| # |
ODE |
CAS classification |
Solved |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime } x +2 y&=3 x \\
y \left (1\right ) &= 5 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.908 |
|
| \begin{align*}
y+3 y^{\prime } x&=12 x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.612 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=x -y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.448 |
|
| \begin{align*}
2 y y^{\prime } x&=x^{2}+2 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.286 |
|
| \begin{align*}
y^{\prime } x&=y+2 \sqrt {y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.144 |
|
| \begin{align*}
\left (x -y\right ) y^{\prime }&=x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.685 |
|
| \begin{align*}
x \left (x +y\right ) y^{\prime }&=y \left (x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
10.536 |
|
| \begin{align*}
\left (x +2 y\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.811 |
|
| \begin{align*}
y^{2} y^{\prime } x&=x^{3}+y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.030 |
|
| \begin{align*}
x^{2} y^{\prime }&=y x +x^{2} {\mathrm e}^{\frac {y}{x}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.604 |
|
| \begin{align*}
x^{2} y^{\prime }&=y x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.547 |
|
| \begin{align*}
y y^{\prime } x&=x^{2}+3 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.789 |
|
| \begin{align*}
\left (x^{2}-y^{2}\right ) y^{\prime }&=2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.230 |
|
| \begin{align*}
y y^{\prime } x&=y^{2}+x \sqrt {4 x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
16.136 |
|
| \begin{align*}
y^{\prime } x&=y+\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.519 |
|
| \begin{align*}
x +y y^{\prime }&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.384 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
13.220 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
8.897 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
8.905 |
|
| \begin{align*}
\frac {2 x^{{5}/{2}}-3 y^{{5}/{3}}}{2 x^{{5}/{2}} y^{{2}/{3}}}+\frac {\left (3 y^{{5}/{3}}-2 x^{{5}/{2}}\right ) y^{\prime }}{3 x^{{3}/{2}} y^{{5}/{3}}}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
✓ |
✓ |
✗ |
3.884 |
|
| \begin{align*}
y^{\prime }&=-\frac {y \left (2 x^{3}-y^{3}\right )}{x \left (2 y^{3}-x^{3}\right )} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.647 |
|
| \begin{align*}
y x +y^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.591 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.161 |
|
| \begin{align*}
x^{2} y^{\prime }&=y x +3 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.840 |
|
| \begin{align*}
x^{3} y^{\prime }&=x^{2} y-y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
51.710 |
|
| \begin{align*}
2 x^{2} y-x^{3} y^{\prime }&=y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
59.398 |
|
| \begin{align*}
y^{\prime }&=-\frac {3 x^{2}+2 y^{2}}{4 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.313 |
|
| \begin{align*}
y^{\prime }&=\frac {x +3 y}{-3 x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.020 |
|
| \begin{align*}
y^{\prime } x +2 y&=3 x \\
y \left (1\right ) &= 5 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.664 |
|
| \begin{align*}
y+3 y^{\prime } x&=12 x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.040 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=x -y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.940 |
|
| \begin{align*}
2 y y^{\prime } x&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.921 |
|
| \begin{align*}
y^{\prime } x&=y+2 \sqrt {y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.381 |
|
| \begin{align*}
\left (x -y\right ) y^{\prime }&=x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.402 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
12.642 |
|
| \begin{align*}
\left (x +2 y\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.334 |
|
| \begin{align*}
y^{2} y^{\prime } x&=x^{3}+y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.384 |
|
| \begin{align*}
x^{2} y^{\prime }&=y x +x^{2} {\mathrm e}^{\frac {y}{x}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
6.094 |
|
| \begin{align*}
x^{2} y^{\prime }&=y x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.347 |
|
| \begin{align*}
y y^{\prime } x&=x^{2}+3 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.027 |
|
| \begin{align*}
\left (x^{2}-y^{2}\right ) y^{\prime }&=2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
14.848 |
|
| \begin{align*}
y y^{\prime } x&=y^{2}+x \sqrt {4 x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
19.106 |
|
| \begin{align*}
y^{\prime } x&=y+\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.641 |
|
| \begin{align*}
x +y y^{\prime }&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.080 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
16.388 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
11.000 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
10.983 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
331.025 |
|
| \begin{align*}
\frac {2 x^{{5}/{2}}-3 y^{{5}/{3}}}{2 x^{{5}/{2}} y^{{2}/{3}}}+\frac {\left (3 y^{{5}/{3}}-2 x^{{5}/{2}}\right ) y^{\prime }}{3 x^{{3}/{2}} y^{{5}/{3}}}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
✓ |
✓ |
✗ |
5.228 |
|
| \begin{align*}
y x +y^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.583 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.887 |
|
| \begin{align*}
x^{2} y^{\prime }&=y x +3 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.379 |
|
| \begin{align*}
x^{3} y^{\prime }&=x^{2} y-y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
54.810 |
|
| \begin{align*}
2 x^{2} y-x^{3} y^{\prime }&=y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
62.264 |
|
| \begin{align*}
y^{\prime }&=\frac {-3 x^{2}-2 y^{2}}{4 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.287 |
|
| \begin{align*}
y^{\prime }&=\frac {x +3 y}{-3 x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.147 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y x +y^{2}}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.302 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+3 y^{2}}{2 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.446 |
|
| \begin{align*}
y^{\prime }&=\frac {4 y-3 x}{2 x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.372 |
|
| \begin{align*}
y^{\prime }&=-\frac {4 x +3 y}{2 x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.576 |
|
| \begin{align*}
y^{\prime }&=\frac {x +3 y}{x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
11.984 |
|
| \begin{align*}
x^{2}+3 y x +y^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.180 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}-3 y^{2}}{2 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.774 |
|
| \begin{align*}
y^{\prime }&=\frac {3 y^{2}-x^{2}}{2 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
55.550 |
|
| \begin{align*}
y^{\prime }&=-\frac {4 t}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.678 |
|
| \begin{align*}
2 x +4 y+\left (2 x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
19.042 |
|
| \begin{align*}
y^{\prime }&=\frac {-a x -b y}{b x +c y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.168 |
|
| \begin{align*}
y^{\prime }&=\frac {-a x +b y}{b x -c y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
12.914 |
|
| \begin{align*}
\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.037 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
11.052 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
18.625 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
10.352 |
|
| \begin{align*}
y^{\prime } x&={\mathrm e}^{\frac {y}{x}} x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
7.127 |
|
| \begin{align*}
3 t +2 y&=-y^{\prime } t \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.440 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.214 |
|
| \begin{align*}
2 y x +3 y^{2}-\left (x^{2}+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
17.675 |
|
| \begin{align*}
y^{\prime } x +3 y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.220 |
|
| \begin{align*}
y^{\prime }+\frac {k y}{x}&=0 \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.779 |
|
| \begin{align*}
x +y y^{\prime }&=0 \\
y \left (3\right ) &= -4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.603 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +3 y}{x -4 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
23.608 |
|
| \begin{align*}
y^{\prime }&=\frac {y+{\mathrm e}^{-\frac {y}{x}} x}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.202 |
|
| \begin{align*}
x^{2} y^{\prime }&=y^{2}+y x -x^{2} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
11.962 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+2 y x}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.323 |
|
| \begin{align*}
x y^{3} y^{\prime }&=y^{4}+x^{4} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
104.283 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\sec \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.690 |
|
| \begin{align*}
x^{2} y^{\prime }&=x^{2}+y x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.365 |
|
| \begin{align*}
y y^{\prime } x&=x^{2}+2 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.820 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y^{2}+x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}}}{2 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.232 |
|
| \begin{align*}
y^{\prime }&=\frac {y x +y^{2}}{x^{2}} \\
y \left (-1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.979 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{3}+y^{3}}{y^{2} x} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.732 |
|
| \begin{align*}
y y^{\prime } x +x^{2}+y^{2}&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.468 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}-3 y x -5 x^{2}}{x^{2}} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
13.043 |
|
| \begin{align*}
x^{2} y^{\prime }&=2 x^{2}+y^{2}+4 y x \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.724 |
|
| \begin{align*}
y y^{\prime } x&=3 x^{2}+4 y^{2} \\
y \left (1\right ) &= \sqrt {3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.731 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.432 |
|
| \begin{align*}
\left (-y+y^{\prime } x \right ) \left (\ln \left (y\right )-\ln \left (x \right )\right )&=x \\
\end{align*} |
[[_homogeneous, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.578 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{3}+2 x y^{2}+x^{2} y+x^{3}}{x \left (x +y\right )^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
19.576 |
|
| \begin{align*}
y^{\prime }&=\frac {x +2 y}{2 x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
25.167 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{y-2 x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
74.194 |
|
| \begin{align*}
y^{\prime }&=\frac {x y^{2}+2 y^{3}}{x^{3}+x^{2} y+x y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
7.072 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{3}+x^{2} y+3 y^{3}}{x^{3}+3 x y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
350.077 |
|
| \begin{align*}
x^{2} y^{\prime }&=y^{2}+y x -4 x^{2} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
14.514 |
|
| \begin{align*}
y y^{\prime } x&=x^{2}-y x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
29.112 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
49.843 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y x +y^{2}}{y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
17.267 |
|
| \begin{align*}
4 x +7 y+\left (3 x +4 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.905 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
21.660 |
|
| \begin{align*}
\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.811 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
15.229 |
|
| \begin{align*}
x^{2}+y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.125 |
|
| \begin{align*}
x^{2} y^{\prime }-y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.082 |
|
| \begin{align*}
3 x^{2} y+2 x^{3} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.102 |
|
| \begin{align*}
y^{\prime } t&=y+\sqrt {t^{2}+y^{2}} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.237 |
|
| \begin{align*}
2 t y y^{\prime }&=3 y^{2}-t^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
56.847 |
|
| \begin{align*}
\left (t -\sqrt {t y}\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.953 |
|
| \begin{align*}
y^{\prime }&=\frac {y+t}{t -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.099 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
10.718 |
|
| \begin{align*}
3 t y+y^{2}+\left (t^{2}+t y\right ) y^{\prime }&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
10.605 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{t}+\frac {y^{2}}{t^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.622 |
|
| \begin{align*}
y^{\prime } t&=y+\sqrt {t^{2}+y^{2}} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.673 |
|
| \begin{align*}
2 t y y^{\prime }&=3 y^{2}-t^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
58.484 |
|
| \begin{align*}
\left (t -\sqrt {t y}\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.395 |
|
| \begin{align*}
y^{\prime }&=\frac {y+t}{t -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.122 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
10.804 |
|
| \begin{align*}
3 t y+y^{2}+\left (t^{2}+t y\right ) y^{\prime }&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
11.603 |
|
| \begin{align*}
