&=\left (1+4 x +9 y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
23.953 |
|
| \begin{align*}
y^{\prime }&=a +b y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.769 |
|
| \begin{align*}
y^{\prime }&=a_{0} +a_{1} y+a_{2} y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.692 |
|
| \begin{align*}
y^{\prime }&=y \left (a +b y^{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
17.643 |
|
| \begin{align*}
y^{\prime }&=a_{0} +a_{1} y+a_{2} y^{2}+a_{3} y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
35.437 |
|
| \begin{align*}
y^{\prime }&=\sqrt {a +b y^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.970 |
|
| \begin{align*}
y^{\prime }&=y \sqrt {a +b y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
39.566 |
|
| \begin{align*}
y^{\prime }&=a +b \cos \left (A x +B y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.319 |
|
| \begin{align*}
y^{\prime }&=a +b \cos \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
6.410 |
|
| \begin{align*}
y^{\prime }&=a +b \sin \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
6.777 |
|
| \begin{align*}
y^{\prime }&=a +b \sin \left (A x +B y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.717 |
|
| \begin{align*}
y^{\prime }&=\sqrt {a +b \cos \left (y\right )} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
12.120 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x +y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.028 |
|
| \begin{align*}
y^{\prime }&=a f \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.188 |
|
| \begin{align*}
y^{\prime }&=f \left (a +b x +c y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.177 |
|
| \begin{align*}
3 y^{\prime }&=x -\sqrt {x^{2}-3 y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
97.709 |
|
| \begin{align*}
x y^{\prime }&=y+\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
15.394 |
|
| \begin{align*}
x y^{\prime }&=y+\sqrt {x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
44.266 |
|
| \begin{align*}
x y^{\prime }&=y+a \sqrt {y^{2}+b^{2} x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
51.185 |
|
| \begin{align*}
x y^{\prime }&=y+a \sqrt {y^{2}-b^{2} x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
51.256 |
|
| \begin{align*}
x y^{\prime }+x -y+x \cos \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.612 |
|
| \begin{align*}
x y^{\prime }&=-x \cos \left (\frac {y}{x}\right )^{2}+y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
9.565 |
|
| \begin{align*}
x y^{\prime }&=y+x \sin \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.758 |
|
| \begin{align*}
x y^{\prime }&=y-x \tan \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.857 |
|
| \begin{align*}
x y^{\prime }&=x +y+{\mathrm e}^{\frac {y}{x}} x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
13.059 |
|
| \begin{align*}
x y^{\prime }&=\left (1+\ln \left (x \right )-\ln \left (y\right )\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
14.752 |
|
| \begin{align*}
x^{2} y^{\prime }&=\left (x +a y\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.296 |
|
| \begin{align*}
x^{2} y^{\prime }&=\left (a x +b y\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
51.834 |
|
| \begin{align*}
x^{2} y^{\prime }+a \,x^{2}+b x y+c y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
28.460 |
|
| \begin{align*}
\left (x -a \right )^{2} y^{\prime }+k \left (x +y-a \right )^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
27.814 |
|
| \begin{align*}
a \,x^{2} y^{\prime }&=x^{2}+a x y+b^{2} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
40.164 |
|
| \begin{align*}
x^{3} y^{\prime }&=\left (2 x^{2}+y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
76.477 |
|
| \begin{align*}
2 x^{3} y^{\prime }&=y \left (x^{2}-y^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
56.664 |
|
| \begin{align*}
2 x^{3} y^{\prime }&=\left (3 x^{2}+a y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
30.688 |
|
| \begin{align*}
\left (y+1\right ) y^{\prime }&=x +y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
45.542 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
29.144 |
|
| \begin{align*}
\left (x -y\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.658 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.753 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=x -y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
28.849 |
|
| \begin{align*}
\left (x -y\right ) y^{\prime }&=\left ({\mathrm e}^{-\frac {x}{y}}+1\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
21.594 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
38.924 |
|
| \begin{align*}
\left (x +y+2\right ) y^{\prime }&=-x -y+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.558 |
|
| \begin{align*}
\left (3-x -y\right ) y^{\prime }&=1+x -3 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
35.369 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
35.657 |
|
| \begin{align*}
\left (2 x +y\right ) y^{\prime }+x -2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.826 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
13.302 |
|
| \begin{align*}
\left (2 x -y+3\right ) y^{\prime }+2&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.920 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
23.540 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
176.494 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
26.398 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
108.333 |
|
| \begin{align*}
\left (6-4 x -y\right ) y^{\prime }&=2 x -y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
39.344 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
24.890 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
16.557 |
|
| \begin{align*}
\left (x -2 y\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
24.723 |
|
| \begin{align*}
\left (x +2 y\right ) y^{\prime }+2 x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
20.416 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
29.954 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
25.073 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
13.781 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
41.601 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
25.133 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
13.451 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
14.340 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
86.715 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
67.437 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
14.172 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
13.309 |
|
| \begin{align*}
\left (-3 y-2 x +5\right ) y^{\prime }+1-2 x -3 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.943 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
13.504 |
|
| \begin{align*}
\left (x +4 y\right ) y^{\prime }+4 x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.485 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
14.498 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
11.281 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
25.143 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
36.280 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
68.718 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
198.494 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
24.580 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
89.759 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
14.990 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
90.015 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
40.445 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
26.431 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
46.876 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
47.658 |
|
| \begin{align*}
\left (a x +b y\right ) y^{\prime }+x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
68.843 |
|
| \begin{align*}
\left (a x +b y\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
45.737 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
48.021 |
|
| \begin{align*}
\left (a x +b y\right ) y^{\prime }&=b x +a y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
26.991 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
97.866 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
96.440 |
|
| \begin{align*}
x y y^{\prime }+x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.833 |
|
| \begin{align*}
x y y^{\prime }&=x^{2}-y x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
39.667 |
|
| \begin{align*}
x y y^{\prime }+2 x^{2}-2 y x -y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
22.504 |
|
| \begin{align*}
x \left (y+2\right ) y^{\prime }+a x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.069 |
|
| \begin{align*}
x \left (x +y\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
125.414 |
|
| \begin{align*}
x \left (x -y\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
80.546 |
|
| \begin{align*}
x \left (x +y\right ) y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
28.326 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
38.129 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
42.600 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
123.256 |
|
| \begin{align*}
x^{2}+y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.964 |
|
| \begin{align*}
2 x y y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
27.068 |
|
| \begin{align*}
x \left (x -2 y\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
57.220 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
43.512 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
45.112 |
|
| \begin{align*}
x \left (2 x +3 y\right ) y^{\prime }&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
70.752 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
38.523 |
|
| \begin{align*}
a x y y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
31.247 |
|
| \begin{align*}
a x y y^{\prime }+x^{2}-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
28.010 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
37.050 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
87.370 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
30.842 |
|
| \begin{align*}
y x +\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
22.639 |
|
| \begin{align*}
\left (x^{2}-y^{2}\right ) y^{\prime }&=2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
32.967 |
|
| \begin{align*}
\left (3 x^{2}-y^{2}\right ) y^{\prime }&=2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
25.152 |
|
| \begin{align*}
\left (x +y\right )^{2} y^{\prime }&=a^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
27.965 |
|
| \begin{align*}
\left (x -y\right )^{2} y^{\prime }&=a^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.620 |
|
| \begin{align*}
\left (x^{2}+2 y x -y^{2}\right ) y^{\prime }+x^{2}-2 y x +y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
26.311 |
|
| \begin{align*}
\left (x +y\right )^{2} y^{\prime }&=\left (x +y+2\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
59.697 |
|
| \begin{align*}
\left (x +y\right )^{2} y^{\prime }&=x^{2}-2 y x +5 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
28.484 |
|
| \begin{align*}
\left (3 x +y\right )^{2} y^{\prime }&=4 \left (3 x +2 y\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
50.755 |
|
| \begin{align*}
\left (2 x^{2}+3 y^{2}\right ) y^{\prime }+x \left (3 x +y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
23.954 |
|
| \begin{align*}
\left (x^{2}+y x +a y^{2}\right ) y^{\prime }&=a \,x^{2}+y x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
108.831 |
|
| \begin{align*}
\left (a \,x^{2}+2 y x -a y^{2}\right ) y^{\prime }+x^{2}-2 a x y-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
89.385 |
|
| \begin{align*}
x \left (2 x^{2}+y^{2}\right ) y^{\prime }&=\left (2 x^{2}+3 y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
28.632 |
|
| \begin{align*}
x \left (x^{2}-y x +y^{2}\right ) y^{\prime }+\left (x^{2}+y x +y^{2}\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
67.832 |
|
| \begin{align*}
x \left (x^{2}-y x -y^{2}\right ) y^{\prime }&=\left (x^{2}+y x -y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
33.581 |
|
| \begin{align*}
x \left (x^{2}-2 y^{2}\right ) y^{\prime }&=\left (2 x^{2}-y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
36.772 |
|
| \begin{align*}
x \left (x^{2}+2 y^{2}\right ) y^{\prime }&=\left (2 x^{2}+3 y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
37.041 |
|
| \begin{align*}
2 x \left (5 x^{2}+y^{2}\right ) y^{\prime }&=x^{2} y-y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
34.059 |
|
| \begin{align*}
x \left (x^{2}+a x y+2 y^{2}\right ) y^{\prime }&=\left (a x +2 y\right ) y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
25.797 |
|
| \begin{align*}
x \left (x^{2}-6 y^{2}\right ) y^{\prime }&=4 \left (x^{2}+3 y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
42.397 |
|
| \begin{align*}
\left (3 x^{2}+y^{2}\right ) y y^{\prime }+x \left (x^{2}+3 y^{2}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
49.789 |
|
| \begin{align*}
\left (3 x^{2}+2 y^{2}\right ) y y^{\prime }+x^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
47.866 |
|
| \begin{align*}
\left (1+a \left (x +y\right )\right )^{n} y^{\prime }+a \left (x +y\right )^{n}&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.866 |
|
| \begin{align*}
\left (1+\sqrt {x +y}\right ) y^{\prime }+1&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.042 |
|
| \begin{align*}
y^{\prime } \sqrt {y x}+x -y&=\sqrt {y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
56.276 |
|
| \begin{align*}
\left (x -2 \sqrt {y x}\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
44.964 |
|
| \begin{align*}
{y^{\prime }}^{2}&=y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.694 |
|
| \begin{align*}
{y^{\prime }}^{2}&=x -y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.310 |
|
| \begin{align*}
{y^{\prime }}^{2}&=1+y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.731 |
|
| \begin{align*}
{y^{\prime }}^{2}&=1-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.406 |
|
| \begin{align*}
{y^{\prime }}^{2}&=a^{2}-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.477 |
|
| \begin{align*}
{y^{\prime }}^{2}&=a +b y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.293 |
|
| \begin{align*}
{y^{\prime }}^{2}&=\left (-1+y\right ) y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
11.982 |
|
| \begin{align*}
{y^{\prime }}^{2}&=a^{2} y^{n} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
48.301 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 y^{\prime }+a \left (x -y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.191 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 y^{\prime }-y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
56.625 |
|
| \begin{align*}
{y^{\prime }}^{2}+a y^{\prime }+b y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.258 |
|
| \begin{align*}
{y^{\prime }}^{2}-x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
4.859 |
|
| \begin{align*}
{y^{\prime }}^{2}+x y^{\prime }+x -y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.628 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.163 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.902 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 \left (1-x \right ) y^{\prime }-2 x +2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.589 |
|
| \begin{align*}
{y^{\prime }}^{2}+3 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.105 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 y y^{\prime }-2 x&=0 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
23.588 |
|
| \begin{align*}
{y^{\prime }}^{2}-\left (4 y+1\right ) y^{\prime }+\left (4 y+1\right ) y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
12.963 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 \left (1-3 y\right ) y^{\prime }-\left (4-9 y\right ) y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
194.513 |
|
| \begin{align*}
{y^{\prime }}^{2}+\left (a +6 y\right ) y^{\prime }+y \left (3 a +b +9 y\right )&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
32.575 |
|
| \begin{align*}
{y^{\prime }}^{2}+a y y^{\prime }-a x&=0 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
9.775 |
|
| \begin{align*}
{y^{\prime }}^{2}-a y y^{\prime }-a x&=0 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
23.668 |
|
| \begin{align*}
{y^{\prime }}^{2}-\left (4+y^{2}\right ) y^{\prime }+4+y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.551 |
|
| \begin{align*}
{y^{\prime }}^{2}&={\mathrm e}^{4 x -2 y} \left (y^{\prime }-1\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
6.946 |
|
| \begin{align*}
2 {y^{\prime }}^{2}+x y^{\prime }-2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.231 |
|
| \begin{align*}
2 {y^{\prime }}^{2}+2 \left (6 y-1\right ) y^{\prime }+3 y \left (6 y-1\right )&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
19.569 |
|
| \begin{align*}
3 {y^{\prime }}^{2}-2 x y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.159 |
|
| \begin{align*}
4 {y^{\prime }}^{2}+2 \,{\mathrm e}^{2 x -2 y} y^{\prime }-{\mathrm e}^{2 x -2 y}&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.409 |
|
| \begin{align*}
5 {y^{\prime }}^{2}+3 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.076 |
|
| \begin{align*}
5 {y^{\prime }}^{2}+6 x y^{\prime }-2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.139 |
|
| \begin{align*}
{y^{\prime }}^{2} x&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.909 |
|
| \begin{align*}
{y^{\prime }}^{2} x +x -2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.494 |
|
| \begin{align*}
{y^{\prime }}^{2} x +y^{\prime }&=y \\
\end{align*} |
[_rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
4.824 |
|
| \begin{align*}
{y^{\prime }}^{2} x +2 y^{\prime }-y&=0 \\
\end{align*} |
[_rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
4.977 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y^{\prime }-y&=0 \\
\end{align*} |
[_rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.017 |
|
| \begin{align*}
{y^{\prime }}^{2} x +4 y^{\prime }-2 y&=0 \\
\end{align*} |
[_rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.323 |
|
| \begin{align*}
{y^{\prime }}^{2} x +x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.888 |
|
| \begin{align*}
{y^{\prime }}^{2} x -y y^{\prime }+a x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.494 |
|
| \begin{align*}
{y^{\prime }}^{2} x -y y^{\prime }+a y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
13.836 |
|
| \begin{align*}
{y^{\prime }}^{2} x -\left (3 x -y\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
23.473 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }+a&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
9.837 |
|
| \begin{align*}
{y^{\prime }}^{2} x +2 y y^{\prime }-x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
115.454 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }+a x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
✓ |
5.905 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }+x +2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.281 |
|
| \begin{align*}
{y^{\prime }}^{2} x -a y y^{\prime }+b&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
58.826 |
|
| \begin{align*}
{y^{\prime }}^{2} x +a y y^{\prime }+b x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
31.047 |
|
| \begin{align*}
\left (x +1\right ) {y^{\prime }}^{2}&=y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.433 |
|
| \begin{align*}
2 {y^{\prime }}^{2} x +\left (2 x -y\right ) y^{\prime }+1-y&=0 \\
\end{align*} |
[_rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
9.694 |
|
| \begin{align*}
3 {y^{\prime }}^{2} x -6 y y^{\prime }+x +2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.881 |
|
| \begin{align*}
\left (5+3 x \right ) {y^{\prime }}^{2}-\left (3+3 y\right ) y^{\prime }+y&=0 \\
\end{align*} |
[_rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.448 |
|
| \begin{align*}
4 {y^{\prime }}^{2} x +2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.506 |
|
| \begin{align*}
4 {y^{\prime }}^{2} x -3 y y^{\prime }+3&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
47.369 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}-x \left (x -2 y\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.671 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}+\left (2 x +y\right ) y y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
66.009 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}+\left (2 x -y\right ) y y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
70.832 |
|
| \begin{align*}
a \,x^{2} {y^{\prime }}^{2}-2 a x y y^{\prime }+a \left (1-a \right ) x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
✓ |
22.135 |
|
| \begin{align*}
\left (-a^{2}+1\right ) x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-a^{2} x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
62.861 |
|
| \begin{align*}
y {y^{\prime }}^{2}&=a^{2} x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
15.418 |
|
| \begin{align*}
y {y^{\prime }}^{2}+2 a x y^{\prime }-a y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.316 |
|
| \begin{align*}
y {y^{\prime }}^{2}-4 a^{2} x y^{\prime }+a^{2} y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
25.589 |
|
| \begin{align*}
y {y^{\prime }}^{2}+a x y^{\prime }+b y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.172 |
|
| \begin{align*}
y {y^{\prime }}^{2}-\left (-2 b x +a \right ) y^{\prime }-b y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
10.619 |
|
| \begin{align*}
y {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
28.529 |
|
| \begin{align*}
\left (x +y\right ) {y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.652 |
|
| \begin{align*}
\left (2 x -y\right ) {y^{\prime }}^{2}-2 \left (1-x \right ) y^{\prime }+2-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.314 |
|
| \begin{align*}
2 y {y^{\prime }}^{2}+\left (5-4 x \right ) y^{\prime }+2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.227 |
|
| \begin{align*}
\left (1-a y\right ) {y^{\prime }}^{2}&=a y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.937 |
|
| \begin{align*}
x \left (x -2 y\right ) {y^{\prime }}^{2}-2 x y y^{\prime }-2 y x +y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
113.907 |
|
| \begin{align*}
x \left (x -2 y\right ) {y^{\prime }}^{2}+6 x y y^{\prime }-2 y x +y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
113.648 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2}+2 y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
8.401 |
|
| \begin{align*}
\left (1-y^{2}\right ) {y^{\prime }}^{2}&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
25.211 |
|
| \begin{align*}
\left (a^{2}-y^{2}\right ) {y^{\prime }}^{2}&=y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.334 |
|
| \begin{align*}
\left (a^{2} x^{2}-y^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+x^{2} \left (a^{2}-1\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
14.899 |
|
| \begin{align*}
\left (\left (-4 a^{2}+1\right ) x^{2}+y^{2}\right ) {y^{\prime }}^{2}-8 a^{2} x y y^{\prime }+x^{2}+\left (-4 a^{2}+1\right ) y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
62.863 |
|
| \begin{align*}
\left (x^{2} \left (-a^{2}+1\right )+y^{2}\right ) {y^{\prime }}^{2}+2 a^{2} x y y^{\prime }+x^{2}+\left (-a^{2}+1\right ) y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
15.934 |
|
| \begin{align*}
\left (a^{2}-\left (x -y\right )^{2}\right ) {y^{\prime }}^{2}+2 a^{2} y^{\prime }+a^{2}-\left (x -y\right )^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.021 |
|
| \begin{align*}
3 y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2}+4 y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.691 |
|
| \begin{align*}
\left (-a^{2}+1\right ) y^{2} {y^{\prime }}^{2}-3 a^{2} x y y^{\prime }-a^{2} x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
14.963 |
|
| \begin{align*}
a^{2} \left (b^{2}-\left (c x -a y\right )^{2}\right ) {y^{\prime }}^{2}+2 a \,b^{2} c y^{\prime }+c^{2} \left (b^{2}-\left (c x -a y\right )^{2}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
16.180 |
|
| \begin{align*}
{y^{\prime }}^{3}+x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.332 |
|
| \begin{align*}
{y^{\prime }}^{3}&=\left (y-a \right )^{2} \left (y-b \right )^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
8.092 |
|
| \begin{align*}
{y^{\prime }}^{3}+y^{\prime }-y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
107.199 |
|
| \begin{align*}
{y^{\prime }}^{3}+y^{\prime }&={\mathrm e}^{y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
13.579 |
|
| \begin{align*}
{y^{\prime }}^{3}-x y^{\prime }+a y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
57.645 |
|
| \begin{align*}
{y^{\prime }}^{3}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
3.364 |
|
| \begin{align*}
{y^{\prime }}^{3}-2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
104.464 |
|
| \begin{align*}
{y^{\prime }}^{3}-2 y y^{\prime }+y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