y^{\prime } x +y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.714 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.037 |
|
| \begin{align*}
y^{\prime } x +2 y&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.663 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=0 \\
y \left (3\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.221 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+x&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.393 |
|
| \begin{align*}
-y+y^{\prime } x&=\sqrt {y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.698 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x -y}{x +4 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.359 |
|
| \begin{align*}
-y+y^{\prime } x&=\sqrt {x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
33.945 |
|
| \begin{align*}
x +y y^{\prime }&=2 y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
6.445 |
|
| \begin{align*}
y^{\prime } x -y+\sqrt {y^{2}-x^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.106 |
|
| \begin{align*}
x^{2}+y^{2}&=y y^{\prime } x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.035 |
|
| \begin{align*}
\left (y x -x^{2}\right ) y^{\prime }-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
60.712 |
|
| \begin{align*}
y^{\prime } x +y&=2 \sqrt {y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.145 |
|
| \begin{align*}
x +y+\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.780 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
56.766 |
|
| \begin{align*}
y^{\prime } x -y-x \sin \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.059 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\cosh \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.303 |
|
| \begin{align*}
x^{2}+y^{2}&=2 y y^{\prime } x \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.094 |
|
| \begin{align*}
\left (\frac {x}{y}+\frac {y}{x}\right ) y^{\prime }+1&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.837 |
|
| \begin{align*}
{\mathrm e}^{\frac {y}{x}} x +y&=y^{\prime } x \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
16.651 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{x -y} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.727 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\tan \left (\frac {y}{x}\right ) \\
y \left (6\right ) &= \pi \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
15.151 |
|
| \begin{align*}
\left (3 y x -2 x^{2}\right ) y^{\prime }&=2 y^{2}-y x \\
y \left (1\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
17.619 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x -k \sqrt {x^{2}+y^{2}}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
66.615 |
|
| \begin{align*}
y^{2} \left (y y^{\prime }-x \right )+x^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.382 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\tanh \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
31.120 |
|
| \begin{align*}
x +y+\left (x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.868 |
|
| \begin{align*}
3 x +y+\left (x +3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.230 |
|
| \begin{align*}
2 y x -\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
34.066 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
18.202 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
39.461 |
|
| \begin{align*}
y+\left (2 x -3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
24.401 |
|
| \begin{align*}
y y^{\prime } x&=x^{2}-y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.798 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.521 |
|
| \begin{align*}
y^{2}+\left (y x +x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
55.491 |
|
| \begin{align*}
2 x +y-\left (x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.488 |
|
| \begin{align*}
x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.064 |
|
| \begin{align*}
y+\left (3 x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
138.223 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
12.005 |
|
| \begin{align*}
y^{\prime } x -y-\sqrt {x^{2}+y^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
14.470 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
15.948 |
|
| \begin{align*}
y \sqrt {x^{2}+y^{2}}+y x&=x^{2} y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
30.243 |
|
| \begin{align*}
y \cos \left (\frac {x}{y}\right )-\left (y+x \cos \left (\frac {x}{y}\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
37.132 |
|
| \begin{align*}
y x -y^{2}-x^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.925 |
|
| \begin{align*}
\left (-2 x^{2}-3 y x \right ) y^{\prime }+y^{2}&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
4.049 |
|
| \begin{align*}
x^{2}+y^{2}&=2 y y^{\prime } x \\
y \left (2\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.125 |
|
| \begin{align*}
y^{3}+2 x^{2} y+\left (-3 x^{3}-2 x y^{2}\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
✗ |
26.633 |
|
| \begin{align*}
y^{\prime }&=-\frac {t}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.602 |
|
| \begin{align*}
2 y^{\prime } x +3 x +y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
18.612 |
|
| \begin{align*}
\left (-x +y\right ) y^{\prime }+2 x +3 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.293 |
|
| \begin{align*}
y^{\prime }-\frac {y^{2}}{x^{2}}&={\frac {1}{4}} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
7.704 |
|
| \begin{align*}
y^{\prime }-\frac {y^{2}}{x^{2}}&={\frac {1}{4}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.345 |
|
| \begin{align*}
\left (3 x -y\right ) y^{\prime }&=3 y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.007 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (x +y\right )^{2}}{2 x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.846 |
|
| \begin{align*}
\sin \left (\frac {y}{x}\right ) \left (-y+y^{\prime } x \right )&=x \cos \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
17.710 |
|
| \begin{align*}
y^{\prime } x&=\sqrt {16 x^{2}-y^{2}}+y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
47.989 |
|
| \begin{align*}
-y+y^{\prime } x&=\sqrt {9 x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
15.366 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
12.776 |
|
| \begin{align*}
y^{\prime } x +y \ln \left (x \right )&=y \ln \left (y\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.188 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+2 y x -2 x^{2}}{x^{2}-y x +y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.941 |
|
| \begin{align*}
2 y y^{\prime } x -2 y^{2}-x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.075 |
|
| \begin{align*}
x^{2} y^{\prime }&=y^{2}+3 y x +x^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.743 |
|
| \begin{align*}
y y^{\prime }&=\sqrt {x^{2}+y^{2}}-x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
18.914 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
17.414 |
|
| \begin{align*}
y^{\prime } x&=x \tan \left (\frac {y}{x}\right )+y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.885 |
|
| \begin{align*}
y^{\prime }&=\frac {x \sqrt {x^{2}+y^{2}}+y^{2}}{y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
38.202 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{2 x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.871 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y x +y^{2}}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
7.302 |
|
| \begin{align*}
\left (3 x -y\right ) y^{\prime }&=3 y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.441 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (x +y\right )^{2}}{2 x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.946 |
|
| \begin{align*}
\sin \left (\frac {y}{x}\right ) \left (-y+y^{\prime } x \right )&=x \cos \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
18.089 |
|
| \begin{align*}
y^{\prime } x&=\sqrt {16 x^{2}-y^{2}}+y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
38.692 |
|
| \begin{align*}
-y+y^{\prime } x&=\sqrt {9 x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
15.804 |
|
| \begin{align*}
y^{\prime } x +y \ln \left (x \right )&=y \ln \left (y\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.527 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+2 y x -2 x^{2}}{x^{2}-y x +y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.132 |
|
| \begin{align*}
2 y y^{\prime } x -2 y^{2}-x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.315 |
|
| \begin{align*}
x^{2} y^{\prime }&=y^{2}+3 y x +x^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.975 |
|
| \begin{align*}
y y^{\prime }&=\sqrt {x^{2}+y^{2}}-x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
18.347 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
17.454 |
|
| \begin{align*}
y^{\prime } x&=x \tan \left (\frac {y}{x}\right )+y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.260 |
|
| \begin{align*}
y^{\prime }&=\frac {x \sqrt {x^{2}+y^{2}}+y^{2}}{y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
38.110 |
|
| \begin{align*}
y^{\prime }&=\frac {-2 x +4 y}{x +y} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
1304.962 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
16.603 |
|
| \begin{align*}
y^{\prime }&=\frac {y-\sqrt {x^{2}+y^{2}}}{x} \\
y \left (3\right ) &= 4 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
18.447 |
|
| \begin{align*}
-y+y^{\prime } x&=\sqrt {4 x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
40.531 |
|
| \begin{align*}
y^{\prime }&=\frac {a y+x}{a x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
21.440 |
|
| \begin{align*}
y^{\prime }&=\frac {x +\frac {y}{2}}{\frac {x}{2}-y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.250 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
13.836 |
|
| \begin{align*}
x^{3}+y^{3}-y^{2} y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.728 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y^{2}}{2 x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.559 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x -y}{2 x +y} \\
y \left (2\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
24.766 |
|
| \begin{align*}
y y^{\prime }&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.162 |
|
| \begin{align*}
y^{\prime } x +y&=x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.592 |
|
| \begin{align*}
x^{2} y^{\prime }-y^{2}&=0 \\
y \left (1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.271 |
|
| \begin{align*}
y y^{\prime } x&=2 x^{2}-y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.263 |
|
| \begin{align*}
x^{2}-y^{2}+y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.808 |
|
| \begin{align*}
x^{2} y^{\prime }-2 y x -2 y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.843 |
|
| \begin{align*}
x^{2} y^{\prime }&=3 \left (x^{2}+y^{2}\right ) \arctan \left (\frac {y}{x}\right )+y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.645 |
|
| \begin{align*}
x \sin \left (\frac {y}{x}\right ) y^{\prime }&=y \sin \left (\frac {y}{x}\right )+x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
24.631 |
|
| \begin{align*}
\left (3 x^{2}-y^{2}\right ) y^{\prime }-2 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
19.199 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=-x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.241 |
|
| \begin{align*}
y^{\prime } x&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
18.117 |
|
| \begin{align*}
\left (y x -x^{2}\right ) y^{\prime }&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
63.724 |
|
| \begin{align*}
y^{2}-3 y x -2 x^{2}&=\left (x^{2}-y x \right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
20.129 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.784 |
|
| \begin{align*}
y^{\prime }+\frac {x}{y}+2&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
6.145 |
|
| \begin{align*}
-y+y^{\prime } x&=x \cot \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.813 |
|
| \begin{align*}
x \cos \left (\frac {y}{x}\right )^{2}-y+y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
6.379 |
|
| \begin{align*}
y^{\prime } x&=y \left (1+\ln \left (y\right )-\ln \left (x \right )\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.342 |
|
| \begin{align*}
y x +\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.278 |
|
| \begin{align*}
\left (1-{\mathrm e}^{-\frac {y}{x}}\right ) y^{\prime }+1-\frac {y}{x}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
14.516 |
|
| \begin{align*}
x^{2}-y x +y^{2}-y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
27.063 |
|
| \begin{align*}
2 y x +\left (x^{2}+2 y x +y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
26.332 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
62.664 |
|
| \begin{align*}
y^{\prime } x&=y-{\mathrm e}^{\frac {y}{x}} x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
6.885 |
|
| \begin{align*}
2 \sqrt {y x}-y-y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
15.175 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{\frac {x y^{\prime }}{y}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
13.448 |
|
| \begin{align*}
-y+y^{\prime } x&=x \tan \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.937 |
|
| \begin{align*}
y^{\prime } x&=y+\sqrt {x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
31.731 |
|
| \begin{align*}
x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
18.363 |
|
| \begin{align*}
x +\sin \left (\frac {y}{x}\right )^{2} \left (-y^{\prime } x +y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
19.241 |
|
| \begin{align*}
y^{\prime } x +x +y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.792 |
|
| \begin{align*}
y^{\prime } x&=a y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.037 |
|
| \begin{align*}
y^{\prime } x&=-a y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.010 |
|
| \begin{align*}
y^{\prime } x&=a x +b y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.438 |
|
| \begin{align*}
y^{\prime } x&=y+\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.579 |
|
| \begin{align*}
y^{\prime } x&=y+\sqrt {x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
31.003 |
|
| \begin{align*}
y^{\prime } x&=y+a \sqrt {y^{2}+b^{2} x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
43.697 |
|
| \begin{align*}
y^{\prime } x&=y+a \sqrt {y^{2}-b^{2} x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
43.089 |
|
| \begin{align*}
y^{\prime } x +x -y+x \cos \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.658 |
|
| \begin{align*}
y^{\prime } x&=-x \cos \left (\frac {y}{x}\right )^{2}+y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
7.059 |
|
| \begin{align*}
y^{\prime } x&=y-x \cot \left (\frac {y}{x}\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
11.118 |
|
| \begin{align*}
y^{\prime } x -y+x \sec \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.896 |
|
| \begin{align*}
y^{\prime } x&=y+x \sec \left (\frac {y}{x}\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
10.224 |
|
| \begin{align*}
y^{\prime } x&=y+x \sin \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.073 |
|
| \begin{align*}
y^{\prime } x&=y-x \tan \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.825 |
|
| \begin{align*}
y^{\prime } x&={\mathrm e}^{\frac {y}{x}} x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
8.385 |
|
| \begin{align*}
y^{\prime } x&=x +y+{\mathrm e}^{\frac {y}{x}} x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
9.514 |
|
| \begin{align*}
y^{\prime } x&=\left (1+\ln \left (x \right )-\ln \left (y\right )\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.676 |
|
| \begin{align*}
y^{\prime } x&=y-2 x \tanh \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
41.081 |
|
| \begin{align*}
x^{2} y^{\prime }+x^{2}+y x +y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.180 |
|
| \begin{align*}
x^{2} y^{\prime }&=\left (a y+x \right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.384 |
|
| \begin{align*}
x^{2} y^{\prime }&=\left (a x +b y\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
43.651 |
|
| \begin{align*}
x^{2} y^{\prime }+a \,x^{2}+b x y+c y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
27.526 |
|
| \begin{align*}
a \,x^{2} y^{\prime }&=x^{2}+a x y+b^{2} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
33.300 |
|
| \begin{align*}
x^{3} y^{\prime }&=\left (2 x^{2}+y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
69.162 |
|
| \begin{align*}
2 x^{3} y^{\prime }&=y \left (x^{2}-y^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
56.142 |
|
| \begin{align*}
2 x^{3} y^{\prime }&=\left (3 x^{2}+a y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
23.963 |
|
| \begin{align*}
x +y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.161 |
|
| \begin{align*}
y y^{\prime }+a x +b y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
58.611 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
24.335 |
|
| \begin{align*}
\left (x -y\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.009 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.482 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=x -y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
24.207 |
|
| \begin{align*}
\left (x -y\right ) y^{\prime }&=\left ({\mathrm e}^{-\frac {x}{y}}+1\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
18.215 |
|
| \begin{align*}
\left (2 x +y\right ) y^{\prime }+x -2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.911 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
70.560 |
|
| \begin{align*}
\left (x -2 y\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
20.782 |
|
| \begin{align*}
\left (x +2 y\right ) y^{\prime }+2 x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.214 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
25.362 |
|
| \begin{align*}
\left (x +4 y\right ) y^{\prime }+4 x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.211 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
20.421 |
|
| \begin{align*}
\left (a x +b y\right ) y^{\prime }+x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
60.758 |
|
| \begin{align*}
\left (a x +b y\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
31.310 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
33.825 |
|
| \begin{align*}
\left (a x +b y\right ) y^{\prime }&=a y+b x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
22.296 |
|
| \begin{align*}
y y^{\prime } x +x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.209 |
|
| \begin{align*}
y y^{\prime } x&=x^{2}-y x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
34.950 |
|
| \begin{align*}
y y^{\prime } x +2 x^{2}-2 y x -y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
18.665 |
|
| \begin{align*}
y y^{\prime } x +x^{2} \operatorname {arccot}\left (\frac {y}{x}\right )-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.810 |
|
| \begin{align*}
y y^{\prime } x +x^{2} {\mathrm e}^{-\frac {2 y}{x}}-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
9.983 |
|
| \begin{align*}
x \left (x +y\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
101.223 |
|
| \begin{align*}
x \left (x -y\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
28.325 |
|
| \begin{align*}
x \left (x +y\right ) y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
23.967 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
29.752 |
|
| \begin{align*}
x \left (x +y\right ) y^{\prime }-y \left (x +y\right )+x \sqrt {x^{2}-y^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
29.708 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
34.565 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
133.621 |
|
| \begin{align*}
x^{2}+y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
19.174 |
|
| \begin{align*}
2 y y^{\prime } x&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
22.339 |
|
| \begin{align*}
x \left (x -2 y\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
70.819 |
|
| \begin{align*}
x \left (x +2 y\right ) y^{\prime }+y \left (2 x -y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
38.920 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
38.972 |
|
| \begin{align*}
x \left (2 x +3 y\right ) y^{\prime }&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
91.431 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
31.570 |
|
| \begin{align*}
a x y y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
26.143 |
|
| \begin{align*}
a x y y^{\prime }+x^{2}-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
23.639 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
29.891 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
135.344 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
27.115 |
|
| \begin{align*}
8 y y^{\prime } x^{3}+3 x^{4}-6 y^{2} x^{2}-y^{4}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
88.825 |
|
| \begin{align*}
y x +\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
21.852 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }&=y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
14.190 |
|
| \begin{align*}
\left (x^{2}-y^{2}\right ) y^{\prime }&=2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
25.884 |
|
| \begin{align*}
\left (x^{2}-y^{2}\right ) y^{\prime }+x \left (x +2 y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
51.514 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }+2 x \left (2 x +y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
49.738 |
|
| \begin{align*}
\left (3 x^{2}-y^{2}\right ) y^{\prime }&=2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
34.345 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
22.928 |
|
| \begin{align*}
\left (x +y\right )^{2} y^{\prime }&=x^{2}-2 y x +5 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
24.646 |
|
| \begin{align*}
\left (2 x^{2}+4 y x -y^{2}\right ) y^{\prime }&=x^{2}-4 y x -2 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
50.967 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
48.434 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
17.286 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
50.329 |
|
| \begin{align*}
\left (x^{2}+a y^{2}\right ) y^{\prime }&=y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
15.536 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
106.220 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
71.869 |
|
| \begin{align*}
\left (a \,x^{2}+2 b x y+c y^{2}\right ) y^{\prime }+k \,x^{2}+2 a x y+b y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
140.224 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
24.312 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
64.520 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
29.250 |
|
| \begin{align*}
x \left (x^{2}+a x y+y^{2}\right ) y^{\prime }&=\left (x^{2}+b x y+y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
19.156 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
31.796 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
39.740 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
29.336 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
22.724 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
41.621 |
|
| \begin{align*}
\left (x^{3}-y^{3}\right ) y^{\prime }+x^{2} y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.243 |
|
| \begin{align*}
\left (x^{3}+y^{3}\right ) y^{\prime }+x^{2} \left (a x +3 y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.206 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
51.364 |
|
| \begin{align*}
2 y^{3} y^{\prime }&=x^{3}-x y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.368 |
|
| \begin{align*}
\left (3 x^{2}+2 y^{2}\right ) y y^{\prime }+x^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
52.639 |
|
| \begin{align*}
\left (5 x^{2}+2 y^{2}\right ) y y^{\prime }+x \left (x^{2}+5 y^{2}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.660 |
|
| \begin{align*}
\left (3 x^{3}+6 x^{2} y-3 x y^{2}+20 y^{3}\right ) y^{\prime }+4 x^{3}+9 x^{2} y+6 x y^{2}-y^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
41.973 |
|
| \begin{align*}
\left (x^{3}+a y^{3}\right ) y^{\prime }&=x^{2} y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.994 |
|
| \begin{align*}
x \left (2 x^{3}+y^{3}\right ) y^{\prime }&=\left (2 x^{3}-x^{2} y+y^{3}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
414.749 |
|
| \begin{align*}
x \left (2 x^{3}-y^{3}\right ) y^{\prime }&=\left (x^{3}-2 y^{3}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
144.448 |
|
| \begin{align*}
x \left (x^{3}+3 x^{2} y+y^{3}\right ) y^{\prime }&=\left (3 x^{2}+y^{2}\right ) y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
39.671 |
|
| \begin{align*}
x \left (x^{3}-2 y^{3}\right ) y^{\prime }&=\left (2 x^{3}-y^{3}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
122.055 |
|
| \begin{align*}
\left (a \,x^{3}+\left (a x +b y\right )^{3}\right ) y y^{\prime }+x \left (\left (a x +b y\right )^{3}+y^{3} b \right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
49.552 |
|
| \begin{align*}
y^{\prime } \sqrt {y x}+x -y&=\sqrt {y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
41.713 |
|
| \begin{align*}
\left (x -2 \sqrt {y x}\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
37.243 |
|
| \begin{align*}
\left (x -\sqrt {x^{2}+y^{2}}\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
31.926 |
|
| \begin{align*}
x \left (x +\sqrt {x^{2}+y^{2}}\right ) y^{\prime }+y \sqrt {x^{2}+y^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
75.979 |
|
| \begin{align*}
x y \left (x +\sqrt {x^{2}-y^{2}}\right ) y^{\prime }&=x y^{2}-\left (x^{2}-y^{2}\right )^{{3}/{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
36.142 |
|
| \begin{align*}
x \left (x -y \tan \left (\frac {y}{x}\right )\right ) y^{\prime }+\left (x +y \tan \left (\frac {y}{x}\right )\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
51.383 |
|
| \begin{align*}
y^{\prime }&=\frac {x y}{x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
33.129 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
52.981 |
|
| \begin{align*}
\left (-x +y\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
33.380 |
|
| \begin{align*}
\left (2 \sqrt {y x}-x \right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
55.744 |
|
| \begin{align*}
y^{\prime } x -y-\sqrt {x^{2}+y^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
39.575 |
|
| \begin{align*}
x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
27.153 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
37.356 |
|
| \begin{align*}
-y+y^{\prime } x&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
38.707 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
36.404 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
41.035 |
|
| \begin{align*}
y^{2}+\left (y x +x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
151.957 |
|
| \begin{align*}
y&=y^{\prime } x +x \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
91.342 |
|
| \begin{align*}
2 y x +\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
336.522 |
|
| \begin{align*}
\left (x +\sqrt {y^{2}-y x}\right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
106.053 |
|
| \begin{align*}
x +y-\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
24.309 |
|
| \begin{align*}
y^{\prime } x -y-x \sin \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
16.918 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
36.696 |
|
| \begin{align*}
y^{2}+\left (x \sqrt {y^{2}-x^{2}}-y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
120.756 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