50.796 |
|
| \begin{align*}
{y^{\prime }}^{3}+{\mathrm e}^{3 x -2 y} \left (y^{\prime }-1\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
12.476 |
|
| \begin{align*}
{y^{\prime }}^{3}+{y^{\prime }}^{2}-y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.763 |
|
| \begin{align*}
{y^{\prime }}^{3}-{y^{\prime }}^{2}+y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.835 |
|
| \begin{align*}
{y^{\prime }}^{3}-a {y^{\prime }}^{2}+b y+a b x&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
29.398 |
|
| \begin{align*}
{y^{\prime }}^{3}+a_{0} {y^{\prime }}^{2}+a_{1} y^{\prime }+a_{2} +a_{3} y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
4.816 |
|
| \begin{align*}
{y^{\prime }}^{3}-y {y^{\prime }}^{2}+y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
98.105 |
|
| \begin{align*}
2 {y^{\prime }}^{3}+x y^{\prime }-2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
12.322 |
|
| \begin{align*}
2 {y^{\prime }}^{3}+{y^{\prime }}^{2}-y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
1.733 |
|
| \begin{align*}
8 {y^{\prime }}^{3}+12 {y^{\prime }}^{2}&=27 x +27 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
2.033 |
|
| \begin{align*}
2 x {y^{\prime }}^{3}-3 y {y^{\prime }}^{2}-x&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.251 |
|
| \begin{align*}
4 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}-x +3 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.503 |
|
| \begin{align*}
8 x {y^{\prime }}^{3}-12 y {y^{\prime }}^{2}+9 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.451 |
|
| \begin{align*}
y {y^{\prime }}^{3}-3 x y^{\prime }+3 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.464 |
|
| \begin{align*}
2 y {y^{\prime }}^{3}-3 x y^{\prime }+2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
30.641 |
|
| \begin{align*}
{y^{\prime }}^{4}&=\left (y-a \right )^{3} \left (y-b \right )^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.667 |
|
| \begin{align*}
{y^{\prime }}^{4}+x y^{\prime }-3 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
8.027 |
|
| \begin{align*}
{y^{\prime }}^{4}+4 y {y^{\prime }}^{3}+6 y^{2} {y^{\prime }}^{2}-\left (1-4 y^{3}\right ) y^{\prime }-\left (3-y^{3}\right ) y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✗ |
✓ |
✓ |
112.394 |
|
| \begin{align*}
2 {y^{\prime }}^{4}-y y^{\prime }-2&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
101.128 |
|
| \begin{align*}
3 {y^{\prime }}^{5}-y y^{\prime }+1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
1.150 |
|
| \begin{align*}
{y^{\prime }}^{6}&=\left (y-a \right )^{4} \left (y-b \right )^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.135 |
|
| \begin{align*}
\left (x -y\right ) \sqrt {y^{\prime }}&=a \left (y^{\prime }+1\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.586 |
|
| \begin{align*}
\sqrt {1+{y^{\prime }}^{2}}+a y^{\prime }&=y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
33.154 |
|
| \begin{align*}
a x \sqrt {1+{y^{\prime }}^{2}}+x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
44.994 |
|
| \begin{align*}
y^{\prime } \sin \left (y^{\prime }\right )+\cos \left (y^{\prime }\right )&=y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
69.026 |
|
| \begin{align*}
{y^{\prime }}^{2} \left (x +\sin \left (y^{\prime }\right )\right )&=y \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.741 |
|
| \begin{align*}
{\mathrm e}^{y^{\prime }-y}-{y^{\prime }}^{2}+1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
12.908 |
|
| \begin{align*}
a \left (\ln \left (y^{\prime }\right )-y^{\prime }\right )-x +y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
16.049 |
|
| \begin{align*}
y^{\prime }&=\frac {-3+x +y}{x -y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
67.729 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
36.369 |
|
| \begin{align*}
\frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
48.891 |
|
| \begin{align*}
y&={y^{\prime }}^{2} x +{y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.205 |
|
| \begin{align*}
\left (-x +y\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
45.234 |
|
| \begin{align*}
\left (2 \sqrt {y x}-x \right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
93.951 |
|
| \begin{align*}
x y^{\prime }-y-\sqrt {x^{2}+y^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
58.004 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
52.338 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
72.880 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
143.994 |
|
| \begin{align*}
x y^{\prime }-y&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
58.749 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
52.658 |
|
| \begin{align*}
x^{2}+2 y x -y^{2}+\left (y^{2}+2 y x -x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
65.674 |
|
| \begin{align*}
y^{2}+\left (y x +x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
176.794 |
|
| \begin{align*}
{y^{\prime }}^{2}+\frac {2 x y^{\prime }}{y}-1&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.135 |
|
| \begin{align*}
y&=a y^{\prime }+b {y^{\prime }}^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.723 |
|
| \begin{align*}
y&=\sqrt {1+{y^{\prime }}^{2}}+a y^{\prime } \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
52.586 |
|
| \begin{align*}
y&=x y^{\prime }+x \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
124.164 |
|
| \begin{align*}
y&=x y^{\prime }+a x \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
52.552 |
|
| \begin{align*}
x -y y^{\prime }&=a {y^{\prime }}^{2} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
32.021 |
|
| \begin{align*}
y y^{\prime }+x&=a \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
55.328 |
|
| \begin{align*}
y-\frac {1}{\sqrt {1+{y^{\prime }}^{2}}}&=x +\frac {y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.301 |
|
| \begin{align*}
y-2 x y^{\prime }&={y^{\prime }}^{2} x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.846 |
|
| \begin{align*}
2 y x +\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
43.831 |
|
| \begin{align*}
\left (x +\sqrt {y^{2}-y x}\right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
134.820 |
|
| \begin{align*}
x +y-\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
39.544 |
|
| \begin{align*}
x y^{\prime }-y-x \sin \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
30.937 |
|
| \begin{align*}
2 x^{2} y+y^{3}+\left (x y^{2}-2 x^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
50.805 |
|
| \begin{align*}
y^{2}+\left (x \sqrt {y^{2}-x^{2}}-y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
186.047 |
|
| \begin{align*}
\frac {y \cos \left (\frac {y}{x}\right )}{x}-\left (\frac {x \sin \left (\frac {y}{x}\right )}{y}+\cos \left (\frac {y}{x}\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
49.798 |
|
| \begin{align*}
y+x \ln \left (\frac {y}{x}\right ) y^{\prime }-2 x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
123.645 |
|
| \begin{align*}
2 \,{\mathrm e}^{\frac {x}{y}} y+\left (y-2 x \,{\mathrm e}^{\frac {x}{y}}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
40.250 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
59.892 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
35.400 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
36.086 |
|
| \begin{align*}
x +y-1-\left (x -y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
68.105 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
32.970 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
35.659 |
|
| \begin{align*}
x +2 y+\left (-1+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
68.704 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
75.375 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
107.801 |
|
| \begin{align*}
x +y+2-\left (x -y-4\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
68.154 |
|
| \begin{align*}
y^{\prime }+a y&=b \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.954 |
|
| \begin{align*}
{\mathrm e}^{y} \left (y^{\prime }+1\right )&={\mathrm e}^{x} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.392 |
|
| \begin{align*}
\left (x -y\right )^{2} y^{\prime }&=4 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
21.859 |
|
| \begin{align*}
x y^{\prime }-y&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
60.513 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
63.796 |
|
| \begin{align*}
\left (x^{2}-y^{2}\right ) y^{\prime }&=2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
62.535 |
|
| \begin{align*}
x y^{\prime }&=x +y+{\mathrm e}^{\frac {y}{x}} x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.734 |
|
| \begin{align*}
x y^{\prime }-y-x \sin \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.299 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
13.667 |
|
| \begin{align*}
x y y^{\prime }+x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.747 |
|
| \begin{align*}
2 x y y^{\prime }+3 x^{2}-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.243 |
|
| \begin{align*}
y {y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.223 |
|
| \begin{align*}
y^{\prime }+b^{2} y^{2}&=a^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.303 |
|
| \begin{align*}
y^{\prime }&=y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.825 |
|
| \begin{align*}
2 y^{\prime }&=3 \left (-2+y\right )^{{1}/{3}} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
3.845 |
|
| \begin{align*}
\left (x -y\right ) y^{\prime }+x +y+1&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.441 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
12.260 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x +y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.602 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}-\tan \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.272 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
14.533 |
|
| \begin{align*}
y^{\prime }-\sin \left (x +y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.684 |
|
| \begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.587 |
|
| \begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
47.765 |
|
| \begin{align*}
u^{\prime }&=\alpha \left (1-u\right )-\beta u \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.934 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
18.011 |
|
| \begin{align*}
2 y x +\left (y^{2}-3 x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
10.434 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
17.747 |
|
| \begin{align*}
2 t x x^{\prime }+t^{2}-x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
43.142 |
|
| \begin{align*}
\left (y-4 x -1\right )^{2}-y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
9.270 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
30.804 |
|
| \begin{align*}
-y+t y^{\prime }&=\sqrt {y t} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.010 |
|
| \begin{align*}
\cos \left (x +y\right ) y^{\prime }&=\sin \left (x +y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.635 |
|
| \begin{align*}
3 x^{2}-y^{2}-\left (y x -\frac {x^{3}}{y}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
22.227 |
|
| \begin{align*}
x^{2}+y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.838 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}-y^{2}}{3 x y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
31.846 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (1+\ln \left (y\right )-\ln \left (x \right )\right )}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.086 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x +y}-1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.974 |
|
| \begin{align*}
y^{\prime }&=\left (x +y+2\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.559 |
|
| \begin{align*}
y^{\prime }&=\left (x -y+5\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.124 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.958 |
|
| \begin{align*}
x +y-1+\left (y-x -5\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.905 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
137.719 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
21.344 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x y}{2 x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
15.072 |
|
| \begin{align*}
x^{2}+y^{2}+3 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.454 |
|
| \begin{align*}
x^{\prime }&=1+\cos \left (t -x\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.772 |
|
| \begin{align*}
y^{\prime }&=2-\sqrt {2 x -y+3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.136 |
|
| \begin{align*}
y^{\prime }&=\left (2 x +y-1\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.918 |
|
| \begin{align*}
x^{2}-3 y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
57.864 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
13.163 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
24.506 |
|
| \begin{align*}
y-x +\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.263 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
52.777 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y-1}{x +y+5} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.425 |
|
| \begin{align*}
y^{\prime }&=2 y^{{2}/{3}} \\
y \left (2\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.578 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {x^{2}+y^{2}}-x}{y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
14.728 |
|
| \begin{align*}
3 y^{\prime }-7 y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.547 |
|
| \begin{align*}
5 y^{\prime }+4 y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.308 |
|
| \begin{align*}
3 z^{\prime }+11 z&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.736 |
|
| \begin{align*}
6 w^{\prime }-13 w&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.823 |
|
| \begin{align*}
\left (-x +2 y\right ) y^{\prime }&=2 x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.748 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
24.576 |
|
| \begin{align*}
x^{3}+y^{3}&=3 x y^{2} y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.731 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
14.953 |
|
| \begin{align*}
\left (x^{3}+3 x y^{2}\right ) y^{\prime }&=y^{3}+3 x^{2} y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
211.522 |
|
| \begin{align*}
\left (3 x +3 y-4\right ) y^{\prime }&=-x -y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.849 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
18.071 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
68.537 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
13.701 |
|
| \begin{align*}
x^{2} y^{\prime }&=y^{2}-x y y^{\prime } \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
22.902 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{3 x -2 y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.526 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=x y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
63.029 |
|
| \begin{align*}
2 x y y^{\prime }&=x^{2}-y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.213 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
5.435 |
|
| \begin{align*}
2 x^{3} y^{\prime }&=y \left (3 x^{2}+y^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
33.371 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
8.900 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
17.145 |
|
| \begin{align*}
2 x y^{\prime }-2 y&=\sqrt {x^{2}+4 y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.036 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
69.290 |
|
| \begin{align*}
y^{2}-x^{2}+x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.808 |
|
| \begin{align*}
x^{3}+y^{3}+3 x y^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.563 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
8.356 |
|
| \begin{align*}
y^{\prime }&=-2 \left (2 x +3 y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
11.639 |
|
| \begin{align*}
x y y^{\prime }+x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.303 |
|
| \begin{align*}
x^{2}+y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.366 |
|
| \begin{align*}
x +y+1-\left (-3+x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.641 |
|
| \begin{align*}
4 x -2 y y^{\prime }+{y^{\prime }}^{2} x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.271 |
|
| \begin{align*}
8 y {y^{\prime }}^{2}-2 x y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.073 |
|
| \begin{align*}
{y^{\prime }}^{2} x -y y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
4.724 |
|
| \begin{align*}
{y^{\prime }}^{2}-x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.290 |
|
| \begin{align*}
y&=x \left (y^{\prime }+1\right )+{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.415 |
|
| \begin{align*}
y&=2 y^{\prime }+\sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
17.598 |
|
| \begin{align*}
y {y^{\prime }}^{2}-x y^{\prime }+3 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.689 |
|
| \begin{align*}
4 x -2 y y^{\prime }+{y^{\prime }}^{2} x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.908 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }+x +2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.237 |
|
| \begin{align*}
2 y&={y^{\prime }}^{2}+4 x y^{\prime } \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.574 |
|
| \begin{align*}
\left (1+{y^{\prime }}^{2}\right ) \left (x -y\right )^{2}&=\left (y y^{\prime }+x \right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
107.757 |
|
| \begin{align*}
\sin \left (y^{\prime }\right )&=x +y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.864 |
|
| \begin{align*}
2 y^{\prime }+y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.378 |
|
| \begin{align*}
y^{\prime }+20 y&=24 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.100 |
|
| \begin{align*}
y^{\prime }&=25+y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
8.641 |
|
| \begin{align*}
2 y+y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.413 |
|
| \begin{align*}
5 y^{\prime }&=2 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.233 |
|
| \begin{align*}
\left (-1+y\right ) y^{\prime }&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.602 |
|
| \begin{align*}
{y^{\prime }}^{2}&=4 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.572 |
|
| \begin{align*}
{y^{\prime }}^{2}&=9-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.002 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 y^{\prime }+4 y&=4 x -1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.587 |
|
| \begin{align*}
y^{\prime }&=\sqrt {1-y^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.489 |
|
| \begin{align*}
y^{\prime }&=5-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.902 |
|
| \begin{align*}
y^{\prime }&=4+y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.160 |
|
| \begin{align*}
y^{\prime }&=3 y^{{2}/{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
10.707 |
|
| \begin{align*}
y^{\prime }&=y^{{2}/{3}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.019 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.765 |
|
| \begin{align*}
\left (-x +y\right ) y^{\prime }&=x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
20.824 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y^{2}-9} \\
y \left (5\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
12.765 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y^{2}-9} \\
y \left (2\right ) &= -3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
11.066 |
|
| \begin{align*}
y^{\prime }&=1+y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
2.997 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.476 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.247 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
5.576 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.359 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (3\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.487 |
|
| \begin{align*}
y^{\prime }&=2 y-4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.006 |
|
| \begin{align*}
\left (-2+2 y\right ) y^{\prime }&=2 x -1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.430 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
9.779 |
|
| \begin{align*}
y^{\prime }&=y \ln \left (y+2\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.653 |
|
| \begin{align*}
y^{\prime }&=\left (y \,{\mathrm e}^{y}-9 y\right ) {\mathrm e}^{-y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.033 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{\pi }-\sin \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.018 |
|
| \begin{align*}
m v^{\prime }&=m g -k v^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.399 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{3 x +2 y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.201 |
|
| \begin{align*}
s^{\prime }&=k s \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.771 |
|
| \begin{align*}
q^{\prime }&=k \left (q-70\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.219 |
|
| \begin{align*}
x^{\prime }&=4 x^{2}+4 \\
x \left (\frac {\pi }{4}\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
48.796 |
|
| \begin{align*}
y^{\prime }+2 y&=1 \\
y \left (0\right ) &= {\frac {5}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.607 |
|
| \begin{align*}
{\mathrm e}^{y}-{\mathrm e}^{-x} y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.788 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
11.430 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
9.974 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 \\
y \left (\frac {1}{4}\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
26.333 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{-3+y} \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.051 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{-3+y} \\
y \left (-1\right ) &= 4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.020 |
|
| \begin{align*}
y^{\prime }&=y^{{2}/{3}}-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
54.648 |
|
| \begin{align*}
y^{\prime }&=y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.592 |
|
| \begin{align*}
{y^{\prime }}^{2}+y^{2}&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.454 |
|
| \begin{align*}
u^{\prime }&=a \sqrt {1+u^{2}} \\
u \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.003 |
|
| \begin{align*}
x^{\prime }&=k \left (A -x\right )^{2} \\
x \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.085 |
|
| \begin{align*}
y^{\prime }&=5 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.799 |
|
| \begin{align*}
2 y+y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.516 |
|
| \begin{align*}
3 y^{\prime }+12 y&=4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.259 |
|
| \begin{align*}
L i^{\prime }+R i&=E \\
i \left (0\right ) &= i_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.363 |
|
| \begin{align*}
T^{\prime }&=k \left (T-T_{m} \right ) \\
T \left (0\right ) &= T_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.287 |
|
| \begin{align*}
e^{\prime }&=-\frac {e}{r c} \\
e \left (4\right ) &= e_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.268 |
|
| \begin{align*}
2 x -1+\left (3 y+7\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.232 |
|
| \begin{align*}
y^{\prime }&=3 y^{{2}/{3}} \\
y \left (2\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.321 |
|
| \begin{align*}
\left (1+z^{\prime }\right ) {\mathrm e}^{-z}&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.231 |
|
| \begin{align*}
\frac {1}{\sqrt {x}}+\frac {y^{\prime }}{\sqrt {y}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
29.169 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x -y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.388 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {y}}{\sqrt {x}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
25.947 |
|
| \begin{align*}
z^{\prime }&=10^{x +z} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.438 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.766 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
35.287 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x -y-1\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.865 |
|
| \begin{align*}
y^{\prime }+\sin \left (x +y\right )^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.694 |
|
| \begin{align*}
y^{\prime }&=2 \sqrt {2 x +y+1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.144 |
|
| \begin{align*}
y^{\prime }&=\left (x +y+1\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.703 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.381 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=x y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
26.126 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }&=2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
41.555 |
|
| \begin{align*}
x y^{\prime }-y&=x \tan \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.326 |
|
| \begin{align*}
x y^{\prime }-y&=\left (x +y\right ) \ln \left (\frac {x +y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.540 |