38.059 |
|
| \begin{align*}
y+x \ln \left (\frac {y}{x}\right ) y^{\prime }-2 y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
76.724 |
|
| \begin{align*}
2 \,{\mathrm e}^{\frac {x}{y}} y+\left (y-2 \,{\mathrm e}^{\frac {x}{y}} x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
24.016 |
|
| \begin{align*}
{\mathrm e}^{\frac {y}{x}} x -y \sin \left (\frac {y}{x}\right )+x \sin \left (\frac {y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
31.639 |
|
| \begin{align*}
x^{2}+y^{2}&=2 y y^{\prime } x \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
34.081 |
|
| \begin{align*}
{\mathrm e}^{\frac {y}{x}} x +y&=y^{\prime } x \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
45.859 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}+\csc \left (\frac {y}{x}\right )&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
15.839 |
|
| \begin{align*}
y x -y^{2}-x^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.274 |
|
| \begin{align*}
y^{\prime }&=1+\frac {y}{x}-\frac {y^{2}}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
32.493 |
|
| \begin{align*}
-y+y^{\prime } x&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
40.987 |
|
| \begin{align*}
\left (x^{2}-y^{2}\right ) y^{\prime }&=2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
38.339 |
|
| \begin{align*}
y^{\prime } x&=x +y+{\mathrm e}^{\frac {y}{x}} x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
22.056 |
|
| \begin{align*}
y^{\prime } x -y-x \sin \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
17.069 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
52.816 |
|
| \begin{align*}
x^{2} y^{\prime }+x^{2}+y x +y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
13.540 |
|
| \begin{align*}
y y^{\prime } x +x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
36.198 |
|
| \begin{align*}
2 y y^{\prime } x +3 x^{2}-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
38.968 |
|
| \begin{align*}
\left (2 x y^{3}-x^{4}\right ) y^{\prime }+2 x^{3} y-y^{4}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
138.685 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }+2 x \left (2 x +y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
57.642 |
|
| \begin{align*}
2 y^{3} y^{\prime }+x y^{2}-x^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
4.651 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}-y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.434 |
|
| \begin{align*}
y y^{\prime }&=\sqrt {x^{2}+y^{2}}-x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
52.791 |
|
| \begin{align*}
y x +\left (y^{2}-x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
36.050 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
39.708 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}-\tan \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
20.125 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
54.106 |
|
| \begin{align*}
3 x^{2} y+x^{3} y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.963 |
|
| \begin{align*}
y^{2}+2 y x -x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.052 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
51.796 |
|
| \begin{align*}
y^{2}+2 y x -x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
17.582 |
|
| \begin{align*}
2 y x +\left (y^{2}-3 x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
57.604 |
|
| \begin{align*}
y^{2}+2 y x -x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.173 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
116.979 |
|
| \begin{align*}
2 t x x^{\prime }+t^{2}-x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
85.622 |
|
| \begin{align*}
-y+y^{\prime } t&=\sqrt {t y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
63.510 |
|
| \begin{align*}
y x +y^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.005 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
88.783 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}-y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.419 |
|
| \begin{align*}
x^{2}+y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
37.328 |
|
| \begin{align*}
x^{\prime }&=\frac {x^{2}+t \sqrt {t^{2}+x^{2}}}{t x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
111.073 |
|
| \begin{align*}
y^{\prime }&=\frac {t \sec \left (\frac {y}{t}\right )+y}{t} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
17.264 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}-y^{2}}{3 x y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
64.862 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (1+\ln \left (y\right )-\ln \left (x \right )\right )}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
40.339 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x y}{2 x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
51.930 |
|
| \begin{align*}
x^{2}+y^{2}+3 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
45.119 |
|
| \begin{align*}
x^{2}-3 y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
89.361 |
|
| \begin{align*}
y-x +\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
65.128 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\
y \left (1\right ) &= -4 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
35.825 |
|
| \begin{align*}
2 y^{2}+4 x^{2}-y y^{\prime } x&=0 \\
y \left (1\right ) &= -2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
45.585 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {x^{2}+y^{2}}-x}{y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
80.680 |
|
| \begin{align*}
\left (x y^{2}+x^{3}\right ) y^{\prime }&=2 y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
32.684 |
|
| \begin{align*}
\left (-x +2 y\right ) y^{\prime }&=2 x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
59.319 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
75.937 |
|
| \begin{align*}
x^{3}+y^{3}&=3 y^{2} y^{\prime } x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
62.382 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
59.312 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
221.299 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
98.227 |
|
| \begin{align*}
x^{2} y^{\prime }&=y^{2}-y y^{\prime } x \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
58.715 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=y y^{\prime } x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
116.785 |
|
| \begin{align*}
2 y y^{\prime } x&=x^{2}-y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
42.770 |
|
| \begin{align*}
y^{\prime } x&=2 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.295 |
|
| \begin{align*}
x +y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
34.773 |
|
| \begin{align*}
2 x^{3} y^{\prime }&=y \left (3 x^{2}+y^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
62.836 |
|
| \begin{align*}
4 y+y^{\prime } x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.735 |
|
| \begin{align*}
y^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
21.790 |
|
| \begin{align*}
x \sin \left (\frac {y}{x}\right )-y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
31.182 |
|
| \begin{align*}
y \sqrt {x^{2}+y^{2}}-x \left (x +\sqrt {x^{2}+y^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
81.642 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
77.583 |
|
| \begin{align*}
2 y^{\prime } x -2 y&=\sqrt {x^{2}+4 y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
68.254 |
|
| \begin{align*}
y^{2}-x^{2}+y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
48.954 |
|
| \begin{align*}
x^{3}+y^{3}+3 y^{2} y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
56.704 |
|
| \begin{align*}
y^{\prime } x +2 y&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.490 |
|
| \begin{align*}
y y^{\prime } x +x^{2}+y^{2}&=0 \\
y \left (1\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
41.983 |
|
| \begin{align*}
y \left (x -2 y\right )-x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
16.802 |
|
| \begin{align*}
y y^{\prime } x +x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
41.068 |
|
| \begin{align*}
x^{2}+y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
44.490 |
|
| \begin{align*}
y^{\prime } x -2 y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.415 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
26.131 |
|
| \begin{align*}
y^{\prime } x&=2 y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
15.990 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
55.517 |
|
| \begin{align*}
\left (-x +y\right ) y^{\prime }&=x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
75.497 |
|
| \begin{align*}
y y^{\prime }&=3 x \\
y \left (-2\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
36.928 |
|
| \begin{align*}
y y^{\prime }&=3 x \\
y \left (2\right ) &= -4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
24.448 |
|
| \begin{align*}
y y^{\prime }&=3 x \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
96.718 |
|
| \begin{align*}
3 y^{\prime } x -2 y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.389 |
|
| \begin{align*}
y^{\prime } x +y&=2 x \\
y \left (x_{0} \right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
35.851 |
|
| \begin{align*}
y y^{\prime }&=-x \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
27.849 |
|
| \begin{align*}
y^{\prime }&=1-\frac {y}{x} \\
y \left (-\frac {1}{2}\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
21.570 |
|
| \begin{align*}
y^{\prime }&=1-\frac {y}{x} \\
y \left (\frac {3}{2}\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
20.884 |
|
| \begin{align*}
y^{\prime } x&=4 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
16.592 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{y} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
34.319 |
|
| \begin{align*}
\frac {1}{\sqrt {x}}+\frac {y^{\prime }}{\sqrt {y}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
119.333 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {y}}{\sqrt {x}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
115.690 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
45.246 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=y y^{\prime } x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
134.401 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }&=2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
171.879 |
|
| \begin{align*}
-y+y^{\prime } x&=x \tan \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
27.871 |
|
| \begin{align*}
y^{\prime } x&=y-{\mathrm e}^{\frac {y}{x}} x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
23.860 |
|
| \begin{align*}
-y+y^{\prime } x&=\left (x +y\right ) \ln \left (\frac {x +y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
47.362 |
|
| \begin{align*}
y^{\prime } x&=y \cos \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
22.731 |
|
| \begin{align*}
y+\sqrt {y x}-y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
81.547 |
|
| \begin{align*}
y^{\prime } x -\sqrt {x^{2}-y^{2}}-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
145.132 |
|
| \begin{align*}
x +y-\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
41.797 |
|
| \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] |
✓ |
✓ |
✗ |
✗ |
79.864 |
|
| \begin{align*}
-y+y^{\prime } x&=y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
46.893 |
|
| \begin{align*}
y^{2}+\left (x^{2}-y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
127.726 |
|
| \begin{align*}
x^{2}+y x +y^{2}&=x^{2} y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
20.687 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
223.430 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y}{3 x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
87.687 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
35.579 |
|
| \begin{align*}
y^{\prime } x&=y+\sqrt {y^{2}-x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
81.378 |
|
| \begin{align*}
\left (2 \sqrt {y x}-x \right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
105.976 |
|
| \begin{align*}
y^{\prime } x&=y \ln \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
46.472 |
|
| \begin{align*}
-y+y^{\prime } x&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
67.829 |
|
| \begin{align*}
y^{\prime }+\frac {x +2 y}{x}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
21.763 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
48.415 |
|
| \begin{align*}
y^{\prime } x&=x +\frac {y}{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
94.428 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
115.592 |
|
| \begin{align*}
y^{\prime } x -2 \sqrt {y x}&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
86.645 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}-y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.395 |
|
| \begin{align*}
x +y-\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
44.343 |
|
| \begin{align*}
y+\sqrt {x^{2}+y^{2}}-y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
76.876 |
|
| \begin{align*}
x^{2}+y^{2}-2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
64.326 |
|
| \begin{align*}
x^{2}-y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
99.434 |
|
| \begin{align*}
x +y y^{\prime }+y-y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
44.607 |
|
| \begin{align*}
y y^{\prime }&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
47.731 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
44.760 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{y x +x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
136.237 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y x +y^{2}}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
21.404 |
|
| \begin{align*}
y^{\prime }&=\frac {y+x \,{\mathrm e}^{-\frac {2 y}{x}}}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