|
| \begin{align*}
x y^{\prime }&=y \cos \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.335 |
|
| \begin{align*}
y+\sqrt {y x}-x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
19.392 |
|
| \begin{align*}
x y^{\prime }-\sqrt {x^{2}-y^{2}}-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
44.678 |
|
| \begin{align*}
x +y-\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.178 |
|
| \begin{align*}
x^{2}+2 y x -y^{2}+\left (y^{2}+2 y x -x^{2}\right ) y^{\prime }&=0 \\
y \left (1\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
✗ |
36.332 |
|
| \begin{align*}
x y^{\prime }-y&=y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.125 |
|
| \begin{align*}
y^{2}+\left (x^{2}-y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
69.950 |
|
| \begin{align*}
\frac {1}{x^{2}-y x +y^{2}}&=\frac {y^{\prime }}{2 y^{2}-y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
77.598 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y}{3 x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
15.361 |
|
| \begin{align*}
x y^{\prime }&=y+\sqrt {y^{2}-x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
17.726 |
|
| \begin{align*}
\left (2 \sqrt {y x}-x \right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
28.088 |
|
| \begin{align*}
x y^{\prime }&=y \ln \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.551 |
|
| \begin{align*}
\left (x y^{\prime }+y\right )^{2}&=y^{2} y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
59.291 |
|
| \begin{align*}
x y^{\prime }-y&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
16.356 |
|
| \begin{align*}
y {y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.802 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.715 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y-2}{y-x -4} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.535 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
34.211 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
62.911 |
|
| \begin{align*}
y^{\prime }&=\frac {x +3 y-5}{x -y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
32.562 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
12.322 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
8.826 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
44.425 |
|
| \begin{align*}
y+2&=\left (2 x +y-4\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
29.802 |
|
| \begin{align*}
\left (y^{\prime }+1\right ) \ln \left (\frac {x +y}{x +3}\right )&=\frac {x +y}{x +3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
22.151 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x -y+1}{2 x +y+4} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
83.615 |
|
| \begin{align*}
3+2 x +\left (-2+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.214 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
32.962 |
|
| \begin{align*}
x y^{\prime }-2 \sqrt {y x}&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
18.566 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y-1}{x -y+3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
27.447 |
|
| \begin{align*}
x +y-\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.241 |
|
| \begin{align*}
y y^{\prime }+x&=a {y^{\prime }}^{2} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
20.769 |
|
| \begin{align*}
y+\sqrt {x^{2}+y^{2}}-x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
17.504 |
|
| \begin{align*}
{y^{\prime }}^{2}&=a^{2}-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.252 |
|
| \begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
19.046 |
|
| \begin{align*}
x^{2}-y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
50.087 |
|
| \begin{align*}
x +y y^{\prime }+y-x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.993 |
|
| \begin{align*}
y^{\prime }+5 y&=2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.301 |
|
| \begin{align*}
y^{\prime }&=k y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.257 |
|
| \begin{align*}
y^{\prime }-2 y&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.259 |
|
| \begin{align*}
L y^{\prime }+R y&=E \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.877 |
|
| \begin{align*}
y^{\prime }&=y+1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.192 |
|
| \begin{align*}
y^{\prime }&=1+y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
3.761 |
|
| \begin{align*}
y^{\prime }&=1+y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
3.388 |
|
| \begin{align*}
y^{\prime }&=2 \sqrt {y} \\
y \left (x_{0} \right ) &= y_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
4.609 |
|
| \begin{align*}
y^{\prime }&=2 \sqrt {y} \\
y \left (x_{0} \right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.164 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.635 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{y x +x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
27.178 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y+2}{x +y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
21.145 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
45.260 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+1}{2 x +2 y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.236 |
|
| \begin{align*}
y^{\prime }&=k y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.041 |
|
| \begin{align*}
2 x y y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.533 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{y x -x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
27.710 |
|
| \begin{align*}
x^{2}-2 y^{2}+x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
62.487 |
|
| \begin{align*}
x -y-\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
32.744 |
|
| \begin{align*}
x y^{\prime }&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
36.569 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+4}{x -y-6} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
26.139 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+4}{x +y-6} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.318 |
|
| \begin{align*}
2 x -2 y+\left (-1+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.161 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y-1}{x +4 y+2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
267.683 |
|
| \begin{align*}
y^{\prime }&=\sin \left (\frac {y}{x}\right )-\cos \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
11.153 |
|
| \begin{align*}
{\mathrm e}^{\frac {x}{y}}-\frac {y y^{\prime }}{x}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
14.589 |
|
| \begin{align*}
y^{\prime }&=\frac {y \tan \left (\frac {y}{x}\right )}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
27.908 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y^{2}}{x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
23.948 |
|
| \begin{align*}
y^{\prime }&=\frac {x +2 y}{2 x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.070 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+2 y^{2}}{x^{2}-2 y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
17.320 |
|
| \begin{align*}
y^{\prime }+y&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.272 |
|
| \begin{align*}
y^{\prime }-y&=2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.189 |
|
| \begin{align*}
y^{\prime }+y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.404 |
|
| \begin{align*}
y^{\prime }-y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.230 |
|
| \begin{align*}
4 x -2 y y^{\prime }+{y^{\prime }}^{2} x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.473 |
|
| \begin{align*}
{y^{\prime }}^{2}-x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.698 |
|
| \begin{align*}
{y^{\prime }}^{3}+{y^{\prime }}^{2} x -y&=0 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
73.093 |
|
| \begin{align*}
4 x -2 y y^{\prime }+{y^{\prime }}^{2} x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.419 |
|
| \begin{align*}
{y^{\prime }}^{2}-x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.613 |
|
| \begin{align*}
2 {y^{\prime }}^{3}+x y^{\prime }-2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
9.645 |
|
| \begin{align*}
2 {y^{\prime }}^{2}+x y^{\prime }-2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.442 |
|
| \begin{align*}
{y^{\prime }}^{3}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
2.511 |
|
| \begin{align*}
4 {y^{\prime }}^{2} x -3 y y^{\prime }+3&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
45.684 |
|
| \begin{align*}
{y^{\prime }}^{3}-x y^{\prime }+2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.448 |
|
| \begin{align*}
5 {y^{\prime }}^{2}+6 x y^{\prime }-2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.716 |
|
| \begin{align*}
2 {y^{\prime }}^{2} x +\left (2 x -y\right ) y^{\prime }+1-y&=0 \\
\end{align*} |
[_rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
7.642 |
|
| \begin{align*}
5 {y^{\prime }}^{2}+3 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.637 |
|
| \begin{align*}
{y^{\prime }}^{2}+3 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.641 |
|
| \begin{align*}
5 {y^{\prime }}^{2}+6 x y^{\prime }-2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.568 |
|
| \begin{align*}
{y^{\prime }}^{4}+x y^{\prime }-3 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
5.536 |
|
| \begin{align*}
{y^{\prime }}^{3}-2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
95.624 |
|
| \begin{align*}
y {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
26.695 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
36.085 |
|
| \begin{align*}
y^{\prime }&=y+1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.197 |
|
| \begin{align*}
y^{\prime }&=y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.492 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=x y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
55.136 |
|
| \begin{align*}
y&={y^{\prime }}^{2} x +{y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.643 |
|
| \begin{align*}
2 t +3 x+\left (x+2\right ) x^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.570 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{1-y} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| \begin{align*}
p^{\prime }&=a p-b p^{2} \\
p \left (\operatorname {t0} \right ) &= \operatorname {p0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.122 |
|
| \begin{align*}
y&={y^{\prime }}^{2} x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.971 |
|
| \begin{align*}
y y^{\prime }&=1-x {y^{\prime }}^{3} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
90.918 |
|
| \begin{align*}
y^{\prime }&=-4 \sin \left (x -y\right )-4 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
24.362 |
|
| \begin{align*}
y^{\prime }+\sin \left (x -y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.616 |
|
| \begin{align*}
x^{\prime }&=4 A k \left (\frac {x}{A}\right )^{{3}/{4}}-3 k x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
97.989 |
|
| \begin{align*}
\frac {y^{\prime } y}{1+\frac {\sqrt {1+{y^{\prime }}^{2}}}{2}}&=-x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.006 |
|
| \begin{align*}
\frac {y^{\prime } y}{1+\frac {\sqrt {1+{y^{\prime }}^{2}}}{2}}&=-x \\
y \left (0\right ) &= 3 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.974 |
|
| \begin{align*}
y^{\prime }&=2 \sqrt {y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.803 |
|
| \begin{align*}
y^{\prime }&=\sqrt {1-y^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.712 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {y}{x}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.099 |
|
| \begin{align*}
\left (y-2 x y^{\prime }\right )^{2}&={y^{\prime }}^{3} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
43.957 |
|
| \begin{align*}
y^{\prime }&=y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.931 |
|
| \begin{align*}
y^{\prime }&=b y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.971 |
|
| \begin{align*}
c y^{\prime }&=y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.157 |
|
| \begin{align*}
c y^{\prime }&=b y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.260 |
|
| \begin{align*}
{y^{\prime }}^{2}&=x +y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.336 |
|
| \begin{align*}
{y^{\prime }}^{2}&=\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.657 |
|
| \begin{align*}
y^{\prime }&=\sqrt {1+6 x +y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.395 |
|
| \begin{align*}
y^{\prime }&=\left (\pi +x +7 y\right )^{{7}/{2}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
38.938 |
|
| \begin{align*}
y^{\prime }&=\left (a +b x +c y\right )^{6} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
6.796 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x +y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.362 |
|
| \begin{align*}
y^{\prime }&=10+{\mathrm e}^{x +y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.069 |
|
| \begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
53.574 |
|
| \begin{align*}
y^{\prime }+y^{2}-1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.830 |
|
| \begin{align*}
y^{\prime }+a y^{2}-b&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.109 |
|
| \begin{align*}
y^{\prime }-\left (A y-a \right ) \left (B y-b \right )&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.875 |
|
| \begin{align*}
y^{\prime }-\operatorname {a3} y^{3}-\operatorname {a2} y^{2}-\operatorname {a1} y-\operatorname {a0}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
27.300 |
|
| \begin{align*}
y^{\prime }-a \cos \left (y\right )+b&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
4.554 |
|
| \begin{align*}
y^{\prime }-\cos \left (b x +a y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.550 |
|
| \begin{align*}
y^{\prime }+a \sin \left (\alpha y+\beta x \right )+b&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.748 |
|
| \begin{align*}
y^{\prime }-f \left (a x +b y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.176 |
|
| \begin{align*}
x y^{\prime }-y-\sqrt {x^{2}+y^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.350 |
|
| \begin{align*}
x y^{\prime }+a \sqrt {x^{2}+y^{2}}-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
21.751 |
|
| \begin{align*}
x y^{\prime }-{\mathrm e}^{\frac {y}{x}} x -y-x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
7.305 |
|
| \begin{align*}
x y^{\prime }-y-x \sin \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.607 |
|
| \begin{align*}
x y^{\prime }+x -y+x \cos \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.966 |
|
| \begin{align*}
x y^{\prime }+x \tan \left (\frac {y}{x}\right )-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.833 |
|
| \begin{align*}
y y^{\prime }-x \,{\mathrm e}^{\frac {x}{y}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.683 |
|
| \begin{align*}
\left (y+1\right ) y^{\prime }-y-x&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
23.541 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
29.993 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
28.249 |
|
| \begin{align*}
\left (1-2 x +y\right ) y^{\prime }+y+x&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
26.854 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
10.489 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
19.391 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
22.015 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
10.893 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
10.477 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
10.654 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
14.461 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
52.737 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
16.082 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
50.236 |
|
| \begin{align*}
x y y^{\prime }+x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.393 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
21.955 |
|
| \begin{align*}
2 x y y^{\prime }-y^{2}+a \,x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.817 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
23.895 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
51.421 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.456 |
|
| \begin{align*}
\left (y^{2}-x^{2}\right ) y^{\prime }+2 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
16.541 |
|
| \begin{align*}
\left (x +y\right )^{2} y^{\prime }-a^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.491 |
|
| \begin{align*}
x^{2}+2 y x -y^{2}+\left (y^{2}+2 y x -x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
15.177 |
|
| \begin{align*}
\left (3 x^{2}+2 y x +4 y^{2}\right ) y^{\prime }+2 x^{2}+6 y x +y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
14.368 |
|
| \begin{align*}
\left (2 y-4 x +1\right )^{2} y^{\prime }-\left (y-2 x \right )^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
15.330 |
|
| \begin{align*}
x \left (y^{2}+y x -x^{2}\right ) y^{\prime }-y^{3}+x y^{2}+x^{2} y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
18.055 |
|
| \begin{align*}
2 x \left (5 x^{2}+y^{2}\right ) y^{\prime }+y^{3}-x^{2} y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
19.746 |
|
| \begin{align*}
\left (1+\sqrt {x +y}\right ) y^{\prime }+1&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.988 |
|
| \begin{align*}
{y^{\prime }}^{2}+y^{2}-a^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.749 |
|
| \begin{align*}
{y^{\prime }}^{2}-y^{3}+y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
8.111 |
|
| \begin{align*}
{y^{\prime }}^{2}-4 y^{3}+a y+b&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.531 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 y^{\prime }-y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
30.715 |
|
| \begin{align*}
{y^{\prime }}^{2}+a y^{\prime }+b y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.258 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.720 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 x y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.504 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 y y^{\prime }-2 x&=0 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
23.918 |
|
| \begin{align*}
{y^{\prime }}^{2}-\left (4 y+1\right ) y^{\prime }+\left (4 y+1\right ) y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
12.357 |
|
| \begin{align*}
{y^{\prime }}^{2}+a y y^{\prime }-b x -c&=0 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
62.069 |
|
| \begin{align*}
3 {y^{\prime }}^{2}-2 x y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.788 |
|
| \begin{align*}
a {y^{\prime }}^{2}+b y^{\prime }-y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.231 |
|
| \begin{align*}
a {y^{\prime }}^{2}+y y^{\prime }-x&=0 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
51.444 |
|
| \begin{align*}
a {y^{\prime }}^{2}-y y^{\prime }-x&=0 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
24.312 |
|
| \begin{align*}
{y^{\prime }}^{2} x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.269 |
|
| \begin{align*}
{y^{\prime }}^{2} x +x -2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.416 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y^{\prime }-y&=0 \\
\end{align*} |
[_rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.654 |
|
| \begin{align*}
{y^{\prime }}^{2} x +4 y^{\prime }-2 y&=0 \\
\end{align*} |
[_rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.868 |
|
| \begin{align*}
{y^{\prime }}^{2} x +x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.137 |
|
| \begin{align*}
{y^{\prime }}^{2} x +\left (y-3 x \right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.584 |
|
| \begin{align*}
{y^{\prime }}^{2} x -y y^{\prime }+a y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.150 |
|
| \begin{align*}
{y^{\prime }}^{2} x +2 y y^{\prime }-x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
90.088 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }+a&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.398 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }-x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.847 |
|
| \begin{align*}
4 x -2 y y^{\prime }+{y^{\prime }}^{2} x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.104 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }+x +2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.163 |
|
| \begin{align*}
{y^{\prime }}^{2} x +a y y^{\prime }+b x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.455 |
|
| \begin{align*}
\left (\operatorname {a2} x +\operatorname {c2} \right ) {y^{\prime }}^{2}+\left (\operatorname {a1} x +\operatorname {b1} y+\operatorname {c1} \right ) y^{\prime }+\operatorname {a0} x +\operatorname {b0} y+\operatorname {c0}&=0 \\
\end{align*} |
[_dAlembert] |
✓ |
✗ |
✓ |
✗ |
1.230 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}-y \left (y-2 x \right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
52.779 |
|
| \begin{align*}
\left (a^{2}-1\right ) x^{2} {y^{\prime }}^{2}+2 x y y^{\prime }-y^{2}+a^{2} x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
35.385 |
|
| \begin{align*}
a \,x^{2} {y^{\prime }}^{2}-2 a x y y^{\prime }+y^{2}-a \left (a -1\right ) x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
✓ |
3.866 |
|
| \begin{align*}
y {y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.607 |
|
| \begin{align*}
y {y^{\prime }}^{2}+2 x y^{\prime }-9 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.634 |
|
| \begin{align*}
y {y^{\prime }}^{2}-2 x y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.687 |
|
| \begin{align*}
y {y^{\prime }}^{2}-4 x y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
27.667 |
|
| \begin{align*}
y {y^{\prime }}^{2}-4 a^{2} x y^{\prime }+a^{2} y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
23.902 |
|
| \begin{align*}
y {y^{\prime }}^{2}+a x y^{\prime }+b y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.757 |
|
| \begin{align*}
\left (x +y\right ) {y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.297 |
|
| \begin{align*}
\left (y-2 x \right ) {y^{\prime }}^{2}-2 \left (x -1\right ) y^{\prime }+y-2&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.873 |
|
| \begin{align*}
2 y {y^{\prime }}^{2}-\left (4 x -5\right ) y^{\prime }+2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.804 |
|
| \begin{align*}
4 y {y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.498 |
|
| \begin{align*}
a y {y^{\prime }}^{2}+\left (2 x -b \right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.632 |
|
| \begin{align*}
\left (b +a y\right ) \left (1+{y^{\prime }}^{2}\right )-c&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.347 |
|
| \begin{align*}
\left (b_{2} y+a_{2} x +c_{2} \right ) {y^{\prime }}^{2}+\left (a_{1} x +b_{1} y+c_{1} \right ) y^{\prime }+a_{0} x +b_{0} y+c_{0}&=0 \\
\end{align*} |
[_rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
117.145 |
|
| \begin{align*}
\left (2 y x -x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+2 y x -y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
108.440 |
|
| \begin{align*}
\left (2 y x -x^{2}\right ) {y^{\prime }}^{2}-6 x y y^{\prime }-y^{2}+2 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
99.341 |
|
| \begin{align*}
\left (y^{2}-a^{2}\right ) {y^{\prime }}^{2}+y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.536 |
|
| \begin{align*}
\left (-a^{2} x^{2}+y^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+x^{2} \left (-a^{2}+1\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.059 |
|
| \begin{align*}
\left (-x +y\right )^{2} \left (1+{y^{\prime }}^{2}\right )-a^{2} \left (y^{\prime }+1\right )^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.270 |
|
| \begin{align*}
3 y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2}+4 y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.248 |
|
| \begin{align*}
\left (3 y-2\right ) {y^{\prime }}^{2}-4+4 y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.276 |
|
| \begin{align*}
\left (-a^{2}+1\right ) y^{2} {y^{\prime }}^{2}-2 a^{2} x y y^{\prime }+y^{2}-a^{2} x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
4.774 |
|
| \begin{align*}
\left (a y-b x \right )^{2} \left (a^{2} {y^{\prime }}^{2}+b^{2}\right )-c^{2} \left (a y^{\prime }+b \right )^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
6.627 |
|
| \begin{align*}
{y^{\prime }}^{2} \left (a \cos \left (y\right )+b \right )-c \cos \left (y\right )+d&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.811 |
|
| \begin{align*}
{y^{\prime }}^{3}-\left (y-a \right )^{2} \left (y-b \right )^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.674 |
|
| \begin{align*}
{y^{\prime }}^{3}+y^{\prime }-y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
79.302 |
|
| \begin{align*}
{y^{\prime }}^{3}-2 y y^{\prime }+y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
47.748 |
|
| \begin{align*}
{y^{\prime }}^{3}+a {y^{\prime }}^{2}+b y+a b x&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
29.176 |
|
| \begin{align*}
{y^{\prime }}^{3}+{y^{\prime }}^{2} x -y&=0 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