27.909 |
|
| \begin{align*}
y^{\prime } x&=2 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
18.408 |
|
| \begin{align*}
y^{\prime }&=\frac {y x}{x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
45.276 |
|
| \begin{align*}
2 y y^{\prime } x&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
59.502 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{y x -x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
132.848 |
|
| \begin{align*}
x^{5} y^{\prime }+y^{5}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
62.638 |
|
| \begin{align*}
x^{2}-2 y^{2}+y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
113.791 |
|
| \begin{align*}
x^{2} y^{\prime }-3 y x -2 y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
58.368 |
|
| \begin{align*}
x^{2} y^{\prime }&=3 \left (x^{2}+y^{2}\right ) \arctan \left (\frac {y}{x}\right )+y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
50.734 |
|
| \begin{align*}
x \sin \left (\frac {y}{x}\right ) y^{\prime }&=y \sin \left (\frac {y}{x}\right )+x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
49.283 |
|
| \begin{align*}
y^{\prime } x&=y+2 \,{\mathrm e}^{-\frac {y}{x}} x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
29.624 |
|
| \begin{align*}
x -y-\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
90.247 |
|
| \begin{align*}
y^{\prime } x&=2 x -6 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
25.212 |
|
| \begin{align*}
y^{\prime } x&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
125.800 |
|
| \begin{align*}
x^{2} y^{\prime }&=y^{2}+2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
34.480 |
|
| \begin{align*}
x^{3}+y^{3}-y^{2} y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
90.978 |
|
| \begin{align*}
y^{\prime }&=\sin \left (\frac {y}{x}\right )-\cos \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
20.586 |
|
| \begin{align*}
{\mathrm e}^{\frac {x}{y}}-\frac {y y^{\prime }}{x}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
42.688 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}-y x}{y^{2} \cos \left (\frac {x}{y}\right )} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
46.105 |
|
| \begin{align*}
y^{\prime }&=\frac {y \tan \left (\frac {y}{x}\right )}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
50.893 |
|
| \begin{align*}
y^{\prime } x +y&=x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
22.496 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y^{2}}{x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
53.498 |
|
| \begin{align*}
y^{\prime }&=\frac {x +2 y}{2 x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
47.743 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.737 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
53.649 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+2 y^{2}}{x^{2}-2 y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
50.139 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
76.682 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
19.936 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.441 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=y y^{\prime } x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
103.072 |
|
| \begin{align*}
y^{\prime }&=\frac {5 x^{2}-y x +y^{2}}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
23.704 |
|
| \begin{align*}
y y^{\prime }-y&=x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
91.007 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {y}{x}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
15.336 |
|
| \begin{align*}
y^{\prime } x -y-\sqrt {x^{2}+y^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.347 |
|
| \begin{align*}
y^{\prime } x +a \sqrt {x^{2}+y^{2}}-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
20.624 |
|
| \begin{align*}
y^{\prime } x -{\mathrm e}^{\frac {y}{x}} x -y-x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
7.139 |
|
| \begin{align*}
y^{\prime } x -y-x \sin \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.585 |
|
| \begin{align*}
y^{\prime } x +x -y+x \cos \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.819 |
|
| \begin{align*}
y^{\prime } x +x \tan \left (\frac {y}{x}\right )-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.891 |
|
| \begin{align*}
x^{2} y^{\prime }+x^{2}+y x +y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.568 |
|
| \begin{align*}
x^{2} y^{\prime }-y^{2}-y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.456 |
|
| \begin{align*}
x^{2} y^{\prime }-y^{2}-y x -x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.786 |
|
| \begin{align*}
3 x^{2} y^{\prime }-7 y^{2}-3 y x -x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.411 |
|
| \begin{align*}
y y^{\prime }+a y+x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
20.904 |
|
| \begin{align*}
y y^{\prime }-{\mathrm e}^{\frac {x}{y}} x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.316 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
22.151 |
|
| \begin{align*}
y y^{\prime } x +x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.796 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
22.296 |
|
| \begin{align*}
2 y y^{\prime } x -y^{2}+a \,x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.900 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
23.533 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
75.658 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }+2 x \left (2 x +y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
46.700 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.339 |
|
| \begin{align*}
\left (y^{2}-x^{2}\right ) y^{\prime }+2 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
16.099 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
13.342 |
|
| \begin{align*}
\left (x^{2}+4 y^{2}\right ) y^{\prime }-y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.117 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
334.441 |
|
| \begin{align*}
\left (a y^{2}+2 b x y+c \,x^{2}\right ) y^{\prime }+b y^{2}+2 c x y+d \,x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
145.948 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
15.816 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
16.023 |
|
| \begin{align*}
\left (y^{3}-x^{3}\right ) y^{\prime }-x^{2} y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.197 |
|
| \begin{align*}
\left (2 y^{3}+5 x^{2} y\right ) y^{\prime }+5 x y^{2}+x^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.419 |
|
| \begin{align*}
\left (3 x^{3}+6 x^{2} y-3 x y^{2}+20 y^{3}\right ) y^{\prime }+4 x^{3}+9 x^{2} y+6 x y^{2}-y^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
23.351 |
|
| \begin{align*}
\left (2 x y^{3}-x^{4}\right ) y^{\prime }+2 x^{3} y-y^{4}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
106.250 |
|
| \begin{align*}
y \left (y^{3}-2 x^{3}\right ) y^{\prime }+\left (2 y^{3}-x^{3}\right ) x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
138.307 |
|
| \begin{align*}
y \left (\left (a y+b x \right )^{3}+b \,x^{3}\right ) y^{\prime }+x \left (\left (a y+b x \right )^{3}+a y^{3}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
41.971 |
|
| \begin{align*}
\left (x +\sqrt {x^{2}+y^{2}}\right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
18.527 |
|
| \begin{align*}
\left (y \sqrt {x^{2}+y^{2}}+\left (y^{2}-x^{2}\right ) \sin \left (\alpha \right )-2 x y \cos \left (\alpha \right )\right ) y^{\prime }+x \sqrt {x^{2}+y^{2}}+2 x y \sin \left (\alpha \right )+\left (y^{2}-x^{2}\right ) \cos \left (\alpha \right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
84.523 |
|
| \begin{align*}
x y^{\prime } \cot \left (\frac {y}{x}\right )+2 x \sin \left (\frac {y}{x}\right )-y \cot \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
31.332 |
|
| \begin{align*}
\left (-y+y^{\prime } x \right ) \cos \left (\frac {y}{x}\right )^{2}+x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
18.218 |
|
| \begin{align*}
\left (y \sin \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right )\right ) x y^{\prime }-\left (x \cos \left (\frac {y}{x}\right )+y \sin \left (\frac {y}{x}\right )\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
21.755 |
|
| \begin{align*}
x \left (y^{\prime }+\sqrt {1+{y^{\prime }}^{2}}\right )-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
59.217 |
|
| \begin{align*}
y^{\prime }&=f \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.168 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
99.994 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
83.632 |
|
| \begin{align*}
y^{\prime } x +x +y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
14.800 |
|
| \begin{align*}
{\mathrm e}^{\frac {y}{x}} x +y-y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
19.306 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
79.145 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}-y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.445 |
|
| \begin{align*}
2 x^{2} y+y^{3}-x^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
102.319 |
|
| \begin{align*}
y^{3}+x^{3} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
37.016 |
|
| \begin{align*}
x +y \cos \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
33.849 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}-y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.814 |
|
| \begin{align*}
x +y-\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
27.154 |
|
| \begin{align*}
x^{2}+y^{2}-2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
60.070 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
57.779 |
|
| \begin{align*}
y^{2}-x^{2}+2 m x y+\left (m y^{2}-x^{2} m -2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
124.566 |
|
| \begin{align*}
x +y y^{\prime }+y-y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
23.544 |
|
| \begin{align*}
\left (-x +y\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
40.499 |
|
| \begin{align*}
-y+y^{\prime } x&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
46.392 |
|
| \begin{align*}
-y+y^{\prime } x&=\sqrt {x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
108.178 |
|
| \begin{align*}
x \sin \left (\frac {y}{x}\right )-y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
21.076 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
95.670 |
|
| \begin{align*}
1+{\mathrm e}^{\frac {y}{x}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
39.000 |
|
| \begin{align*}
\left (2 \sqrt {y x}-x \right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
74.998 |
|
| \begin{align*}
x^{\prime }&=\frac {2 x}{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.362 |
|
| \begin{align*}
x^{\prime }&=-\frac {t}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
24.318 |
|
| \begin{align*}
2 t x^{\prime }&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.058 |
|
| \begin{align*}
x^{\prime }&=\frac {4 t^{2}+3 x^{2}}{2 t x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
42.251 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+2 t y}{t^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
17.909 |
|
| \begin{align*}
x^{\prime }&=\frac {2 x}{3 t}+\frac {2 t}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
95.923 |
|
| \begin{align*}
t^{2} y^{\prime }+2 t y-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
59.793 |
|
| \begin{align*}
x^{2}-t^{2} x^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
17.852 |
|
| \begin{align*}
x^{2}+y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
40.582 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
73.760 |
|
| \begin{align*}
y^{2}+2 y x -x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.141 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
75.483 |
|
| \begin{align*}
v^{3}+\left (u^{3}-u v^{2}\right ) v^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
71.523 |
|
| \begin{align*}
x \tan \left (\frac {y}{x}\right )+y-y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
23.735 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
410.394 |
|
| \begin{align*}
x^{3}+y^{2} \sqrt {x^{2}+y^{2}}-x y \sqrt {x^{2}+y^{2}}\, y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
52.378 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
67.087 |
|
| \begin{align*}
x^{2}+3 y^{2}-2 y y^{\prime } x&=0 \\
y \left (2\right ) &= 6 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
40.322 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
110.159 |
|
| \begin{align*}
3 x^{2}+9 y x +5 y^{2}-\left (6 x^{2}+4 y x \right ) y^{\prime }&=0 \\
y \left (2\right ) &= -6 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
58.467 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
59.893 |
|
| \begin{align*}
3 x -y-\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
75.781 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
437.006 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
80.935 |
|
| \begin{align*}
3 x -5 y+\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
244.321 |
|
| \begin{align*}
2 x^{2}+y x +y^{2}+2 x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
114.525 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x -7 y}{3 y-8 x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
219.725 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
110.099 |
|
| \begin{align*}
x^{2}+y^{2}-2 y y^{\prime } x&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
44.879 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +7 y}{2 x -2 y} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
80.521 |
|
| \begin{align*}
y x +x^{2} y^{\prime }&=\frac {y^{3}}{x} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
209.023 |
|
| \begin{align*}
y^{\prime } x&=k y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.369 |
|
| \begin{align*}
y x +y^{2}+x^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
15.445 |
|
| \begin{align*}
x^{\prime }&=\frac {x^{2}+t \sqrt {t^{2}+x^{2}}}{t x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
117.687 |
|
| \begin{align*}
y^{\prime } x&=y+\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
47.924 |
|
| \begin{align*}
x \left (\ln \left (x \right )-\ln \left (y\right )\right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
85.620 |
|
| \begin{align*}
x^{\prime }&={\mathrm e}^{\frac {x}{t}}+\frac {x}{t} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
21.458 |
|
| \begin{align*}
y \left (x -y\right )-x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.533 |
|
| \begin{align*}
y \left (x -y\right )-x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.479 |
|
| \begin{align*}
\left (y^{2}-x^{2}\right ) y^{\prime }+2 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
43.948 |
|
| \begin{align*}
y-x +\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
73.060 |
|
| \begin{align*}
y^{\prime } x +x +y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
16.059 |
|
| \begin{align*}
x +y+\left (-x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
37.145 |
|
| \begin{align*}
-y+y^{\prime } x&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
51.167 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
52.191 |
|
| \begin{align*}
2 \sqrt {t s}-s+t s^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
57.783 |
|
| \begin{align*}
y^{2} y^{\prime } x&=x^{3}+y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
73.218 |
|
| \begin{align*}
x \cos \left (\frac {y}{x}\right ) \left (y^{\prime } x +y\right )&=y \sin \left (\frac {y}{x}\right ) \left (-y+y^{\prime } x \right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
58.589 |
|
| \begin{align*}
\frac {-y^{\prime } x +y}{\sqrt {x^{2}+y^{2}}}&=m \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
130.158 |
|
| \begin{align*}
\frac {x +y y^{\prime }}{\sqrt {x^{2}+y^{2}}}&=m \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
155.533 |
|
| \begin{align*}
y+\frac {x}{y^{\prime }}&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
38.959 |
|
| \begin{align*}
y y^{\prime }&=\sqrt {x^{2}+y^{2}}-x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
72.721 |
|
| \begin{align*}
\frac {x}{\left (x +y\right )^{2}}+\frac {\left (2 x +y\right ) y^{\prime }}{\left (x +y\right )^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
26.042 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
48.213 |
|
| \begin{align*}
\frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
19.550 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{x}-\sqrt {3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
11.289 |
|
| \begin{align*}
\frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
19.960 |
|
| \begin{align*}
x \cos \left (\frac {y}{x}\right ) y^{\prime }&=y \cos \left (\frac {y}{x}\right )-x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
34.307 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
16.385 |
|
| \begin{align*}
2 y^{\prime } x -y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.292 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
43.132 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x -y}{x +3 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
75.565 |
|
| \begin{align*}
y^{\prime }&=\frac {y x}{x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
38.707 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{-x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
76.944 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
78.688 |
|
| \begin{align*}
x -y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
32.115 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{-x +y} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
63.520 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{-x +y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
62.193 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{-x +y} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
55.956 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{-x +y} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
59.786 |
|
| \begin{align*}
y^{\prime }&=\frac {y x}{x^{2}+y^{2}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
75.197 |
|
| \begin{align*}
y^{\prime }&=\frac {t}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
55.782 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{t}+2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
22.765 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{t}+2 \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
23.108 |
|
| \begin{align*}
y y^{\prime }&=2 x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
37.375 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
53.077 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
55.201 |
|
| \begin{align*}
x^{2} y^{\prime }-y x&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
20.062 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
37.320 |
|
| \begin{align*}
\cos \left (\frac {y}{x}\right ) \left (y^{\prime }-\frac {y}{x}\right )&=1+\sin \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
27.490 |
|
| \begin{align*}
y^{\prime }-\frac {3 y}{x}&=\frac {y^{2}}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
62.461 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\frac {x^{2}}{y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
85.847 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
56.566 |
|
| \begin{align*}
\left (2 y x +2 x^{2}\right ) y^{\prime }&=x^{2}+2 y x +2 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
107.858 |
|
| \begin{align*}
-y+y^{\prime } x&=\sqrt {y x +x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
105.503 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
111.761 |
|
| \begin{align*}
4 x^{3} y+\left (x^{4}-y^{4}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
175.879 |
|
| \begin{align*}
y y^{\prime } x -y^{2}&=\sqrt {y^{2} x^{2}+x^{4}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
168.904 |
|
| \begin{align*}
x^{3}+y^{3}+y^{2} y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
116.822 |
|
| \begin{align*}
y y^{\prime } x&=2 x^{2}+2 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
66.973 |
|
| \begin{align*}
y^{\prime }&=\frac {x +2 y}{2 x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
52.486 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\tan \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
28.780 |
|
| \begin{align*}
y y^{\prime } x&=x^{2}+y x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
103.284 |
|
| \begin{align*}
2 x -y-y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.292 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.217 |
|
| \begin{align*}
y^{\prime }&=-\frac {2 y}{x}-3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.186 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+2 y x}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.984 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
15.169 |
|
| \begin{align*}
y^{\prime }&=\sqrt {\frac {y}{t}} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
14.462 |
|
| \begin{align*}
y^{\prime } t +y&=t \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.306 |
|
| \begin{align*}
\frac {t}{\sqrt {t^{2}+y^{2}}}+\frac {y y^{\prime }}{\sqrt {t^{2}+y^{2}}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.800 |
|
| \begin{align*}
{\mathrm e}^{t y}+\frac {t \,{\mathrm e}^{t y} y^{\prime }}{y}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.138 |
|
| \begin{align*}
\frac {3 t^{2}}{y}-\frac {t^{3} y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.141 |
|
| \begin{align*}
2 t y+\left (t^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
300.106 |
|
| \begin{align*}
3 t^{2}+3 y^{2}+6 t y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.523 |
|
| \begin{align*}
-\frac {y^{2} {\mathrm e}^{\frac {y}{t}}}{t^{2}}+1+{\mathrm e}^{\frac {y}{t}} \left (1+\frac {y}{t}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.793 |
|
| \begin{align*}
2 t \sin \left (\frac {y}{t}\right )-y \cos \left (\frac {y}{t}\right )+t \cos \left (\frac {y}{t}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.282 |
|
| \begin{align*}
t^{2} y+t^{3} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.985 |
|
| \begin{align*}
2 t y+y^{2}-t^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.142 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
60.895 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
39.595 |
|
| \begin{align*}
y^{\prime }-\frac {y}{t}&=\frac {y^{2}}{t^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.394 |
|
| \begin{align*}
\cos \left (\frac {t}{y+t}\right )+{\mathrm e}^{\frac {2 y}{t}} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
21.872 |
|
| \begin{align*}
y \ln \left (\frac {t}{y}\right )+\frac {t^{2} y^{\prime }}{y+t}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
6.491 |
|
| \begin{align*}
\frac {2}{t}+\frac {1}{y}+\frac {t y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.334 |
|
| \begin{align*}
2 t +\left (y-3 t \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
33.659 |
|
| \begin{align*}
2 y-3 t +y^{\prime } t&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.350 |
|
| \begin{align*}
t y-y^{2}+t \left (t -3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
21.076 |
|
| \begin{align*}
t^{2}+t y+y^{2}-t y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
25.853 |
|
| \begin{align*}
t^{3}+y^{3}-t y^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.105 |
|
| \begin{align*}
y^{\prime }&=\frac {t +4 y}{4 t +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.322 |
|
| \begin{align*}
y+\left (y+t \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.323 |
|
| \begin{align*}
2 t^{2}-7 t y+5 y^{2}+t y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
55.447 |
|
| \begin{align*}
y+2 \sqrt {t^{2}+y^{2}}-y^{\prime } t&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
14.050 |
|
| \begin{align*}
y^{2}&=\left (t y-4 t^{2}\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
14.675 |
|
| \begin{align*}
y-\left (3 \sqrt {t y}+t \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.730 |
|
| \begin{align*}
t y y^{\prime }-t^{2} {\mathrm e}^{-\frac {y}{t}}-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.395 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{\frac {2 y \,{\mathrm e}^{-\frac {t}{y}}}{t}+\frac {t}{y}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.013 |
|
| \begin{align*}
t \left (\ln \left (t \right )-\ln \left (y\right )\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
17.270 |
|
| \begin{align*}
y^{\prime } t -y-\sqrt {t^{2}+y^{2}}&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.689 |
|
| \begin{align*}
t^{3}+y^{2} \sqrt {t^{2}+y^{2}}-t y \sqrt {t^{2}+y^{2}}\, y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
14.474 |
|
| \begin{align*}
y^{3}-t^{3}-t y^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 3 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.054 |
|
| \begin{align*}
t y^{3}-\left (t^{4}+y^{4}\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
18.926 |
|
| \begin{align*}
y^{4}+\left (t^{4}-t y^{3}\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
✓ |
12.062 |
|
| \begin{align*}
t^{{1}/{3}} y^{{2}/{3}}+t +\left (t^{{2}/{3}} y^{{1}/{3}}+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
20.058 |
|
| \begin{align*}
y^{\prime }&=\frac {-t^{2}+y^{2}}{t y} \\
y \left (4\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.207 |
|
| \begin{align*}
y \sin \left (\frac {t}{y}\right )-\left (t +t \sin \left (\frac {t}{y}\right )\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.806 |
|
| \begin{align*}
3 t +\left (t -4 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
18.287 |
|
| \begin{align*}
y-t +\left (y+t \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.640 |
|
| \begin{align*}
y^{2}+\left (t^{2}+t y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
65.733 |
|
| \begin{align*}
r^{\prime }&=\frac {r^{2}+t^{2}}{r t} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.678 |
|
| \begin{align*}
x^{\prime }&=\frac {5 t x}{t^{2}+x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
22.162 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.716 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.730 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.875 |
|
| \begin{align*}
y^{\prime } x&=2 x -y \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.984 |
|
| \begin{align*}
y^{\prime } x&=y+x \cos \left (\frac {y}{x}\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
6.776 |
|
| \begin{align*}
y^{\prime } x&=y \left (\ln \left (y\right )-\ln \left (x \right )\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.288 |
|
| \begin{align*}
x^{2} y^{\prime }&=x^{2}-y x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.569 |
|
| \begin{align*}
y^{\prime } x&=y+\sqrt {y^{2}-x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
16.025 |
|
| \begin{align*}
2 x^{2} y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.477 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
27.411 |
|
| \begin{align*}
y-x +\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
20.608 |
|
| \begin{align*}
y^{\prime } x +y&=2 x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.822 |
|
| \begin{align*}
3 y^{2} y^{\prime } x -2 y^{3}&=x^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.755 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
37.033 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