68.173 |
|
| \begin{align*}
{y^{\prime }}^{3}-y {y^{\prime }}^{2}+y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
97.479 |
|
| \begin{align*}
a {y^{\prime }}^{3}+b {y^{\prime }}^{2}+c y^{\prime }-y-d&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
2.734 |
|
| \begin{align*}
4 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}-x +3 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.290 |
|
| \begin{align*}
8 x {y^{\prime }}^{3}-12 y {y^{\prime }}^{2}+9 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.158 |
|
| \begin{align*}
{y^{\prime }}^{4}-\left (y-a \right )^{3} \left (y-b \right )^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.552 |
|
| \begin{align*}
{y^{\prime }}^{4}+3 \left (x -1\right ) {y^{\prime }}^{2}-3 \left (-1+2 y\right ) y^{\prime }+3 x&=0 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
25.403 |
|
| \begin{align*}
{y^{\prime }}^{6}-\left (y-a \right )^{4} \left (y-b \right )^{3}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.972 |
|
| \begin{align*}
a {y^{\prime }}^{m}+b {y^{\prime }}^{n}-y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
2.261 |
|
| \begin{align*}
\sqrt {1+{y^{\prime }}^{2}}+{y^{\prime }}^{2} x +y&=0 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
22.423 |
|
| \begin{align*}
x \left (y^{\prime }+\sqrt {1+{y^{\prime }}^{2}}\right )-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
40.004 |
|
| \begin{align*}
a x \sqrt {1+{y^{\prime }}^{2}}+x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
103.264 |
|
| \begin{align*}
a \left (1+{y^{\prime }}^{3}\right )^{{1}/{3}}+b x y^{\prime }-y&=0 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
21.585 |
|
| \begin{align*}
{y^{\prime }}^{2} \sin \left (y^{\prime }\right )-y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
2.933 |
|
| \begin{align*}
y^{\prime }&=\frac {b^{3}+y^{2} b^{3}+2 a \,b^{2} x y+a^{2} b \,x^{2}+b^{3} y^{3}+3 a \,b^{2} x y^{2}+3 a^{2} b \,x^{2} y+a^{3} x^{3}}{b^{3}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Abel] |
✓ |
✓ |
✓ |
✗ |
8.109 |
|
| \begin{align*}
y^{\prime }&=\frac {\alpha ^{3}+y^{2} \alpha ^{3}+2 y \alpha ^{2} \beta x +\alpha \,\beta ^{2} x^{2}+y^{3} \alpha ^{3}+3 y^{2} \alpha ^{2} \beta x +3 y \alpha \,\beta ^{2} x^{2}+\beta ^{3} x^{3}}{\alpha ^{3}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Abel] |
✓ |
✓ |
✓ |
✗ |
8.130 |
|
| \begin{align*}
y^{\prime }&=\frac {a^{3}+y^{2} a^{3}+2 y a^{2} b x +b^{2} x^{2} a +y^{3} a^{3}+3 a^{2} b x y^{2}+3 a \,b^{2} x^{2} y+b^{3} x^{3}}{a^{3}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Abel] |
✓ |
✓ |
✓ |
✗ |
8.240 |
|
| \begin{align*}
y^{\prime }&=f \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.838 |
|
| \begin{align*}
y y^{\prime }-y&=A x +B \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
53.872 |
|
| \begin{align*}
\left (A y+B x +a \right ) y^{\prime }+B y+k x +b&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
95.445 |
|
| \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‘]] |
✓ |
✓ |
✗ |
✗ |
82.632 |
|
| \begin{align*}
\frac {y^{2}-2 x^{2}}{-x^{3}+x y^{2}}+\frac {\left (2 y^{2}-x^{2}\right ) y^{\prime }}{y^{3}-x^{2} y}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
51.938 |
|
| \begin{align*}
\frac {1}{\sqrt {x^{2}+y^{2}}}+\left (\frac {1}{y}-\frac {x}{y \sqrt {x^{2}+y^{2}}}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
47.372 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
26.004 |
|
| \begin{align*}
2 x^{2} y+3 y^{3}-\left (x^{3}+2 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
30.731 |
|
| \begin{align*}
2 x^{2} y+y^{3}-x^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
77.725 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
41.441 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
30.691 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
14.238 |
|
| \begin{align*}
x +y-\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.590 |
|
| \begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
30.736 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
36.036 |
|
| \begin{align*}
y^{2}-x^{2}+2 m x y+\left (m y^{2}-m \,x^{2}-2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
60.839 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }-1&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.019 |
|
| \begin{align*}
x +y y^{\prime }+y-x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.555 |
|
| \begin{align*}
\left (-x +y\right )^{2} y^{\prime }&=1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.411 |
|
| \begin{align*}
\left (-x +y\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
22.279 |
|
| \begin{align*}
x y^{\prime }-y&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
19.194 |
|
| \begin{align*}
x y^{\prime }-y&=\sqrt {x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
53.450 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
15.404 |
|
| \begin{align*}
y^{3}-2 x^{2} y+\left (2 x y^{2}-x^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
42.540 |
|
| \begin{align*}
\left (2 \sqrt {y x}-x \right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
36.996 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }-x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.369 |
|
| \begin{align*}
{y^{\prime }}^{2}+y^{2}&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.227 |
|
| \begin{align*}
4 {y^{\prime }}^{2} x +2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.273 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }-x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.203 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
4.659 |
|
| \begin{align*}
a^{2} y {y^{\prime }}^{2}-2 x y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.886 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }-x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.201 |
|
| \begin{align*}
4 \,{\mathrm e}^{2 y} {y^{\prime }}^{2}+2 \,{\mathrm e}^{2 x} y^{\prime }-{\mathrm e}^{2 x}&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
4.445 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) \left (y^{\prime }+1\right )^{2}-2 \left (x +y\right ) \left (y^{\prime }+1\right ) \left (y y^{\prime }+x \right )+\left (y y^{\prime }+x \right )^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
106.999 |
|
| \begin{align*}
a^{2} y {y^{\prime }}^{2}-2 x y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.664 |
|
| \begin{align*}
3 {y^{\prime }}^{2} x -6 y y^{\prime }+x +2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.851 |
|
| \begin{align*}
y&=\left (x +1\right ) {y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.440 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }-x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.292 |
|
| \begin{align*}
8 \left (y^{\prime }+1\right )^{3}&=27 \left (x +y\right ) \left (1-y^{\prime }\right )^{3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
22.626 |
|
| \begin{align*}
x^{\prime }&=-x^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.506 |
|
| \begin{align*}
x^{\prime }&={\mathrm e}^{-x} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.599 |
|
| \begin{align*}
x^{\prime }&=\sqrt {x} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
5.046 |
|
| \begin{align*}
x^{\prime }&={\mathrm e}^{-2 x} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.075 |
|
| \begin{align*}
y^{\prime }&=1+y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.562 |
|
| \begin{align*}
u^{\prime }&=\frac {1}{5-2 u} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.603 |
|
| \begin{align*}
x^{\prime }&=a x+b \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.002 |
|
| \begin{align*}
x^{\prime }&={\mathrm e}^{x^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.293 |
|
| \begin{align*}
y^{\prime }&=r \left (a -y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.017 |
|
| \begin{align*}
\left (2 u+1\right ) u^{\prime }-t -1&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.597 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{2 y+1} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.513 |
|
| \begin{align*}
x^{\prime }&={\mathrm e}^{t +x} \\
x \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.116 |
|
| \begin{align*}
x^{\prime }&=\frac {4 t^{2}+3 x^{2}}{2 x t} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
20.826 |
|
| \begin{align*}
x^{\prime }&=a x+b \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.865 |
|
| \begin{align*}
x^{\prime }&=\frac {2 x}{3 t}+\frac {2 t}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
68.100 |
|
| \begin{align*}
x^{\prime }&=a x+b x^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
25.169 |
|
| \begin{align*}
x^{2}+y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
19.989 |
|
| \begin{align*}
{y^{\prime }}^{2}-4 y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.474 |
|
| \begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
75.683 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
38.899 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
38.812 |
|
| \begin{align*}
x \tan \left (\frac {y}{x}\right )+y-x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
16.479 |
|
| \begin{align*}
\left (2 s^{2}+2 t s+t^{2}\right ) s^{\prime }+s^{2}+2 t s-t^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
22.707 |
|
| \begin{align*}
\sqrt {x +y}+\sqrt {x -y}+\left (\sqrt {x -y}-\sqrt {x +y}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
36.319 |
|
| \begin{align*}
\left (4 x -y\right ) y^{\prime }+2 x -5 y&=0 \\
y \left (1\right ) &= 4 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
59.433 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
37.228 |
|
| \begin{align*}
3 x -y-\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
41.424 |
|
| \begin{align*}
x^{2}+2 y^{2}+\left (4 y x -y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
24.094 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
51.360 |
|
| \begin{align*}
3 x -5 y+\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
113.406 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x -7 y}{3 y-8 x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
113.792 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x^{2}+y^{2}}{2 y x -x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
54.047 |
|
| \begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
35.500 |
|
| \begin{align*}
y x +x^{2} y^{\prime }&=\frac {y^{3}}{x} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
204.229 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
24.212 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
18.336 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
36.794 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
56.347 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
32.226 |
|
| \begin{align*}
x^{\prime }&=1-x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.694 |
|
| \begin{align*}
x^{\prime }&=\left (1+x\right ) \left (2-x\right ) \sin \left (x\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
16.070 |
|
| \begin{align*}
x^{\prime }&=-x^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.676 |
|
| \begin{align*}
x^{\prime }+p x&=q \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.587 |
|
| \begin{align*}
x^{\prime }&=\lambda x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.323 |
|
| \begin{align*}
m v^{\prime }&=-m g +k v^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
10.318 |
|
| \begin{align*}
x^{\prime }&=-x \left (k^{2}+x^{2}\right ) \\
x \left (0\right ) &= x_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✗ |
✓ |
✗ |
183.655 |
|
| \begin{align*}
x^{\prime }&=k x-x^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
13.918 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
54.057 |
|
| \begin{align*}
x y^{\prime }&=y+\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
24.208 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x -y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.672 |
|
| \begin{align*}
x \left (\ln \left (x \right )-\ln \left (y\right )\right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
50.999 |
|
| \begin{align*}
y&={y^{\prime }}^{4}-{y^{\prime }}^{3}-2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
123.819 |
|
| \begin{align*}
{y^{\prime }}^{2}+y^{2}&=4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.637 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
18.685 |
|
| \begin{align*}
y&=5 x y^{\prime }-{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.519 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
19.574 |
|
| \begin{align*}
y^{\prime }&=\frac {-3+x +y}{y-x +1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
32.722 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
18.650 |
|
| \begin{align*}
\left (y^{2}-x^{2}\right ) y^{\prime }+2 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
31.506 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 x y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.408 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x +y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.096 |
|
| \begin{align*}
y {y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.348 |
|
| \begin{align*}
y-x +\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
46.894 |
|
| \begin{align*}
x +y+\left (-x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
22.634 |
|
| \begin{align*}
x y^{\prime }-y&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
27.001 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
35.845 |
|
| \begin{align*}
2 \sqrt {t s}-s+t s^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
35.827 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
101.931 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
20.075 |
|
| \begin{align*}
\frac {y y^{\prime }+x}{\sqrt {x^{2}+y^{2}}}&=m \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
127.216 |
|
| \begin{align*}
y+\frac {x}{y^{\prime }}&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
19.545 |
|
| \begin{align*}
\frac {1}{x^{2}}+\frac {3 y^{2}}{x^{4}}&=\frac {2 y y^{\prime }}{x^{3}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
30.918 |
|
| \begin{align*}
y&=2 x y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.847 |
|
| \begin{align*}
y&={y^{\prime }}^{2} x +{y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.054 |
|
| \begin{align*}
y&=x \left (y^{\prime }+1\right )+{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.750 |
|
| \begin{align*}
y&=y {y^{\prime }}^{2}+2 x y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.329 |
|
| \begin{align*}
y&={y^{\prime }}^{2} x +{y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.966 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
19.314 |
|
| \begin{align*}
y^{\prime }-y^{2}&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.461 |
|
| \begin{align*}
y^{\prime }+3 y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.884 |
|
| \begin{align*}
{y^{\prime }}^{2}-4 y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.262 |
|
| \begin{align*}
y^{\prime }&=3 y^{{2}/{3}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.897 |
|
| \begin{align*}
y^{\prime }&=1-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.807 |
|
| \begin{align*}
y^{\prime }&=y+1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.654 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
16.870 |
|
| \begin{align*}
y^{\prime }&=4-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
14.454 |
|
| \begin{align*}
y^{\prime }&=1+y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.459 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x -y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.851 |
|
| \begin{align*}
y^{\prime }&=\ln \left (x +y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.345 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x -y}{x +3 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
43.434 |
|
| \begin{align*}
y^{\prime }&=\ln \left (-1+y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.378 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{-x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
43.339 |
|
| \begin{align*}
y^{\prime }&=\sqrt {\frac {y-4}{x}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
20.937 |
|
| \begin{align*}
y^{\prime }&=4 y-5 \\
y \left (1\right ) &= 4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.230 |
|
| \begin{align*}
y^{\prime }+3 y&=1 \\
y \left (-2\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.798 |
|
| \begin{align*}
y^{\prime }&=b +a y \\
y \left (c \right ) &= d \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.058 |
|
| \begin{align*}
y^{\prime }&=3 y \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.204 |
|
| \begin{align*}
y^{\prime }&=1-y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.548 |
|
| \begin{align*}
y^{\prime }&=1-y \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.804 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
55.773 |
|
| \begin{align*}
y^{\prime }&=4 y+1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.155 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
20.183 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.992 |
|
| \begin{align*}
y^{\prime }&=y^{3} \\
y \left (-1\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
20.897 |
|
| \begin{align*}
y^{\prime }&=y^{3} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
36.233 |
|
| \begin{align*}
y^{\prime }&=y^{3} \\
y \left (-1\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
19.490 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{-x +y} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.573 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{-x +y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.429 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{-x +y} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.658 |
|
| \begin{align*}
y^{\prime }&=2 y+1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.829 |
|
| \begin{align*}
y^{\prime }&=2-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{-y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.007 |
|
| \begin{align*}
x^{\prime }&=x^{2}+1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.571 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{2 y+1} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.338 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.747 |
|
| \begin{align*}
y^{\prime }&=\sec \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.943 |
|
| \begin{align*}
y^{\prime }&=-y^{2} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.576 |
|
| \begin{align*}
y^{\prime }&=-y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
5.343 |
|
| \begin{align*}
y^{\prime }&=2 y+1 \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.212 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{2 y+3} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.830 |
|
| \begin{align*}
y^{\prime }&=1-2 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.878 |
|
| \begin{align*}
y^{\prime }&=4 y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.078 |
|
| \begin{align*}
S^{\prime }&=S^{3}-2 S^{2}+S \\
S \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
18.746 |
|
| \begin{align*}
y^{\prime }&=y^{3}+y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
9.285 |
|
| \begin{align*}
\theta ^{\prime }&=\frac {9}{10}-\frac {11 \cos \left (\theta \right )}{10} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
23.875 |
|
| \begin{align*}
\theta ^{\prime }&=\frac {11}{10}-\frac {9 \cos \left (\theta \right )}{10} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
23.684 |
|
| \begin{align*}
v^{\prime }&=-\frac {v}{R C} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.251 |
|
| \begin{align*}
v^{\prime }&=\frac {K -v}{R C} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.544 |
|
| \begin{align*}
y^{\prime }&=2 y+1 \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.178 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
2.131 |
|
| \begin{align*}
y^{\prime }&=2-y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.052 |
|
| \begin{align*}
y^{\prime }&=-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.038 |
|
| \begin{align*}
y^{\prime }&=y^{3} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
8.336 |
|
| \begin{align*}
w^{\prime }&=w \cos \left (w\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.077 |
|
| \begin{align*}
w^{\prime }&=w \cos \left (w\right ) \\
w \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.931 |
|
| \begin{align*}
w^{\prime }&=\left (1-w\right ) \sin \left (w\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.545 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{-2+y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.404 |
|
| \begin{align*}
w^{\prime }&=3 w^{3}-12 w^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
10.692 |
|
| \begin{align*}
y^{\prime }&=1+\cos \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.385 |
|
| \begin{align*}
y^{\prime }&=\tan \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.073 |
|
| \begin{align*}
y^{\prime }&=y \cos \left (\frac {\pi y}{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.260 |
|
| \begin{align*}
y^{\prime }&=y \sin \left (\frac {\pi y}{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.275 |
|
| \begin{align*}
y^{\prime }&=y^{3}-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
11.307 |
|
| \begin{align*}
y^{\prime }&=\cos \left (\frac {\pi y}{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
5.023 |
|
| \begin{align*}
y^{\prime }&=y \sin \left (\frac {\pi y}{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.969 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
9.151 |
|
| \begin{align*}
y^{\prime }&=3 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.289 |
|
| \begin{align*}
y^{\prime }&=-\sin \left (y\right )^{5} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
16.146 |
|
| \begin{align*}
y^{\prime }&=\sin \left (y\right )^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.457 |
|
| \begin{align*}
y^{\prime }&=3-2 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.881 |
|
| \begin{align*}
y^{\prime }&=3+y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.806 |
|
| \begin{align*}
y^{\prime }&=1-y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
4.732 |
|
| \begin{align*}
y^{\prime }&=3-y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
3.143 |
|
| \begin{align*}
y^{\prime }&=3-\sin \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
24.619 |
|
| \begin{align*}
\left (-2+y\right ) y^{\prime }&=x -3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.656 |
|
| \begin{align*}
y^{\prime }&=2 \sqrt {y} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.251 |
|
| \begin{align*}
y^{\prime }+4 y&=8 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.908 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x +y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.190 |
|
| \begin{align*}
y^{\prime }&=y^{2}+9 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.905 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{2 x -3 y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.578 |
|
| \begin{align*}
y^{\prime }-4 y&=2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.937 |
|
| \begin{align*}
y^{\prime }&=\sin \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
23.487 |
|
| \begin{align*}
y^{\prime }&=\tan \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.178 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{-y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.041 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{-y}+1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.530 |
|
| \begin{align*}
y^{\prime }-2 y&=-10 \\
y \left (0\right ) &= 8 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.435 |
|
| \begin{align*}
y^{\prime }&=4 y+8 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.914 |
|
| \begin{align*}
2 y+y^{\prime }&=6 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.861 |
|
| \begin{align*}
y^{\prime }-3 y&=6 \\
y \left (0\right ) &= 5 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.540 |
|
| \begin{align*}
y^{\prime }-3 y&=6 \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.012 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{\left (3 x +3 y+2\right )^{2}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.556 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
19.673 |
|
| \begin{align*}
\cos \left (-4 y+8 x -3\right ) y^{\prime }&=2+2 \cos \left (-4 y+8 x -3\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.137 |
|
| \begin{align*}
y^{\prime }&=1+\left (-x +y\right )^{2} \\
y \left (0\right ) &= {\frac {1}{4}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.332 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.340 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
35.777 |
|
| \begin{align*}
3 y^{\prime }&=-2+\sqrt {2 x +3 y+4} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.568 |