34.486 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
73.716 |
|
| \begin{align*}
5 y x -4 y^{2}-6 x^{2}+\left (y^{2}-8 y x +\frac {5 x^{2}}{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
45.068 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
64.401 |
|
| \begin{align*}
1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
15.744 |
|
| \begin{align*}
x^{2}+y^{2}-y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.283 |
|
| \begin{align*}
y^{\prime }&=\frac {t -y}{2 t +5 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
25.451 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
30.460 |
|
| \begin{align*}
y^{\prime }&=-\frac {4 x +2 y}{2 x +3 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
24.058 |
|
| \begin{align*}
y^{\prime }&=-\frac {4 x -2 y}{2 x -3 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
36.496 |
|
| \begin{align*}
\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.694 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
18.536 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
34.191 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
19.510 |
|
| \begin{align*}
y+\sqrt {x^{2}-y^{2}}&=y^{\prime } x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
42.432 |
|
| \begin{align*}
y y^{\prime } x&=\left (x +y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
21.525 |
|
| \begin{align*}
y^{\prime }&=\frac {4 y-7 x}{5 x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
26.662 |
|
| \begin{align*}
y^{\prime } x -4 \sqrt {y^{2}-x^{2}}&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
36.488 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{4}+2 x y^{3}-3 y^{2} x^{2}-2 x^{3} y}{2 y^{2} x^{2}-2 x^{3} y-2 x^{4}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
121.152 |
|
| \begin{align*}
\left (y+{\mathrm e}^{\frac {x}{y}} x \right ) y^{\prime }&={\mathrm e}^{\frac {x}{y}} y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.146 |
|
| \begin{align*}
y y^{\prime } x&=x^{2}+y^{2} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
17.691 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{x -y} \\
y \left (5\right ) &= 8 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
50.324 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
28.247 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
40.266 |
|
| \begin{align*}
4 y y^{\prime } x&=8 x^{2}+5 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
31.412 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y x}{x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
42.534 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (1+\ln \left (y\right )-\ln \left (x \right )\right )}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
17.011 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=y y^{\prime } x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
27.467 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=-x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.993 |
|
| \begin{align*}
x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
20.075 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
30.843 |
|
| \begin{align*}
y^{\prime } x&=2 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.405 |
|
| \begin{align*}
y^{\prime }&=\frac {y x}{x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
14.936 |
|
| \begin{align*}
2 y y^{\prime } x&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.731 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{y x -x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
76.585 |
|
| \begin{align*}
x^{5} y^{\prime }+y^{5}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
21.931 |
|
| \begin{align*}
x^{2}-2 y^{2}+y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
62.810 |
|
| \begin{align*}
x^{2} y^{\prime }-3 y x -2 y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.293 |
|
| \begin{align*}
x^{2} y^{\prime }&=3 \left (x^{2}+y^{2}\right ) \arctan \left (\frac {y}{x}\right )+y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
18.685 |
|
| \begin{align*}
x \sin \left (\frac {y}{x}\right ) y^{\prime }&=y \sin \left (\frac {y}{x}\right )+x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
29.504 |
|
| \begin{align*}
y^{\prime } x&=y+2 \,{\mathrm e}^{-\frac {y}{x}} x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.840 |
|
| \begin{align*}
x -y-\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
32.206 |
|
| \begin{align*}
y^{\prime } x&=2 x +3 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
10.308 |
|
| \begin{align*}
y^{\prime } x&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
39.579 |
|
| \begin{align*}
x^{2} y^{\prime }&=y^{2}+2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.986 |
|
| \begin{align*}
x^{3}+y^{3}-y^{2} y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
29.124 |
|
| \begin{align*}
\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
18.410 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
46.464 |
|
| \begin{align*}
\left (3 x^{2}-y^{2}\right ) y^{\prime }-2 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
35.740 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=-x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
20.280 |
|
| \begin{align*}
y^{\prime } x +y&=y^{\prime } \sqrt {y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
164.438 |
|
| \begin{align*}
y^{\prime } x&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
38.088 |
|
| \begin{align*}
y y^{\prime } x&=x^{2} y^{\prime }+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
32.663 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
34.696 |
|
| \begin{align*}
x^{2} y^{4}+x^{6}-x^{3} y^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
110.931 |
|
| \begin{align*}
y^{\prime }&=1+\frac {y}{x}-\frac {y^{2}}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
19.658 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
134.595 |
|
| \begin{align*}
\frac {-x +y}{\left (x +y\right )^{3}}-\frac {2 x y^{\prime }}{\left (x +y\right )^{3}}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
44.735 |
|
| \begin{align*}
3 x^{2} y-y^{3}-\left (3 x y^{2}-x^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.370 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
40.654 |
|
| \begin{align*}
x^{2} y^{\prime }&=x^{2}+y x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
11.411 |
|
| \begin{align*}
x^{2} y^{\prime }-y^{2}&=2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.168 |
|
| \begin{align*}
x^{\prime }&=\cos \left (\frac {x}{t}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.119 |
|
| \begin{align*}
\left (t^{2}-x^{2}\right ) x^{\prime }&=t x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
23.891 |
|
| \begin{align*}
v^{\prime }+\frac {2 v}{u}&=3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
12.048 |
|
| \begin{align*}
y^{2}&=x \left (-x +y\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
83.742 |
|
| \begin{align*}
2 x^{2} y+y^{3}-x^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
78.564 |
|
| \begin{align*}
x +y y^{\prime }&=m y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
54.616 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
38.211 |
|
| \begin{align*}
y^{\prime }&=1+\frac {2 y}{x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
20.802 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
65.895 |
|
| \begin{align*}
5 y y^{\prime } x -x^{2}-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
36.305 |
|
| \begin{align*}
\left (x^{2}+3 y x -y^{2}\right ) y^{\prime }-3 y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
34.868 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
40.592 |
|
| \begin{align*}
3 x^{2} y^{\prime }+2 x^{2}-3 y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
13.053 |
|
| \begin{align*}
x^{2}+y^{2}-2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
27.438 |
|
| \begin{align*}
y^{2}+\left (y x +x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
129.649 |
|
| \begin{align*}
x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.307 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
91.135 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
361.434 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
34.421 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
60.499 |
|
| \begin{align*}
-y+y^{\prime } x&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
29.967 |
|
| \begin{align*}
y^{\prime } x +\frac {y^{2}}{x}&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.177 |
|
| \begin{align*}
x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.122 |
|
| \begin{align*}
x +y y^{\prime }&=m \left (-y+y^{\prime } x \right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
38.178 |
|
| \begin{align*}
y y^{\prime }&=a x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
16.895 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
23.721 |
|
| \begin{align*}
\left (y^{2}-x^{2}\right ) y^{\prime }+2 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
28.471 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=y y^{\prime } x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
82.931 |
|
| \begin{align*}
\sqrt {x}\, y^{\prime }&=\sqrt {y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
47.707 |
|
| \begin{align*}
y^{\prime } x +x +y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
13.318 |
|
| \begin{align*}
y-x +\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
40.966 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
64.429 |
|
| \begin{align*}
x +y y^{\prime }&=m \left (-y+y^{\prime } x \right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
40.487 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }&=y x +x^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
33.835 |
|
| \begin{align*}
\left (x \cos \left (\frac {y}{x}\right )+y \sin \left (\frac {y}{x}\right )\right ) y-\left (y \sin \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right )\right ) x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
40.550 |
|
| \begin{align*}
x^{2}-y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
38.718 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\tan \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
20.559 |
|
| \begin{align*}
y^{2}&=\left (y x -x^{2}\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
40.664 |
|
| \begin{align*}
x \sin \left (\frac {y}{x}\right ) y^{\prime }&=y \sin \left (\frac {y}{x}\right )-x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
27.332 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }&=y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
20.757 |
|
| \begin{align*}
x^{2} y^{\prime }+y \left (x +y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
32.464 |
|
| \begin{align*}
2 y^{\prime }&=\frac {y}{x}+\frac {y^{2}}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
69.573 |
|
| \begin{align*}
-y+y^{\prime } x&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
32.364 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
51.404 |
|
| \begin{align*}
x^{2}+3 y^{2}-2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
29.277 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
37.491 |
|
| \begin{align*}
x^{2}+y^{2}-2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
29.924 |
|
| \begin{align*}
-y+y^{\prime } x&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
32.671 |
|
| \begin{align*}
x +y y^{\prime }&=m \left (-y+y^{\prime } x \right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
42.250 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=y y^{\prime } x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
42.342 |
|
| \begin{align*}
y&=y^{\prime } x +x \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
83.642 |
|
| \begin{align*}
-y^{\prime } x +y&=x +y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
26.828 |
|
| \begin{align*}
\left (x \cos \left (\frac {y}{x}\right )+y \sin \left (\frac {y}{x}\right )\right ) y&=\left (y \sin \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right )\right ) x y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
42.235 |
|
| \begin{align*}
y^{2}+\left (y x +x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
144.713 |
|
| \begin{align*}
x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.612 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
74.295 |
|
| \begin{align*}
y^{\prime }&=\frac {y x +y^{2}}{x^{2}} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.263 |
|
| \begin{align*}
x^{2}-y x +y^{2}-y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
42.074 |
|
| \begin{align*}
y x -\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
23.083 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
35.425 |
|
| \begin{align*}
y&=y^{\prime } x -\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
36.760 |
|
| \begin{align*}
x^{\prime }&=\frac {t}{x} \\
x \left (\sqrt {2}\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
27.991 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
47.161 |
|
| \begin{align*}
x +y+\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
45.376 |
|
| \begin{align*}
x^{2}+2 y x -y^{2}+\left (x -y\right )^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
28.020 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
228.030 |
|
| \begin{align*}
x^{2}+a_{1} x y+a_{2} y^{2}+\left (x^{2}+b_{1} x y+b_{2} y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.744 |
|
| \begin{align*}
x^{\prime }&=\frac {t x}{t^{2}+x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
28.685 |
|
| \begin{align*}
x^{\prime }&=\frac {3 x^{2}-2 t^{2}}{t x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
39.451 |
|
| \begin{align*}
x^{\prime }&=\frac {t^{2}+x^{2}}{2 t x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