|
| \begin{align*}
y^{\prime }&=4+\frac {1}{\sin \left (4 x -y\right )} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.254 |
|
| \begin{align*}
\left (-x +y\right ) y^{\prime }&=1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.941 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.358 |
|
| \begin{align*}
y^{\prime }&=2 \sqrt {2 x +y-3}-2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.582 |
|
| \begin{align*}
y^{\prime }&=2 \sqrt {2 x +y-3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.368 |
|
| \begin{align*}
x y^{\prime }-y&=\sqrt {y x +x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
15.310 |
|
| \begin{align*}
y^{\prime }&=\left (x -y+3\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.896 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
23.250 |
|
| \begin{align*}
4 x^{3} y+\left (x^{4}-y^{4}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
130.420 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x +y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.053 |
|
| \begin{align*}
x^{3}+y^{3}+x y^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.812 |
|
| \begin{align*}
x y y^{\prime }&=2 x^{2}+2 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.858 |
|
| \begin{align*}
y^{\prime }&=\frac {x +2 y}{x +2 y+3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.744 |
|
| \begin{align*}
y^{\prime }&=\frac {x +2 y}{2 x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.201 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\tan \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.954 |
|
| \begin{align*}
1-\left (x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.242 |
|
| \begin{align*}
y^{2}+1-y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.247 |
|
| \begin{align*}
x y y^{\prime }&=x^{2}+y x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
28.738 |
|
| \begin{align*}
\left (3-x +y\right )^{2} \left (y^{\prime }-1\right )&=1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.420 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{4 x +3 y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.904 |
|
| \begin{align*}
y^{\prime }&=\tan \left (6 x +3 y+1\right )-2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.948 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{4 x +3 y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.385 |
|
| \begin{align*}
{y^{\prime }}^{2}+y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.816 |
|
| \begin{align*}
2 y+y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.474 |
|
| \begin{align*}
2 y+y^{\prime }&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.016 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
21.208 |
|
| \begin{align*}
y^{\prime }&=y^{{1}/{5}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
48.957 |
|
| \begin{align*}
y^{\prime }&=6 y^{{2}/{3}} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.917 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y^{2}-1} \\
y \left (4\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
15.518 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y^{2}-1} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
15.845 |
|
| \begin{align*}
y^{\prime }&=\sqrt {25-y^{2}} \\
y \left (0\right ) &= 5 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
10.347 |
|
| \begin{align*}
y^{\prime }&=\sqrt {25-y^{2}} \\
y \left (4\right ) &= -5 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
86.464 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.189 |
|
| \begin{align*}
y^{\prime }&=-y^{3} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
26.314 |
|
| \begin{align*}
y^{\prime }+k y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.998 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{2 y+10 t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.556 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{3 y+2 t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.493 |
|
| \begin{align*}
y^{\prime }&=y^{3}-1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
59.776 |
|
| \begin{align*}
y^{\prime }&=y^{3}-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
12.286 |
|
| \begin{align*}
y^{\prime }&=\sqrt {\frac {y}{t}} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
23.931 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{t -y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
16.835 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x -y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.913 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{2 x -y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.405 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+3}{3 x +3 y+1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.388 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y+2}{2 x -2 y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.173 |
|
| \begin{align*}
y^{\prime }&=\left (x +y-4\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.647 |
|
| \begin{align*}
y^{\prime }&=3 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.801 |
|
| \begin{align*}
y^{\prime }&=-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.490 |
|
| \begin{align*}
-y+y^{\prime }&=10 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.588 |
|
| \begin{align*}
2 y t +\left (t^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
14.218 |
|
| \begin{align*}
3 t^{2}+3 y^{2}+6 t y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.535 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
17.158 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
70.855 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
50.546 |
|
| \begin{align*}
y t -y^{2}+t \left (t -3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
21.751 |
|
| \begin{align*}
t^{2}+y t +y^{2}-t y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
35.491 |
|
| \begin{align*}
y^{\prime }&=\frac {t +4 y}{4 t +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
23.000 |
|
| \begin{align*}
y+\left (t +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
27.817 |
|
| \begin{align*}
2 t^{2}-7 y t +5 y^{2}+t y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
77.904 |
|
| \begin{align*}
y+2 \sqrt {t^{2}+y^{2}}-t y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
24.272 |
|
| \begin{align*}
y^{2}&=\left (y t -4 t^{2}\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
27.619 |
|
| \begin{align*}
y-\left (3 \sqrt {y t}+t \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
29.286 |
|
| \begin{align*}
t \left (\ln \left (t \right )-\ln \left (y\right )\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
32.511 |
|
| \begin{align*}
t y^{\prime }-y-\sqrt {t^{2}+y^{2}}&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
18.143 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
40.165 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
18.999 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
12.731 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
12.522 |
|
| \begin{align*}
y&=-t y^{\prime }+\frac {{y^{\prime }}^{5}}{5} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.793 |
|
| \begin{align*}
y&=t {y^{\prime }}^{2}+3 {y^{\prime }}^{2}-2 {y^{\prime }}^{3} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
28.129 |
|
| \begin{align*}
y&=t \left (2-y^{\prime }\right )+2 {y^{\prime }}^{2}+1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.098 |
|
| \begin{align*}
3 t +\left (t -4 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
26.168 |
|
| \begin{align*}
y-t +\left (t +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
28.254 |
|
| \begin{align*}
y^{2}+\left (t^{2}+y t \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
93.879 |
|
| \begin{align*}
r^{\prime }&=\frac {r^{2}+t^{2}}{r t} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.959 |
|
| \begin{align*}
x^{\prime }&=\frac {5 t x}{t^{2}+x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
33.369 |
|
| \begin{align*}
y+y^{\prime }&=5 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.226 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
18.851 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x -y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✗ |
✓ |
9.928 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x -y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.735 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x^{2}-y}-x \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
23.424 |
|
| \begin{align*}
y^{\prime }&=\sqrt {1-y^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.357 |
|
| \begin{align*}
y^{\prime }&=\frac {y+1}{x -y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
24.931 |
|
| \begin{align*}
y^{\prime }&=\left (3 x -y\right )^{{1}/{3}}-1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.688 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.245 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.415 |
|
| \begin{align*}
y^{\prime }&=y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.384 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.761 |
|
| \begin{align*}
{\mathrm e}^{-y} y^{\prime }&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.360 |
|
| \begin{align*}
y^{\prime }&=a^{x +y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.635 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.424 |
|
| \begin{align*}
\left (x +y\right )^{2} y^{\prime }&=a^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
22.116 |
|
| \begin{align*}
{\mathrm e}^{y}&={\mathrm e}^{4 y} y^{\prime }+1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
91.768 |
|
| \begin{align*}
x y^{\prime }&=y+x \cos \left (\frac {y}{x}\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
9.022 |
|
| \begin{align*}
x y^{\prime }&=y \left (\ln \left (y\right )-\ln \left (x \right )\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
19.852 |
|
| \begin{align*}
x y^{\prime }&=y+\sqrt {y^{2}-x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
24.330 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
40.005 |
|
| \begin{align*}
y-x +\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
30.046 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
82.389 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
23.595 |
|
| \begin{align*}
x +y+\left (x -y-2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
24.181 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
21.321 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
10.606 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
14.153 |
|
| \begin{align*}
x +y+\left (x +y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.145 |
|
| \begin{align*}
3 x y^{2} y^{\prime }-2 y^{3}&=x^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
20.244 |
|
| \begin{align*}
x \left (2 x^{2}+y^{2}\right )+y \left (x^{2}+2 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
40.166 |
|
| \begin{align*}
\frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}}&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
89.704 |
|
| \begin{align*}
3 x^{2} y+y^{3}+\left (x^{3}+3 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
24.286 |
|
| \begin{align*}
y&={y^{\prime }}^{2} {\mathrm e}^{y^{\prime }} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.675 |
|
| \begin{align*}
y&=y^{\prime } \ln \left (y^{\prime }\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
11.707 |
|
| \begin{align*}
y&=\left (y^{\prime }-1\right ) {\mathrm e}^{y^{\prime }} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.788 |
|
| \begin{align*}
y^{{2}/{5}}+{y^{\prime }}^{{2}/{5}}&=a^{{2}/{5}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
9.696 |
|
| \begin{align*}
y&=y^{\prime } \left (1+y^{\prime } \cos \left (y^{\prime }\right )\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
2.585 |
|
| \begin{align*}
y&=\arcsin \left (y^{\prime }\right )+\ln \left (1+{y^{\prime }}^{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
6.201 |
|
| \begin{align*}
y&=x \left (y^{\prime }+1\right )+{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.928 |
|
| \begin{align*}
y&=2 x y^{\prime }+\sin \left (y^{\prime }\right ) \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.279 |
|
| \begin{align*}
y&={y^{\prime }}^{2} x -\frac {1}{y^{\prime }} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
109.871 |
|
| \begin{align*}
y&=\frac {3 x y^{\prime }}{2}+{\mathrm e}^{y^{\prime }} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
4.151 |
|
| \begin{align*}
{y^{\prime }}^{2}-4 y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.250 |
|
| \begin{align*}
y^{\prime }&=y^{{2}/{3}}+a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
9.023 |
|
| \begin{align*}
8 {y^{\prime }}^{3}-12 {y^{\prime }}^{2}&=-27 x +27 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
1.567 |
|
| \begin{align*}
y&={y^{\prime }}^{2}-x y^{\prime }+x \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
7.474 |
|
| \begin{align*}
\left (x y^{\prime }+y\right )^{2}&=y^{2} y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
55.093 |
|
| \begin{align*}
3 {y^{\prime }}^{2} x -6 y y^{\prime }+x +2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.109 |
|
| \begin{align*}
y^{\prime }&=\left (x -y\right )^{2}+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.815 |
|
| \begin{align*}
x^{3}-3 x y^{2}+\left (y^{3}-3 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
72.484 |
|
| \begin{align*}
\frac {1}{x^{2}-y x +y^{2}}&=\frac {y^{\prime }}{2 y^{2}-y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
95.180 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
36.191 |
|
| \begin{align*}
x^{2}+y^{2}-x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
16.543 |
|
| \begin{align*}
x -y+2+\left (x -y+3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.971 |
|
| \begin{align*}
y^{\prime }-1&={\mathrm e}^{x +2 y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.449 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
18.118 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
194.849 |
|
| \begin{align*}
y^{\prime }+{y^{\prime }}^{2} x -y&=0 \\
\end{align*} |
[_rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
4.136 |
|
| \begin{align*}
y^{\prime }&=\frac {3-2 x}{y} \\
y \left (1\right ) &= -6 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.894 |
|
| \begin{align*}
y^{\prime }&=\frac {b +a y}{d +c y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.643 |
|
| \begin{align*}
y^{\prime }&=\frac {t -y}{2 t +5 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
36.542 |
|
| \begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
77.033 |
|
| \begin{align*}
y^{3}+y^{\prime }&=0 \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
22.333 |
|
| \begin{align*}
3+2 x +\left (-2+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
18.656 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
42.231 |
|
| \begin{align*}
y^{\prime }&=-\frac {4 x +2 y}{2 x +3 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
32.685 |
|
| \begin{align*}
y^{\prime }&=-\frac {4 x -2 y}{2 x -3 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
49.365 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
35.695 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
38.631 |
|
| \begin{align*}
\frac {\left (3 x^{3}-x y^{2}\right ) y^{\prime }}{y^{3}+3 x^{2} y}&=1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
25.856 |
|
| \begin{align*}
y+\sqrt {x^{2}-y^{2}}&=x y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
69.402 |
|
| \begin{align*}
x y y^{\prime }&=\left (x +y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
32.530 |
|
| \begin{align*}
y^{\prime }&=\frac {4 y-7 x}{5 x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
36.452 |
|
| \begin{align*}
x y^{\prime }-4 \sqrt {y^{2}-x^{2}}&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
48.076 |
|
| \begin{align*}
\left (y+x \,{\mathrm e}^{\frac {x}{y}}\right ) y^{\prime }&={\mathrm e}^{\frac {x}{y}} y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
17.769 |
|
| \begin{align*}
y^{\prime }&=r y-k^{2} y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
16.880 |
|
| \begin{align*}
y^{\prime }&=a y+b y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
25.325 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
39.157 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
24.655 |
|
| \begin{align*}
4 x y y^{\prime }&=8 x^{2}+5 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
36.504 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y x}{x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
16.089 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (1+\ln \left (y\right )-\ln \left (x \right )\right )}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.046 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=x y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
54.034 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=-x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.053 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
54.477 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
6.309 |
|
| \begin{align*}
\left (x +y\right )^{2} y^{\prime }&=a^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.575 |
|
| \begin{align*}
\frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
8.301 |
|
| \begin{align*}
{y^{\prime }}^{2} x +2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.321 |
|
| \begin{align*}
{y^{\prime }}^{3}+y^{3}-3 y y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
68.551 |
|
| \begin{align*}
y&={y^{\prime }}^{2} {\mathrm e}^{y^{\prime }} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.086 |
|
| \begin{align*}
y^{2} \left (y^{\prime }-1\right )&=\left (2-y^{\prime }\right )^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.290 |
|
| \begin{align*}
y&=\frac {k \left (y y^{\prime }+x \right )}{\sqrt {1+{y^{\prime }}^{2}}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
✗ |
216.297 |
|
| \begin{align*}
x&=y y^{\prime }+a {y^{\prime }}^{2} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
68.192 |
|
| \begin{align*}
y&={y^{\prime }}^{2} x +{y^{\prime }}^{3} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
69.066 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 x y^{\prime }+2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.096 |
|
| \begin{align*}
y^{\prime }&=\sqrt {-x +y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.019 |
|
| \begin{align*}
y^{\prime }&=\sqrt {-x +y}+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.844 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.457 |
|
| \begin{align*}
4 x -2 y y^{\prime }+{y^{\prime }}^{2} x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.454 |
|
| \begin{align*}
{y^{\prime }}^{2} x +2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.629 |
|
| \begin{align*}
y^{2} \left (y^{\prime }-1\right )&=\left (2-y^{\prime }\right )^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.200 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}-2 x y y^{\prime }+2 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.532 |
|
| \begin{align*}
y^{\prime }&=k y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.188 |
|
| \begin{align*}
2 x y y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
16.709 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{y x -x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
68.040 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{3 x -2 y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.791 |
|
| \begin{align*}
v^{\prime }&=g -\frac {k v^{2}}{m} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.849 |
|
| \begin{align*}
x^{2}-2 y^{2}+x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
55.444 |
|
| \begin{align*}
x -y-\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
20.634 |
|
| \begin{align*}
x y^{\prime }&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
18.402 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x -y+1\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.260 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+4}{x -y-6} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.919 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+4}{x +y-6} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.999 |
|
| \begin{align*}
2 x -2 y+\left (-1+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.858 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y-1}{x +4 y+2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
223.433 |
|
| \begin{align*}
\frac {4 y^{2}-2 x^{2}}{4 x y^{2}-x^{3}}+\frac {\left (8 y^{2}-x^{2}\right ) y^{\prime }}{4 y^{3}-x^{2} y}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
36.023 |
|
| \begin{align*}
\left (3 x^{2}-y^{2}\right ) y^{\prime }-2 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
16.442 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=-x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.554 |
|
| \begin{align*}
x y^{\prime }+y&=y^{\prime } \sqrt {y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
857.964 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
21.967 |
|
| \begin{align*}
x y^{\prime }&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
23.434 |
|
| \begin{align*}
x y y^{\prime }&=x^{2} y^{\prime }+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
68.481 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
9.253 |
|
| \begin{align*}
y^{\prime } \ln \left (x -y\right )&=1+\ln \left (x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.539 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
22.507 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y \,{\mathrm e}^{\frac {x^{2}}{y^{2}}}}{y^{2}+y^{2} {\mathrm e}^{\frac {x^{2}}{y^{2}}}+2 x^{2} {\mathrm e}^{\frac {x^{2}}{y^{2}}}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
115.187 |
|
| \begin{align*}
y^{\prime }&=\frac {x +2 y+2}{y-2 x} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.552 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
15.418 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
17.699 |
|
| \begin{align*}
x^{\prime }&=b \,{\mathrm e}^{x} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.957 |
|
| \begin{align*}
x^{\prime }&=\sqrt {x^{2}-1} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.194 |
|
| \begin{align*}
x^{\prime }&=2 \sqrt {x} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
3.029 |
|
| \begin{align*}
x^{\prime }&=\cos \left (\frac {x}{t}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.649 |
|
| \begin{align*}
x^{\prime }&=-\lambda x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.467 |
|
| \begin{align*}
y^{\prime }+c y&=a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.099 |
|
| \begin{align*}
x^{\prime }&=k \left (A -n x\right ) \left (M -m x\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.576 |
|
| \begin{align*}
y^{2}&=x \left (-x +y\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
69.461 |
|
| \begin{align*}
2 x^{2} y+y^{3}-x^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
78.055 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
69.056 |
|
| \begin{align*}
\frac {2 x}{y^{3}}+\left (\frac {1}{y^{2}}-\frac {3 x^{2}}{y^{4}}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
14.498 |
|
| \begin{align*}
{y^{\prime }}^{2} x +2 y^{\prime }-y&=0 \\
\end{align*} |
[_rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.323 |
|
| \begin{align*}
2 {y^{\prime }}^{3}+{y^{\prime }}^{2}-y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
0.835 |
|
| \begin{align*}
y^{\prime }&=1+\frac {2 y}{x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.047 |
|
| \begin{align*}
y-2 x y^{\prime }-y {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.172 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
23.999 |
|
| \begin{align*}
5 x y y^{\prime }-x^{2}-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
20.125 |
|
| \begin{align*}
\left (x^{2}+3 y x -y^{2}\right ) y^{\prime }-3 y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
22.998 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
23.458 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
25.715 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
82.740 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
61.193 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
56.342 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
10.398 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
10.398 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
10.405 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
10.010 |
|
| \begin{align*}
x&={y^{\prime }}^{2}+y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.896 |
|
| \begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
20.672 |
|
| \begin{align*}
y^{2}+\left (y x +x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
78.357 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
61.677 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
74.422 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
84.217 |
|
| \begin{align*}
x^{2}-4 y x -2 y^{2}+\left (y^{2}-4 y x -2 x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
17.678 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
69.279 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
17.734 |
|
| \begin{align*}
y^{3}-2 x^{2} y+\left (2 x y^{2}-x^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
32.306 |
|
| \begin{align*}
\left (x +y\right )^{2} y^{\prime }&=a^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.718 |
|
| \begin{align*}
x y^{\prime }-y&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.821 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
16.220 |
|
| \begin{align*}
y y^{\prime }+x&=m \left (x y^{\prime }-y\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
26.259 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.359 |
|
| \begin{align*}
\left (y^{2}-x^{2}\right ) y^{\prime }+2 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
19.536 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
11.342 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=x y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
9.362 |
|
| \begin{align*}
\left (x -y\right )^{2} y^{\prime }&=a^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.461 |
|
| \begin{align*}
x -y y^{\prime }&=a {y^{\prime }}^{2} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
58.990 |
|
| \begin{align*}
y&=-a y^{\prime }+\frac {c +a \arcsin \left (y^{\prime }\right )}{\sqrt {1-{y^{\prime }}^{2}}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
9.349 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }+a x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
✓ |
1.029 |
|
| \begin{align*}
y&=2 y^{\prime }+3 {y^{\prime }}^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.693 |
|
| \begin{align*}
y^{2}&=a^{2} \left (1+{y^{\prime }}^{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.812 |
|
| \begin{align*}
y&=y {y^{\prime }}^{2}+2 x y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.069 |
|
| \begin{align*}
y&=x \left (y^{\prime }+1\right )+{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.732 |
|
| \begin{align*}
{\mathrm e}^{4 x} \left (y^{\prime }-1\right )+{\mathrm e}^{2 y} {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.483 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}-2 x y y^{\prime }+2 y^{2}-x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.849 |
|
| \begin{align*}
a y {y^{\prime }}^{2}+\left (2 x -b \right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.705 |
|
| \begin{align*}
3 y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2}+4 y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.227 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) \left (y^{\prime }+1\right )^{2}-2 \left (x +y\right ) \left (y^{\prime }+1\right ) \left (y y^{\prime }+x \right )+\left (y y^{\prime }+x \right )^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
90.435 |
|
| \begin{align*}
\left (y y^{\prime }+n x \right )^{2}&=\left (y^{2}+n \,x^{2}\right ) \left (1+{y^{\prime }}^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
✓ |
4.053 |
|
| \begin{align*}
{y^{\prime }}^{3}+m {y^{\prime }}^{2}&=a \left (y+m x \right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
25.817 |
|
| \begin{align*}
{\mathrm e}^{3 x} \left (y^{\prime }-1\right )+{\mathrm e}^{2 y} {y^{\prime }}^{3}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
86.372 |
|
| \begin{align*}
y-\frac {1}{\sqrt {1+{y^{\prime }}^{2}}}&=b \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.599 |
|
| \begin{align*}
\sqrt {x}\, y^{\prime }&=\sqrt {y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.427 |
|
| \begin{align*}
\left (y^{\prime }+1\right )^{3}&=\frac {7 \left (x +y\right ) \left (1-y^{\prime }\right )^{3}}{4 a} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
23.838 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.592 |
|
| \begin{align*}
a {y^{\prime }}^{3}&=27 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.237 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }+a x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
✓ |
1.444 |
|
| \begin{align*}
\left (8 {y^{\prime }}^{3}-27\right ) x&=12 y {y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.925 |
|
| \begin{align*}
y-x +\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
21.783 |
|
| \begin{align*}
x^{3}+3 x y^{2}+\left (y^{3}+3 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
21.372 |
|
| \begin{align*}
y y^{\prime }+x&=m \left (x y^{\prime }-y\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
12.747 |
|
| \begin{align*}
\left (x +y-1\right ) y^{\prime }&=x +y+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.760 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
10.839 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
10.372 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }&=y x +x^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.934 |
|
| \begin{align*}
x^{2}-y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.635 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\tan \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.603 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
10.421 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
10.309 |
|
| \begin{align*}
y^{2}&=\left (y x -x^{2}\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
19.349 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
65.970 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
43.992 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
11.832 |
|
| \begin{align*}
x y^{\prime }-y&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.245 |
|
| \begin{align*}
\left (3 x^{2}+y^{2}\right ) y y^{\prime }+x \left (x^{2}+3 y^{2}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
20.524 |
|
| \begin{align*}
x^{2}+3 y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.559 |
|
| \begin{align*}
y^{\prime }&=\frac {1+2 x -y}{x +2 y-3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.276 |
|
| \begin{align*}
\left (x -y\right ) y^{\prime }&=x +y+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
24.910 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
12.457 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
19.260 |
|
| \begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
17.232 |
|
| \begin{align*}
\frac {\left (x +y-a \right ) y^{\prime }}{x +y-b}&=\frac {x +y+a}{x +y+b} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.732 |
|
| \begin{align*}
\left (x -y\right )^{2} y^{\prime }&=a^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.040 |
|
| \begin{align*}
\left (x +y\right )^{2} y^{\prime }&=a^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.488 |
|
| \begin{align*}
y^{\prime }&=\left (4 x +y+1\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.637 |
|
| \begin{align*}
x y^{\prime }-y&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.537 |
|
| \begin{align*}
y y^{\prime }+x&=m \left (x y^{\prime }-y\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
12.541 |
|
| \begin{align*}
{x^{\prime }}^{2}&=k^{2} \left (1-{\mathrm e}^{-\frac {2 g x}{k^{2}}}\right ) \\
x \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
4.583 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
8.525 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x +y\right )+\cos \left (x +y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
52.549 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=x y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
15.824 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
72.490 |
|
| \begin{align*}
y&=3 x +a \ln \left (y^{\prime }\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.319 |
|
| \begin{align*}
{y^{\prime }}^{2}-y y^{\prime }+x&=0 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.973 |
|
| \begin{align*}
y&=x +a \arctan \left (y^{\prime }\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
33.810 |
|
| \begin{align*}
3 {y^{\prime }}^{5}-y y^{\prime }+1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.577 |
|
| \begin{align*}
y&={y^{\prime }}^{2} x +y^{\prime } \\
\end{align*} |
[_rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.792 |
|
| \begin{align*}
{y^{\prime }}^{2} x +a x&=2 y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
✓ |
1.811 |
|
| \begin{align*}
{y^{\prime }}^{3}+y^{\prime }&={\mathrm e}^{y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
5.104 |
|
| \begin{align*}
y&=\sin \left (y^{\prime }\right )-y^{\prime } \cos \left (y^{\prime }\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
12.833 |
|
| \begin{align*}
x&=y y^{\prime }-{y^{\prime }}^{2} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.518 |
|
| \begin{align*}
\left (2 x -b \right ) y^{\prime }&=y-a y {y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.181 |
|
| \begin{align*}
x&=y+a \ln \left (y^{\prime }\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.169 |
|
| \begin{align*}
y {y^{\prime }}^{2}+2 x y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.661 |
|
| \begin{align*}
4 y {y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.350 |
|
| \begin{align*}
y {y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.662 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}-2 x y y^{\prime }+2 y^{2}&=x^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.428 |
|
| \begin{align*}
y&=x y^{\prime }+x \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
40.855 |
|
| \begin{align*}
y&=\frac {2 a {y^{\prime }}^{2}}{\left (1+{y^{\prime }}^{2}\right )^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.546 |
|
| \begin{align*}
-x y^{\prime }+y&=y y^{\prime }+x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.508 |
|
| \begin{align*}
a^{2} y {y^{\prime }}^{2}-4 x y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
28.566 |
|
| \begin{align*}
y y^{\prime }+x&=a {y^{\prime }}^{2} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
24.375 |
|
| \begin{align*}
2 y&=x y^{\prime }+\frac {a}{y^{\prime }} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
4.319 |
|
| \begin{align*}
y&=\sqrt {1+{y^{\prime }}^{2}}+a y^{\prime } \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
16.930 |
|
| \begin{align*}
y&=a y^{\prime }+b {y^{\prime }}^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.502 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }+a x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
✓ |
1.922 |
|
| \begin{align*}
{y^{\prime }}^{2}+y^{2}&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.147 |
|
| \begin{align*}
y {y^{\prime }}^{2}-2 x y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.911 |
|
| \begin{align*}
3 {y^{\prime }}^{2} x -6 y y^{\prime }+x +2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.234 |
|
| \begin{align*}
\left (1-y^{2}\right ) {y^{\prime }}^{2}&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
10.911 |
|
| \begin{align*}
{y^{\prime }}^{2}&=\left (4 y+1\right ) \left (y^{\prime }-y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
9.090 |
|
| \begin{align*}
8 x {y^{\prime }}^{3}&=y \left (12 {y^{\prime }}^{2}-9\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.414 |
|
| \begin{align*}
y^{2}+\left (y x +x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
91.812 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
49.796 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
14.701 |
|
| \begin{align*}
y^{3}-2 x^{2} y+\left (2 x y^{2}-x^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
47.792 |
|
| \begin{align*}
y-\frac {1}{\sqrt {1+{y^{\prime }}^{2}}}&=b \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.918 |
|
| \begin{align*}
y&=\frac {x}{y^{\prime }}-a y^{\prime } \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
72.451 |
|
| \begin{align*}
{y^{\prime }}^{3}+m {y^{\prime }}^{2}&=a \left (y+m x \right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
31.217 |
|
| \begin{align*}
a y {y^{\prime }}^{2}+\left (2 x -b \right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.901 |
|
| \begin{align*}
y&=x \left (y^{\prime }+1\right )+{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.295 |
|
| \begin{align*}
{\mathrm e}^{3 x} \left (y^{\prime }-1\right )+{\mathrm e}^{2 y} {y^{\prime }}^{3}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
96.226 |
|
| \begin{align*}
y-2 x y^{\prime }+a y {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.917 |
|
| \begin{align*}
\left (y y^{\prime }+n x \right )^{2}&=\left (y^{2}+n \,x^{2}\right ) \left (1+{y^{\prime }}^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
✓ |
10.938 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) \left (y^{\prime }+1\right )^{2}-2 \left (x +y\right ) \left (y^{\prime }+1\right ) \left (y y^{\prime }+x \right )+\left (y y^{\prime }+x \right )^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
121.760 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.158 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{3}+\left (2 x +y\right ) y y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
52.036 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }+x +2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.849 |
|
| \begin{align*}
{y^{\prime }}^{2} y^{2} \cos \left (a \right )^{2}-2 y^{\prime } x y \sin \left (a \right )^{2}+y^{2}-x^{2} \sin \left (a \right )^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
77.649 |
|
| \begin{align*}
x^{2}-y x +y^{2}-x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
21.276 |
|
| \begin{align*}
x^{2}+2 y x -4 y^{2}-\left (x^{2}-8 y x -4 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
15.933 |
|
| \begin{align*}
y^{\prime }&=k y-c y^{2} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
12.830 |
|
| \begin{align*}
y^{\prime }&=\cos \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
21.832 |
|
| \begin{align*}
y^{\prime }&=y^{2} \left (y+1\right ) \left (y-4\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
126.154 |
|
| \begin{align*}
x^{\prime }&=\mu -x^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
8.496 |
|
| \begin{align*}
x^{\prime }&=x-\frac {\mu x}{x^{2}+1} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
12.865 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+1}{x +2}-{\mathrm e}^{\frac {x +y+1}{x +2}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
25.829 |
|
| \begin{align*}
y^{\prime }&=\frac {x +2 y+1}{2 x +2+y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
37.201 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +y+1}{x +2 y+2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
121.046 |
|
| \begin{align*}
y^{\prime }&=3 y^{{2}/{3}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.264 |
|
| \begin{align*}
y^{\prime }&=\left (x -y+3\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.252 |
|
| \begin{align*}
y&=x y^{\prime }-\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.271 |
|
| \begin{align*}
y&={y^{\prime }}^{2} x +\ln \left ({y^{\prime }}^{2}\right ) \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
21.053 |
|
| \begin{align*}
x&=y \left (y^{\prime }+\frac {1}{y^{\prime }}\right )+{y^{\prime }}^{5} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.436 |
|
| \begin{align*}
x^{\prime }+\ln \left (3\right ) x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.799 |
|
| \begin{align*}
x^{\prime }+4 x&=4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.199 |
|
| \begin{align*}
x^{\prime }&=-2 x+3 \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.862 |
|
| \begin{align*}
x^{\prime }&=k x \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.141 |
|
| \begin{align*}
x^{\prime }+k x&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.235 |
|
| \begin{align*}
x^{\prime }-k^{2} x&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.297 |
|
| \begin{align*}
x^{\prime }&=\frac {3 x^{{1}/{3}}}{2} \\
x \left (0\right ) &= a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
5.973 |
|
| \begin{align*}
x^{\prime }&=\sqrt {1-x^{2}} \\
x \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
38.750 |
|
| \begin{align*}
x^{\prime }&=x^{{1}/{4}} \\
x \left (0\right ) &= a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
4.329 |
|
| \begin{align*}
x^{\prime }&=x^{p} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.151 |
|
| \begin{align*}
x^{\prime }&=\sin \left (x\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
22.309 |
|
| \begin{align*}
x^{\prime }&=\arctan \left (x\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.130 |
|
| \begin{align*}
x^{\prime }&=\ln \left (x^{2}+1\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.269 |
|
| \begin{align*}
x^{\prime }&=x^{2}+1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.125 |
|
| \begin{align*}
x^{\prime }&=x^{2}-1 \\
x \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
2.853 |
|
| \begin{align*}
x^{\prime }&=\sqrt {1-x^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.789 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
26.770 |
|
| \begin{align*}
x +y+\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
21.436 |
|
| \begin{align*}
x^{2}+2 y x +2 y^{2}+\left (x^{2}+4 y x +5 y^{2}\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
63.518 |
|
| \begin{align*}
x^{\prime }&=\frac {3 x^{2}-2 t^{2}}{x t} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
20.326 |
|
| \begin{align*}
x^{\prime }&=\frac {t^{2}+x^{2}}{2 x t} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
24.088 |
|
| \begin{align*}
x^{\prime }&=\frac {x-t +1}{x-t +2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.062 |
|
| \begin{align*}
x^{\prime }&=\frac {x-t}{x-t +1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.944 |
|
| \begin{align*}
x^{\prime }&=-\frac {x+t +1}{x-t +1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.634 |
|
| \begin{align*}
{x^{\prime }}^{2}&=-4 x+4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.646 |
|
| \begin{align*}
x^{\prime }&=\lambda x-x^{5} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.292 |
|
| \begin{align*}
x^{\prime }&=\lambda x-x^{3}-x^{5} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
1.878 |
|
| \begin{align*}
y^{\prime }&=y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.218 |
|
| \begin{align*}
y^{\prime }&=6 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.658 |
|
| \begin{align*}
y^{\prime }&=-5 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.613 |
|
| \begin{align*}
y^{\prime }-k y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.671 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
11.910 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
11.711 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
47.916 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
42.184 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
12.718 |
|
| \begin{align*}
x -y+\left (x -4 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
64.798 |
|
| \begin{align*}
x^{2}-y x +y^{2}-x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
24.475 |
|
| \begin{align*}
x^{2}-2 y^{2}+x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✗ |
60.649 |
|
| \begin{align*}
y x +\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.553 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+3 x +y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
28.211 |
|
| \begin{align*}
y^{2}-x^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
53.719 |
|
| \begin{align*}
y^{\prime }&=\sqrt {1-\frac {y^{2}}{x^{2}}}+\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
45.870 |
|
| \begin{align*}
2 x y y^{\prime }&=y^{2}-x^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.270 |
|
| \begin{align*}
x +y-\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.587 |
|
| \begin{align*}
x^{2}-3 y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
64.792 |
|
| \begin{align*}
x y y^{\prime }+x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.643 |
|
| \begin{align*}
x y^{\prime }-y&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.872 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y}{x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
17.758 |
|
| \begin{align*}
y+\sqrt {x^{2}+y^{2}}-x y^{\prime }&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
14.957 |
|
| \begin{align*}
2 y+y^{\prime }&=1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.923 |
|
| \begin{align*}
y^{\prime }-3 y&=6 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.206 |
|
| \begin{align*}
y^{\prime }&=\frac {x -2 y}{2 x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
25.436 |
|
| \begin{align*}
y^{\prime } \left (x +\frac {x^{2}}{y}\right )&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
79.336 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
24.365 |
|
| \begin{align*}
2 y+y^{\prime }&=0 \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.821 |
|
| \begin{align*}
2 y-1+\left (3 x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
38.070 |
|
| \begin{align*}
2 y+y^{\prime }&=1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.059 |
|
| \begin{align*}
y^{\prime }-5 y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.081 |
|
| \begin{align*}
y^{\prime }&=-x^{2}-x -1-\left (2 x +1\right ) y-y^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
8.164 |
|
| \begin{align*}
2 y^{\prime }+y-2 y^{\prime } \ln \left (y^{\prime }\right )&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
8.387 |
|
| \begin{align*}
{y^{\prime }}^{2}-4 y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.125 |
|
| \begin{align*}
y-\frac {x y^{\prime }}{2}-\frac {x}{2 y^{\prime }}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.861 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+1}{x +2 y+3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
72.520 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+1}{x +y+2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.352 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
9.842 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
18.066 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
49.704 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x +y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.440 |
|
| \begin{align*}
y^{\prime }&=\alpha \left (A -y\right ) y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
13.689 |
|
| \begin{align*}
y^{\prime }-k y&=A \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.347 |
|
| \begin{align*}
L i^{\prime }+R i&=E_{0} \\
i \left (0\right ) &= i_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.156 |
|
| \begin{align*}
x&=y-{y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.735 |
|
| \begin{align*}
y&=2 x y^{\prime }-{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.504 |
|
| \begin{align*}
y&=2 x +y^{\prime }-\frac {{y^{\prime }}^{3}}{3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
92.661 |
|
| \begin{align*}
y {y^{\prime }}^{2}-2 x y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.348 |
|
| \begin{align*}
2 {y^{\prime }}^{2}-2 y y^{\prime }-1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.974 |
|
| \begin{align*}
y&=x y^{\prime }-\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
16.950 |
|
| \begin{align*}
3 x^{2}+2 y x +4 y^{2}+\left (20 x^{2}+6 y x +y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
27.231 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
28.576 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
19.582 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) \left (x y^{\prime }+y\right )&=x y \left (x y^{\prime }-y\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
60.937 |
|
| \begin{align*}
2-x -y+\left (x +y+3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.860 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
39.650 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
13.401 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
52.687 |
|
| \begin{align*}
x y \left (x y^{\prime }+y\right )&=4 x^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
19.104 |
|
| \begin{align*}
\left (1+{\mathrm e}^{-\frac {y}{x}}\right ) y^{\prime }+1-\frac {y}{x}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
21.015 |
|
| \begin{align*}
R q^{\prime }+\frac {q}{c}&=E \\
q \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.968 |
|
| \begin{align*}
3 x^{2}+2 y x -2 y^{2}+\left (2 x^{2}+6 y x +y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
21.754 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
129.203 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
14.410 |
|
| \begin{align*}
2 {y^{\prime }}^{3}+3 {y^{\prime }}^{2}&=x +y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
1.447 |
|
| \begin{align*}
x +y {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.760 |
|
| \begin{align*}
2 {y^{\prime }}^{2}+y y^{\prime }-y^{4}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
15.159 |
|
| \begin{align*}
y&=4 {y^{\prime }}^{2} x +2 x y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.286 |
|
| \begin{align*}
y-{y^{\prime }}^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.807 |
|
| \begin{align*}
{y^{\prime }}^{2} x&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.691 |
|
| \begin{align*}
y^{\prime }+y&=0 \\
y \left (3\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.730 |
|
| \begin{align*}
y^{\prime }&=5 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.199 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y}{x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
21.774 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y \,{\mathrm e}^{\frac {x^{2}}{y^{2}}}}{y^{2}+y^{2} {\mathrm e}^{\frac {x^{2}}{y^{2}}}+2 x^{2} {\mathrm e}^{\frac {x^{2}}{y^{2}}}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
116.869 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y \,{\mathrm e}^{\frac {x^{2}}{y^{2}}}}{y^{2}+y^{2} {\mathrm e}^{\frac {x^{2}}{y^{2}}}+2 x^{2} {\mathrm e}^{\frac {x^{2}}{y^{2}}}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
81.734 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+2 y^{2}}{y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.612 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y^{2}}{y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
16.925 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x +\sqrt {y x}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
38.560 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.795 |
|
| \begin{align*}
y^{\prime }-3 y&=6 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.396 |
|
| \begin{align*}
y^{\prime }-5 y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.313 |
|
| \begin{align*}
y^{\prime }+5 y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.258 |
|
| \begin{align*}
y^{\prime }-2 y&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.129 |
|
| \begin{align*}
y^{\prime }-5 y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.437 |
|
| \begin{align*}
{y^{\prime }}^{3}&=y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
218.561 |
|
| \begin{align*}
y+\left (2 x -3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
35.551 |
|
| \begin{align*}
y^{\prime }-2 y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.329 |
|
| \begin{align*}
y^{\prime }&=\frac {-x +3}{y+5} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.756 |
|
| \begin{align*}
y^{\prime }&=y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.250 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{y} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.364 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
39.967 |
|
| \begin{align*}
y^{\prime }&=y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
16.164 |
|
| \begin{align*}
y^{\prime }&=y^{p} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
14.644 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.452 |
|
| \begin{align*}
y^{\prime }&=\sqrt {-x +y}+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.764 |
|
| \begin{align*}
i^{\prime }+5 i&=10 \\
i \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.246 |
|
| \begin{align*}
x^{2}-y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
23.269 |
|
| \begin{align*}
x +2+\left (2 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
45.917 |
|
| \begin{align*}
x y^{\prime }&=y-\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
24.693 |
|
| \begin{align*}
y&=\left (2 x +3 y\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
82.610 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{2 y}+\frac {y}{2 x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
33.470 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {x^{2}+y^{2}}}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
53.872 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +5 y}{2 x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
146.321 |
|
| \begin{align*}
y^{\prime }&=\frac {6 x^{2}-5 y x -2 y^{2}}{6 x^{2}-8 y x +y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
44.560 |
|
| \begin{align*}
y^{\prime }&=\sqrt {2 x +3 y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.613 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
34.838 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
215.521 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
19.717 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
17.679 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {x +y}+\sqrt {x -y}}{-\sqrt {x -y}+\sqrt {x +y}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
47.717 |
|
| \begin{align*}
y^{\prime }&=\frac {1+\sqrt {x -y}}{1-\sqrt {x -y}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.090 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y}{x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
44.822 |
|
| \begin{align*}
2 x y y^{\prime }&=x^{2}-y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
26.336 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
42.015 |
|
| \begin{align*}
y^{2}+2 x^{2}+x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
27.763 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
23.158 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x -3 y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.938 |
|
| \begin{align*}
x -\sqrt {x^{2}+y^{2}}+\left (y-\sqrt {x^{2}+y^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
97.595 |
|
| \begin{align*}
y^{\prime }&=3 y^{{2}/{3}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
10.281 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.769 |
|
| \begin{align*}
x^{2}+y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
29.408 |
|
| \begin{align*}
y^{\prime }&=\frac {x +2 y}{y-2 x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
47.430 |
|
| \begin{align*}
x^{2}-y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
50.194 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.026 |
|
| \begin{align*}
x y^{\prime }-y&=x \cos \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
18.408 |
|
| \begin{align*}
n^{\prime }&=-a n \\
n \left (0\right ) &= n_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.971 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
33.207 |
|
| \begin{align*}
y^{2}&=\left (x^{2}+2 y x \right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
91.246 |
|
| \begin{align*}
s^{\prime }&=\frac {1}{s+t +1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.892 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
25.041 |
|
| \begin{align*}
x y^{\prime }+y \ln \left (x \right )&=\ln \left (y\right ) y+y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
35.946 |
|
| \begin{align*}
y^{\prime }&=\frac {x +3 y}{x -3 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
65.322 |
|
| \begin{align*}
{\mathrm e}^{2 x -y}+{\mathrm e}^{y-2 x} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.953 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
67.201 |
|
| \begin{align*}
y^{\prime }&=1-\left (x -y\right )^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
11.848 |
|
| \begin{align*}
y^{\prime }&=\frac {2}{x +2 y-3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.992 |
|
| \begin{align*}
y^{\prime }&=\tan \left (x +y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.961 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x +3 y}+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.787 |
|
| \begin{align*}
{y^{\prime }}^{2}+\left (3 y-2 x \right ) y^{\prime }-6 y&=0 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
56.033 |
|
| \begin{align*}
y^{\prime }&=\sqrt {\frac {5 x -6 y}{5 x +6 y}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
101.184 |
|
| \begin{align*}
x^{2}+y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
33.440 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y}{x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
57.458 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y^{2}}{y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
27.235 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}-\frac {x}{y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
26.312 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y+1}{x +y+1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
43.102 |
|
| \begin{align*}
y^{\prime }+3 y&=5 \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.543 |
|
| \begin{align*}
p^{\prime }&=15-20 p \\
p \left (0\right ) &= {\frac {7}{10}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.839 |
|
| \begin{align*}
y^{\prime }+y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.944 |
|
| \begin{align*}
y^{\prime }-y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.826 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.323 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y^{2}}{2 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.977 |
|
| \begin{align*}
y^{\prime }&=-\frac {x^{2}+y^{2}}{2 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.395 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
1.575 |
|
| \begin{align*}
y^{\prime }&=y^{{2}/{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.754 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
9.497 |
|
| \begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.276 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.516 |
|
| \begin{align*}
p^{\prime }&=a p-b p^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.704 |
|
| \begin{align*}
x^{\prime }&=k \left (a -x\right ) \left (b -x\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
10.875 |
|
| \begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.411 |
|
| \begin{align*}
x -y+\left (y-x +2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.414 |
|
| \begin{align*}
x +y+\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.214 |
|
| \begin{align*}
y^{\prime }&=\frac {y-x +1}{3-x +y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.021 |
|
| \begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.603 |
|
| \begin{align*}
x^{2}+y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.957 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.557 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
4.655 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
23.953 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
4.108 |
|
| \begin{align*}
y-\left (x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.655 |
|
| \begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.560 |
|
| \begin{align*}
3 y+\left (7 x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.363 |
|
| \begin{align*}
x -y+\left (2 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.425 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.709 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y}{x +y+2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.595 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +y-4}{x -y+1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
21.463 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
26.398 |
|
| \begin{align*}
y^{\prime }&=\frac {5 x -y-2}{x +y+4} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.174 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y+5}{2 x -y-3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
32.261 |
|
| \begin{align*}
y^{\prime }&=\frac {y-x +1}{3 x -y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.095 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x -y+1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.653 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x}{x -y+1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.766 |
|
| \begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.413 |
|
| \begin{align*}
y^{\prime }-3 y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.308 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}-\frac {x}{y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.411 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=x -y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
21.217 |
|
| \begin{align*}
\left (x +y+1\right ) y^{\prime }&=x +y+2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.096 |
|
| \begin{align*}
x \left (6 x^{2}+14 y^{2}\right )+y \left (13 x^{2}+30 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
24.363 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x -y}{x +2 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.710 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\sin \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.710 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y}{x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
15.430 |
|
| \begin{align*}
y^{\prime }&=\frac {y+\sqrt {x^{2}-y^{2}}}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
35.565 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
59.445 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y^{3}+2 x^{2} y}{x^{3}+2 x y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
15.737 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
28.036 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
13.089 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=\frac {x^{2}}{y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.467 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
10.767 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
15.385 |
|
| \begin{align*}
x^{2} y+2 y^{3}-\left (2 x^{3}+3 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
22.293 |
|
| \begin{align*}
{\mathrm e}^{2 x +3 y}+{\mathrm e}^{4 x -5 y} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.946 |
|
| \begin{align*}
3 y^{2}-2 x^{2}&=2 x y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
57.045 |
|
| \begin{align*}
\left (2 x +y\right ) y^{\prime }+x -2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.502 |
|
| \begin{align*}
2 y^{2}+4 x^{2}-x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.231 |
|
| \begin{align*}
x^{2}+2 y^{2}-x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.590 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
97.486 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
60.165 |
|
| \begin{align*}
x^{2}+2 y x -4 y^{2}-\left (x^{2}-8 y x -4 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
15.602 |
|
| \begin{align*}
x^{2}+2 y x -4 y^{2}-\left (x^{2}-8 y x -4 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.846 |
|
| \begin{align*}
x y y^{\prime }+x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.015 |
|
| \begin{align*}
y x -\left (x +2 y\right )^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
17.774 |
|
| \begin{align*}
v^{2}+x \left (x +v\right ) v^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
72.504 |
|
| \begin{align*}
t \left (s^{2}+t^{2}\right ) s^{\prime }-s \left (s^{2}-t^{2}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
16.031 |
|
| \begin{align*}
y-\left (x +\sqrt {y^{2}-x^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
21.861 |
|
| \begin{align*}
y+\sqrt {x^{2}+y^{2}}-x y^{\prime }&=0 \\
y \left (\sqrt {3}\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
12.291 |
|
| \begin{align*}
x +y+\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
23.576 |
|
| \begin{align*}
2 y x +\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
12.621 |
|
| \begin{align*}
\left (y^{2}-x^{2}\right ) y^{\prime }+2 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
19.927 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
23.599 |
|
| \begin{align*}
y-2+\left (3 x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
133.786 |
|
| \begin{align*}
L i^{\prime }+R i&=e \\
i \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.173 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x +y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.276 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
59.910 |
|
| \begin{align*}
y^{\prime }+a y&=b \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.339 |
|
| \begin{align*}
x -y-\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
25.851 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
19.693 |
|
| \begin{align*}
y \left (y^{2}-3 x^{2}\right )+x^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
49.968 |
|
| \begin{align*}
x^{3}-3 x y^{2}+\left (y^{3}-3 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
72.566 |
|
| \begin{align*}
y^{3}-x^{3}&=x y \left (y y^{\prime }+x \right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
14.602 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
13.679 |
|
| \begin{align*}
y^{\prime }&=\left (9 x +4 y+1\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
20.426 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x +y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.675 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
8.039 |
|
| \begin{align*}
2 x^{3} y^{\prime }&=y \left (3 x^{2}+y^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
39.565 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
13.698 |
|
| \begin{align*}
y^{\prime }&=2 \left (3 x +y\right )^{2}-1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
38.848 |
|
| \begin{align*}
y-2-\left (x -y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
24.196 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
26.165 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
31.938 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
73.102 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
24.936 |
|
| \begin{align*}
\left (2 x -y+3\right ) y^{\prime }+2&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.724 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
14.022 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
19.316 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
30.386 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
27.068 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
13.438 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
19.921 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
34.934 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
39.858 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
58.352 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
33.421 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
34.342 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
27.445 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
19.888 |
|
| \begin{align*}
a_{1} x +k y+c_{1} +\left (k x +b_{2} y+c_{2} \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
85.750 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
37.600 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
14.323 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
28.596 |
|
| \begin{align*}
4+\left (x -y+2\right )^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
17.379 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
14.254 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
31.533 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
14.094 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
34.754 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
13.702 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
33.193 |
|
| \begin{align*}
x -y-1-2 \left (-2+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
28.235 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
24.778 |
|
| \begin{align*}
4 x -2 y y^{\prime }+{y^{\prime }}^{2} x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.320 |
|
| \begin{align*}
{y^{\prime }}^{2}-x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.962 |
|
| \begin{align*}
{y^{\prime }}^{3}+{y^{\prime }}^{2} x -y&=0 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
68.927 |
|
| \begin{align*}
4 x -2 y y^{\prime }+{y^{\prime }}^{2} x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.442 |
|
| \begin{align*}
{y^{\prime }}^{2}-x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.923 |
|
| \begin{align*}
2 {y^{\prime }}^{3}+x y^{\prime }-2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
7.058 |
|
| \begin{align*}
2 {y^{\prime }}^{2}+x y^{\prime }-2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.993 |
|
| \begin{align*}
{y^{\prime }}^{3}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
1.899 |
|
| \begin{align*}
4 {y^{\prime }}^{2} x -3 y y^{\prime }+3&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
46.932 |
|
| \begin{align*}
{y^{\prime }}^{3}-x y^{\prime }+2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.102 |
|
| \begin{align*}
5 {y^{\prime }}^{2}+6 x y^{\prime }-2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.269 |
|
| \begin{align*}
2 {y^{\prime }}^{2} x +\left (2 x -y\right ) y^{\prime }+1-y&=0 \\
\end{align*} |
[_rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.538 |
|
| \begin{align*}
5 {y^{\prime }}^{2}+3 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.278 |
|
| \begin{align*}
{y^{\prime }}^{2}+3 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.289 |
|
| \begin{align*}
4 y {y^{\prime }}^{2}-2 x y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.220 |
|
| \begin{align*}
{y^{\prime }}^{2} x -y y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
7.421 |
|
| \begin{align*}
y {y^{\prime }}^{2}-x y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.795 |
|
| \begin{align*}
y {y^{\prime }}^{3}-3 x y^{\prime }+3 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.774 |
|
| \begin{align*}
5 {y^{\prime }}^{2}+6 x y^{\prime }-2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.959 |
|
| \begin{align*}
{y^{\prime }}^{4}+x y^{\prime }-3 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
3.930 |
|
| \begin{align*}
{y^{\prime }}^{3}-2 x y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
1.868 |
|
| \begin{align*}
y {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
27.113 |
|
| \begin{align*}
{y^{\prime }}^{2}+y y^{\prime }-x -1&=0 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.148 |
|
| \begin{align*}
y^{\prime }&=2 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.875 |
|
| \begin{align*}
y^{\prime }&=3 y+12 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.072 |
|
| \begin{align*}
y^{\prime }&=-{\mathrm e}^{y}-1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.108 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.332 |
|
| \begin{align*}
y^{\prime }&=3 y+12 \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.921 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.243 |
|
| \begin{align*}
y^{\prime }&=1-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.411 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.691 |
|
| \begin{align*}
y^{\prime }&=1-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.769 |
|
| \begin{align*}
\left (t^{2}+3 y^{2}\right ) y^{\prime }&=-2 y t \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
13.181 |
|
| \begin{align*}
y^{\prime }&=1+y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.045 |
|
| \begin{align*}
y^{\prime }+a y&=b \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.513 |
|
| \begin{align*}
y^{\prime }&=\frac {4 t -3 y}{t -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
19.551 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+2 y t}{t^{2}+y t} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
22.048 |
|
| \begin{align*}
y^{\prime }&=\frac {3 y^{2}-t^{2}}{2 y t} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
65.507 |
|
| \begin{align*}
y^{\prime }&=\frac {t^{2}+y^{2}}{y t} \\
y \left ({\mathrm e}\right ) &= 2 \,{\mathrm e} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
20.294 |
|
| \begin{align*}
t y^{\prime }&=y+\sqrt {t^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
✗ |
55.099 |
|
| \begin{align*}
t^{2} y^{\prime }&=y t +y \sqrt {t^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
51.465 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{2 t -2 y+1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.412 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{\left (t +y\right )^{2}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
19.882 |
|
| \begin{align*}
y^{\prime }&=\sin \left (t -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.275 |
|
| \begin{align*}
y^{\prime }&=-{\mathrm e}^{y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.345 |
|
| \begin{align*}
y-t +\left (t +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
29.851 |
|
| \begin{align*}
y^{2}+2 t y y^{\prime }+3 t^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
19.092 |
|
| \begin{align*}
3 y-5 t +2 y y^{\prime }-t y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
32.379 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
44.018 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.500 |
|
| \begin{align*}
y^{\prime }&=\frac {t -y}{t +y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
62.964 |
|
| \begin{align*}
y^{\prime }&=1+\left (t -y\right )^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
4.761 |
|
| \begin{align*}
y^{\prime }&=1+y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.036 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.796 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
4.186 |
|
| \begin{align*}
y^{\prime }&=\frac {t -y}{t +y} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
26.089 |
|
| \begin{align*}
y^{\prime }&=a y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.931 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.020 |
|
| \begin{align*}
y^{\prime }&=y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.831 |
|
| \begin{align*}
y^{\prime }&=2-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.214 |
|
| \begin{align*}
y^{\prime }&=2-y \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.421 |
|
| \begin{align*}
y^{\prime }&=2-y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.470 |
|
| \begin{align*}
y^{\prime }&=-2 y+8 \\
y \left (0\right ) &= 6 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.052 |
|
| \begin{align*}
y^{\prime }-9 y&=90 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.254 |
|
| \begin{align*}
y^{\prime }+9 y&=90 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.923 |
|
| \begin{align*}
y^{\prime }-4 y&=-8 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.300 |
|
| \begin{align*}
y^{\prime }+4 y&=8 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.296 |
|
| \begin{align*}
y^{\prime }+2 y&=6 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.599 |
|
| \begin{align*}
y^{\prime }+2 y&=-6 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.418 |
|
| \begin{align*}
y^{\prime }&=1+y \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.784 |
|
| \begin{align*}
y^{\prime }&=-1+y \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.554 |
|
| \begin{align*}
y^{\prime }&=a y-b y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
13.635 |
|
| \begin{align*}
y^{\prime }&=1+y \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.766 |
|
| \begin{align*}
y^{\prime }&=1+y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.251 |
|
| \begin{align*}
y^{\prime }&=a y-b y^{n} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
5.776 |
|
| \begin{align*}
y^{\prime }&=2 \left (1-y\right ) \left (1-{\mathrm e}^{y}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.460 |
|
| \begin{align*}
y^{\prime }&=a y-y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
23.509 |
|
| \begin{align*}
y^{\prime }&=\sin \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
26.020 |
|
| \begin{align*}
y^{\prime }&=\sin \left (y\right )^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.882 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.330 |
|
| \begin{align*}
y^{\prime }&=\frac {c t -a y}{A t +b y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
81.775 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{t +y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.407 |
|
| \begin{align*}
y^{\prime }&=\frac {-3 t^{2}-2 y^{2}}{4 y t +6 y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
26.016 |
|
| \begin{align*}
y^{\prime }&=\frac {4 t -y}{t -6 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
29.609 |
|
| \begin{align*}
y^{\prime }&=-\frac {3 t^{2}+2 y^{2}}{4 y t +6 y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
21.307 |
|
| \begin{align*}
y^{\prime }&=a y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.276 |
|
| \begin{align*}
y^{\prime }&=1-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.481 |
|
| \begin{align*}
2 y^{\prime }+y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.119 |
|
| \begin{align*}
y^{\prime }+20 y&=24 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.434 |
|
| \begin{align*}
\left (-x +y\right ) y^{\prime }&=y-x +8 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.917 |
|
| \begin{align*}
y^{\prime }&=25+y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
10.872 |
|
| \begin{align*}
2 y+y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.207 |
|
| \begin{align*}
3 y^{\prime }&=4 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.871 |
|
| \begin{align*}
\left (-1+y\right ) y^{\prime }&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.610 |
|
| \begin{align*}
y^{\prime }&=3 y^{{2}/{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
24.825 |
|
| \begin{align*}
y^{\prime }&=y^{{2}/{3}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.934 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
26.760 |
|
| \begin{align*}
\left (-x +y\right ) y^{\prime }&=x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
31.602 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y^{2}-9} \\
y \left (5\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
27.882 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y^{2}-9} \\
y \left (2\right ) &= -3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
23.355 |
|
| \begin{align*}
y^{\prime }&=1+y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.024 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.864 |
|
| \begin{align*}
y^{\prime }&=2 y-4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.358 |
|
| \begin{align*}
\left (-2+2 y\right ) y^{\prime }&=2 x -1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✓ |
21.074 |
|
| \begin{align*}
y^{\prime }&=y \ln \left (y+2\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.324 |
|
| \begin{align*}
y^{\prime }&=\left (y \,{\mathrm e}^{y}-9 y\right ) {\mathrm e}^{-y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.263 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{\pi }-\sin \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.434 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{3 x +2 y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.145 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y}{x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
32.523 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y-1}{3-x +y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
28.638 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
15.349 |
|
| \begin{align*}
y^{\prime }&=\frac {6 x^{2}-7 y^{2}}{14 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
24.695 |
|
| \begin{align*}
2 x +3 y+\left (y+2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
46.335 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
16.125 |
|
| \begin{align*}
y^{\prime }&=\frac {y+\sqrt {x^{2}-y^{2}}}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
77.147 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\sin \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.303 |
|
| \begin{align*}
x^{2}-y^{2}-\frac {2 y^{3} y^{\prime }}{x}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
85.551 |
|
| \begin{align*}
x^{2}+2 y x -4 y^{2}-\left (x^{2}-8 y x -4 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
30.961 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
33.015 |
|
| \begin{align*}
y^{2}+\left (y x +x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
129.173 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
97.901 |
|
| \begin{align*}
x -2 y+1&=\left (x -2 y\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
21.544 |
|
| \begin{align*}
x -y+\left (y-x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.650 |
|
| \begin{align*}
3 x^{2} y+y^{3}+\left (x^{3}+3 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
29.077 |
|
| \begin{align*}
x y^{\prime }&=y+\sqrt {y^{2}-x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.483 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y-2}{y-x -4} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.429 |
|
| \begin{align*}
x y y^{\prime }&=2 y^{2}-3 x^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
62.950 |
|
| \begin{align*}
2 y&=x y^{\prime }+y^{\prime } \ln \left (y^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.339 |
|
| \begin{align*}
x^{\prime }+x&=1 \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.835 |
|
| \begin{align*}
x^{\prime }-x&=1 \\
x \left (0\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.750 |
|
| \begin{align*}
y^{\prime }&=3 y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.635 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x -y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.730 |
|
| \begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.979 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{\left (\ln \left (x \right )-\ln \left (y\right )\right ) x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.803 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.505 |
|
| \begin{align*}
3 x^{2}-8 y x +2 y^{2}-\left (4 x^{2}-4 y x +3 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
8.536 |
|
| \begin{align*}
y {y^{\prime }}^{2}+2 x y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.228 |
|
| \begin{align*}
x +y-\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.816 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x -y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.842 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x^{2}-y}-x \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
9.981 |
|
| \begin{align*}
y^{\prime }&=\sqrt {1-y^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.415 |
|
| \begin{align*}
y^{\prime }&=\frac {y+1}{x -y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.964 |
|
| \begin{align*}
y^{\prime }&=\left (3 x -y\right )^{{1}/{3}}-1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.839 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.578 |
|
| \begin{align*}
y^{\prime }&=2-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.702 |
|
| \begin{align*}
y^{\prime }&=-\sin \left (2 x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
24.191 |
|
| \begin{align*}
y^{\prime }&=\frac {x -1}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.318 |
|
| \begin{align*}
{\mathrm e}^{-y} \left (y^{\prime }+1\right )&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.058 |
|
| \begin{align*}
y^{\prime }&=a^{x +y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.707 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.730 |
|
| \begin{align*}
\left (x +y\right )^{2} y^{\prime }&=a^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.751 |
|
| \begin{align*}
y^{\prime }&=y^{a} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
6.056 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
16.563 |
|
| \begin{align*}
x y^{\prime }&=y+\sqrt {y^{2}-x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.069 |
|
| \begin{align*}
4 x^{2}-y x +y^{2}+y^{\prime } \left (x^{2}-y x +4 y^{2}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
12.755 |
|
| \begin{align*}
4 x^{2}+y x -3 y^{2}+y^{\prime } \left (-5 x^{2}+2 y x +y^{2}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
18.140 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y}{3 x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
7.879 |
|
| \begin{align*}
2 x \left (x^{2}+y^{2}\right ) y^{\prime }&=\left (2 x^{2}+y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.559 |
|
| \begin{align*}
\left (-x y^{\prime }+y\right )^{2}&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.296 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
7.709 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
58.395 |
|
| \begin{align*}
y^{3} y^{\prime }+3 x y^{2}+2 x^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.871 |
|
| \begin{align*}
\left (2 \sqrt {y x}-x \right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.074 |
|
| \begin{align*}
3 x y^{\prime }-2 y&=\frac {x^{3}}{y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.157 |
|
| \begin{align*}
x \left (2 x^{2}+y^{2}\right )+y \left (x^{2}+2 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
17.671 |
|
| \begin{align*}
\frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}}&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✗ |
✗ |
23.904 |
|
| \begin{align*}
{y^{\prime }}^{2} x +2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.572 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }+x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.593 |
|
| \begin{align*}
\left (x^{2}-2 y x \right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2}-2 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
98.398 |
|
| \begin{align*}
y&={y^{\prime }}^{2} {\mathrm e}^{y^{\prime }} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.007 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{\frac {x y^{\prime }}{y}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
8.436 |
|
| \begin{align*}
y&=y^{\prime } \ln \left (y^{\prime }\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.679 |
|
| \begin{align*}
y&=\arcsin \left (y^{\prime }\right )+\ln \left (1+{y^{\prime }}^{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
3.341 |
|
| \begin{align*}
y&=\left (y^{\prime }-1\right ) {\mathrm e}^{y^{\prime }} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.872 |
|
| \begin{align*}
y^{{2}/{5}}+{y^{\prime }}^{{2}/{5}}&=a^{{2}/{5}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.016 |
|
| \begin{align*}
y^{4}-{y^{\prime }}^{4}-y {y^{\prime }}^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
9.106 |
|
| \begin{align*}
y&=y^{\prime } \left (1+y^{\prime } \cos \left (y^{\prime }\right )\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
1.747 |
|
| \begin{align*}
2 y&=x y^{\prime }+y^{\prime } \ln \left (y^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.690 |
|
| \begin{align*}
y&=x \left (y^{\prime }+1\right )+{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.157 |
|
| \begin{align*}
y&=2 x y^{\prime }+\sin \left (y^{\prime }\right ) \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.170 |
|
| \begin{align*}
y&={y^{\prime }}^{2} x -\frac {1}{y^{\prime }} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
94.456 |
|
| \begin{align*}
y&=\frac {3 x y^{\prime }}{2}+{\mathrm e}^{y^{\prime }} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.034 |
|
| \begin{align*}
y^{\prime }&=\left (x -y\right )^{2}+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
2.404 |
|
| \begin{align*}
x^{3}-3 x y^{2}+\left (y^{3}-3 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
63.154 |
|
| \begin{align*}
5 y x -4 y^{2}-6 x^{2}+\left (y^{2}-2 y x +6 x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.979 |
|
| \begin{align*}
2 y^{2}-y x -\left (x^{2}-y x +y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
38.037 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
17.414 |
|
| \begin{align*}
y^{\prime }&=\tan \left (a x +b y+c \right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.321 |
|
| \begin{align*}
x^{2}+y^{2}-x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.799 |
|
| \begin{align*}
y^{\prime }-1&={\mathrm e}^{x +2 y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.080 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
8.464 |
|
| \begin{align*}
y^{\prime }+y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.069 |
|
| \begin{align*}
y^{\prime }+y&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.740 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
12.391 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.744 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.622 |
|
| \begin{align*}
\left (x -2 y\right ) y^{\prime }&=2 x -y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.646 |
|
| \begin{align*}
x y^{\prime }&=x \cos \left (\frac {y}{x}\right )+y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.464 |
|
| \begin{align*}
x^{3} y^{\prime }&=x^{2} y-y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
269.159 |
|
| \begin{align*}
y^{\prime }&=\frac {-3+y}{x +y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.090 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x -y-9}{x +y+1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.551 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y+x +7}{-2 x +y-9} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.556 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
69.109 |
|
| \begin{align*}
y^{\prime }&=\ln \left (x -y\right ) \\
y \left (3\right ) &= \pi \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.758 |
|
| \begin{align*}
y^{\prime }&=2-y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.227 |
|
| \begin{align*}
y^{\prime }&=4+y \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.226 |
|
| \begin{align*}
y^{\prime }&=3+2 y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.647 |
|
| \begin{align*}
y^{\prime }+1&=2 \left (-x +y\right ) \left (y^{\prime }-1\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.418 |
|
| \begin{align*}
y^{\prime }&=\frac {y-3 x}{x +3 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.222 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.907 |
|
| \begin{align*}
y^{\prime }&=3 y^{{2}/{3}} \\
y \left (2\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.529 |
|
| \begin{align*}
{\mathrm e}^{-s} \left (1+s^{\prime }\right )&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.966 |
|
| \begin{align*}
z^{\prime }&=10^{x +z} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.804 |
|
| \begin{align*}
x x^{\prime }+t&=1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.460 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.441 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
7.999 |
|
| \begin{align*}
y^{\prime }&=\sqrt {4 x +2 y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.986 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.902 |
|
| \begin{align*}
2 x^{3} y^{\prime }&=\left (2 x^{2}-y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
138.127 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=x y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
10.556 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }&=2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
16.550 |
|
| \begin{align*}
x y^{\prime }-y&=x \tan \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.446 |
|
| \begin{align*}
x y^{\prime }-y&=\left (x +y\right ) \ln \left (\frac {x +y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.814 |
|
| \begin{align*}
y+\sqrt {y x}&=x y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.526 |
|
| \begin{align*}
x y^{\prime }&=y+\sqrt {x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
23.101 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
20.234 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
8.005 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
12.279 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
33.993 |
|
| \begin{align*}
y+2&=\left (2 x +y-4\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.506 |
|
| \begin{align*}
\left (y^{\prime }+1\right ) \ln \left (\frac {x +y}{x +3}\right )&=\frac {x +y}{x +3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
34.667 |
|
| \begin{align*}
y^{\prime }-2 y x +y^{2}&=-x^{2}+5 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.125 |
|
| \begin{align*}
2 y x +\left (x^{2}-y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
54.755 |
|
| \begin{align*}
y^{\prime }&=y+{\mathrm e}^{y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
2.105 |
|
| \begin{align*}
y^{\prime }&=3 y^{{2}/{3}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.227 |
|
| \begin{align*}
y^{\prime }&=\frac {y+2}{x +y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.061 |
|
| \begin{align*}
y^{\prime }&=\frac {x +2 y-4}{x -y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.704 |
|
| \begin{align*}
y^{\prime }&=\tan \left (y\right )+1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.683 |
|
| \begin{align*}
y^{\prime }&=\sqrt {\sin \left (y\right )} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.123 |
|
| \begin{align*}
y^{\prime }&=2+\left (y-2 x \right )^{{1}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.805 |
|
| \begin{align*}
x y^{\prime }&=y+\sqrt {y^{2}-x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.701 |
|
| \begin{align*}
8 {y^{\prime }}^{3}&=27 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.759 |
|
| \begin{align*}
\left (y^{\prime }+1\right )^{3}&=27 \left (x +y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✗ |
✓ |
1.250 |
|
| \begin{align*}
{y^{\prime }}^{2}-4 y^{3}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.553 |
|
| \begin{align*}
{y^{\prime }}^{2}&=4 y^{3} \left (1-y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.802 |
|
| \begin{align*}
{y^{\prime }}^{2} x&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.947 |
|
| \begin{align*}
y {y^{\prime }}^{3}+x&=1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.551 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }+x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.524 |
|
| \begin{align*}
{y^{\prime }}^{2} x&=y \left (2 y^{\prime }-1\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.652 |
|
| \begin{align*}
{y^{\prime }}^{2}+x&=2 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.907 |
|
| \begin{align*}
y y^{\prime } \left (y y^{\prime }-2 x \right )&=x^{2}-2 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.508 |
|
| \begin{align*}
y&={y^{\prime }}^{2}+2 {y^{\prime }}^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
0.913 |
|
| \begin{align*}
y&=\ln \left (1+{y^{\prime }}^{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
1.664 |
|
| \begin{align*}
y&=\left (y^{\prime }-1\right ) {\mathrm e}^{y^{\prime }} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.145 |
|
| \begin{align*}
{y^{\prime }}^{4}-{y^{\prime }}^{2}&=y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
597.000 |
|
| \begin{align*}
{y^{\prime }}^{2}-{y^{\prime }}^{3}&=y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.944 |
|
| \begin{align*}
{y^{\prime }}^{4}&=2 y y^{\prime }+y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
562.776 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{\frac {x y^{\prime }}{y}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
20.619 |
|
| \begin{align*}
x y^{\prime }+y&=4 \sqrt {y^{\prime }} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
182.532 |
|
| \begin{align*}
y&=3 x y^{\prime }-7 {y^{\prime }}^{3} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
9.090 |
|
| \begin{align*}
\left (1+{y^{\prime }}^{2}\right ) x&=2 y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.136 |
|
| \begin{align*}
y&={y^{\prime }}^{2} x -2 {y^{\prime }}^{3} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
52.640 |
|
| \begin{align*}
x y^{\prime } \left (y^{\prime }+2\right )&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.135 |
|
| \begin{align*}
2 x y^{\prime }-y&=\ln \left (y^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
53.631 |
|
| \begin{align*}
\left (x y^{\prime }+y\right )^{2}&=x^{2} y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.704 |
|
| \begin{align*}
2 {y^{\prime }}^{3}-3 {y^{\prime }}^{2}+x&=y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
1.293 |
|
| \begin{align*}
\left (x +y\right )^{2} y^{\prime }&=1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
151.775 |
|
| \begin{align*}
\frac {-x y^{\prime }+y}{y y^{\prime }+x}&=2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.676 |
|
| \begin{align*}
{y^{\prime }}^{2} x&=y-y^{\prime } \\
\end{align*} |
[_rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.012 |
|
| \begin{align*}
y \left (-x y^{\prime }+y\right )&=\sqrt {y^{4}+x^{4}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
44.915 |
|
| \begin{align*}
\sqrt {x}\, y^{\prime }&=\sqrt {-x +y}+\sqrt {x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
31.358 |
|
| \begin{align*}
3 {y^{\prime }}^{4}&=y^{\prime }+y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
573.396 |
|
| \begin{align*}
y^{\prime }&=\left (4 x +y-3\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
13.030 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}-2 x y y^{\prime }&=x^{2}+3 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.118 |
|
| \begin{align*}
x \left (\ln \left (y\right )-\ln \left (x \right )\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
48.231 |
|
| \begin{align*}
y y^{\prime }&=4 x +3 y-2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
32.055 |
|
| \begin{align*}
2 x y^{\prime }-y&=\sin \left (y^{\prime }\right ) \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.869 |
|
| \begin{align*}
y^{\prime }&=\left (2 x -y\right )^{{1}/{3}}+2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.047 |
|
| \begin{align*}
{y^{\prime }}^{3}+\left (-2 y^{\prime }+{y^{\prime }}^{2}\right ) x&=3 y^{\prime }-y \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
60.621 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
16.722 |
|
| \begin{align*}
y&=y^{\prime } \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
24.944 |
|
| \begin{align*}
y^{\prime }&=-\tan \left (2 x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.287 |
|
| \begin{align*}
x y^{\prime }&=2 y+\sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[_rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
676.727 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
625.926 |
|
| \begin{align*}
y^{3} {y^{\prime }}^{3}&=27 x \left (y^{2}-2 x^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
9.418 |
|