42.246 |
|
| \begin{align*}
x +y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
25.553 |
|
| \begin{align*}
y^{\prime } x +y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.262 |
|
| \begin{align*}
y^{\prime } x -2 y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.625 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
21.034 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.949 |
|
| \begin{align*}
x -y+\left (x -4 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
110.702 |
|
| \begin{align*}
x^{2}-y x +y^{2}-y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
59.713 |
|
| \begin{align*}
x^{2}-2 y^{2}+y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✗ |
89.158 |
|
| \begin{align*}
y x +\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
36.838 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+3 x +y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
51.914 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y \,{\mathrm e}^{\frac {2 x}{y}}}{y^{2}+y^{2} {\mathrm e}^{\frac {2 x}{y}}+2 x^{2} {\mathrm e}^{\frac {2 x}{y}}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
89.810 |
|
| \begin{align*}
y^{2}-x^{2}-2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
80.217 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{3}-2 x^{3}}{x y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
55.548 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y^{4}+x^{4}}{x y^{3}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
136.889 |
|
| \begin{align*}
y^{\prime }&=\sqrt {1-\frac {y^{2}}{x^{2}}}+\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
92.359 |
|
| \begin{align*}
2 y y^{\prime } x&=y^{2}-x^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
70.312 |
|
| \begin{align*}
x +y-\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
27.686 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y}{y^{2}-x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
54.221 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y^{4}+x^{4}}{x y^{3}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
132.489 |
|
| \begin{align*}
x^{2}-3 y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
91.184 |
|
| \begin{align*}
y y^{\prime } x +x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
40.240 |
|
| \begin{align*}
-y+y^{\prime } x&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
49.104 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y}{x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
41.622 |
|
| \begin{align*}
y+\sqrt {x^{2}+y^{2}}-y^{\prime } x&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
45.629 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y^{2}}{y x} \\
y \left (1\right ) &= -2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✗ |
30.359 |
|
| \begin{align*}
\frac {y^{2}-y x}{x y^{2}}+\frac {x y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
19.062 |
|
| \begin{align*}
y^{\prime }&=\frac {x -2 y}{2 x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
59.276 |
|
| \begin{align*}
y^{\prime } \left (x +\frac {x^{2}}{y}\right )&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
104.777 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
48.741 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y}{y^{2}-x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
54.454 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +y}{y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
38.546 |
|
| \begin{align*}
y^{\prime } x&=x +2 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
12.088 |
|
| \begin{align*}
x +y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
27.828 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{4 y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
23.231 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
33.230 |
|
| \begin{align*}
x +y y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
26.055 |
|
| \begin{align*}
y&=y^{\prime } x -\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
49.115 |
|
| \begin{align*}
x^{3}-y^{3}+y^{2} y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
57.997 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}-\csc \left (\frac {y}{x}\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
20.066 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
59.976 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
81.114 |
|
| \begin{align*}
x^{2}+2 y x -2 y^{2}+\left (y^{2}+2 y x -2 x^{2}\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 3 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
49.088 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
53.889 |
|
| \begin{align*}
a \,x^{2}+2 b x y+c y^{2}+\left (b \,x^{2}+2 c x y+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
133.017 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) \left (y^{\prime } x +y\right )&=x y \left (-y+y^{\prime } x \right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
81.690 |
|
| \begin{align*}
x^{2} y^{\prime }-y x&=x^{2}-y^{2} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
42.197 |
|
| \begin{align*}
x y \left (y^{\prime } x +y\right )&=4 x^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
42.644 |
|
| \begin{align*}
\left (1+{\mathrm e}^{-\frac {y}{x}}\right ) y^{\prime }+1-\frac {y}{x}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
46.598 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
49.321 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=y y^{\prime } x \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
69.639 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y \,{\mathrm e}^{\frac {y}{x}}}{x^{2}+y^{2} \sin \left (\frac {x}{y}\right )} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
48.057 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}}{y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
64.533 |
|
| \begin{align*}
y^{\prime }&=-\frac {2 y}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
16.028 |
|
| \begin{align*}
y^{\prime }&=\frac {x y^{2}}{x^{2} y+y^{3}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
33.323 |
|
| \begin{align*}
x +y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
27.737 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y^{4}+x^{4}}{x y^{3}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
141.427 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y}{x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
43.762 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
148.441 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
131.956 |
|
| \begin{align*}
y^{\prime }&=\frac {x +2 y}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
13.807 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+2 y^{2}}{y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
43.591 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y^{2}}{y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
31.945 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y}{y^{2}-x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
55.787 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x +\sqrt {y x}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
71.727 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{4}+3 y^{2} x^{2}+y^{4}}{x^{3} y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
149.950 |
|
| \begin{align*}
y^{\prime } x +y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.233 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
35.158 |
|
| \begin{align*}
y+3 y^{\prime } x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.451 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{x}&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
17.841 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{x}&=0 \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.207 |
|
| \begin{align*}
y+\left (2 x -3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
128.455 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
57.046 |
|
| \begin{align*}
y^{\prime }&=\frac {x -2 y}{y-2 x} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
✗ |
206.578 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{y} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
30.326 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{x} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.387 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\frac {y^{2}}{x^{2}} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
24.777 |
|
| \begin{align*}
y^{\prime } x&=2 x +3 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
23.803 |
|
| \begin{align*}
x^{2}-y^{2}-2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
48.459 |
|
| \begin{align*}
y^{\prime } x&=y-\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
68.480 |
|
| \begin{align*}
y&=\left (2 x +3 y\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
137.812 |
|
| \begin{align*}
x^{3}+y^{3}-y^{2} y^{\prime } x&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
51.914 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{2 y}+\frac {y}{2 x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
54.501 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\sec \left (\frac {y}{x}\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
22.993 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {x^{2}+y^{2}}}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
95.124 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +5 y}{2 x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
193.618 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
78.349 |
|
| \begin{align*}
2 x \sin \left (\frac {y}{x}\right )+2 x \tan \left (\frac {y}{x}\right )-y \cos \left (\frac {y}{x}\right )-y \sec \left (\frac {y}{x}\right )^{2}+\left (x \cos \left (\frac {y}{x}\right )+x \sec \left (\frac {y}{x}\right )^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
122.549 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {x +y}+\sqrt {x -y}}{-\sqrt {x -y}+\sqrt {x +y}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
89.524 |
|
| \begin{align*}
3 x +4 y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
37.168 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y}{x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
74.490 |
|
| \begin{align*}
2 y y^{\prime } x&=x^{2}-y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
49.353 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
77.408 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
54.569 |
|
| \begin{align*}
y^{2}+2 x^{2}+y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
51.806 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
40.483 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
25.874 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
135.548 |
|
| \begin{align*}
x^{2}+y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
56.460 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\arctan \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
24.793 |
|
| \begin{align*}
u^{2} v-\left (u^{3}+v^{3}\right ) v^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.037 |
|
| \begin{align*}
y^{\prime }&=\frac {x +2 y}{y-2 x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
88.042 |
|
| \begin{align*}
x^{2}-y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
110.533 |
|
| \begin{align*}
x +2 y+y^{\prime } x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
27.966 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{\frac {y}{x}}+\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
34.819 |
|
| \begin{align*}
-y+y^{\prime } x&=x \cos \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
34.352 |
|
| \begin{align*}
2 y+3 x +y^{\prime } x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
24.666 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
62.364 |
|
| \begin{align*}
y^{2}&=\left (x^{2}+2 y x \right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
132.098 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
45.786 |
|
| \begin{align*}
y^{\prime } x +y \ln \left (x \right )&=y \ln \left (y\right )+y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
64.208 |
|
| \begin{align*}
y^{\prime }&=2-\frac {y}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
28.202 |
|
| \begin{align*}
i^{\prime }&=\frac {i t^{2}}{t^{3}-i^{3}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.661 |
|
| \begin{align*}
y^{\prime }&=\frac {x +3 y}{x -3 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
94.363 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
101.263 |
|
| \begin{align*}
y^{\prime }&=\sqrt {\frac {5 x -6 y}{5 x +6 y}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
154.944 |
|
| \begin{align*}
x^{2}+y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
59.105 |
|
| \begin{align*}
y^{\prime } x +y&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
20.205 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
22.147 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y}{x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
91.100 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y^{2}}{y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
47.223 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}-\frac {x}{y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
47.518 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y^{2}}{2 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
66.495 |
|
| \begin{align*}
y^{\prime }&=-\frac {x^{2}+y^{2}}{2 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
56.851 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
79.780 |
|
| \begin{align*}
x^{2}+y^{2}-2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
61.259 |
|
| \begin{align*}
y^{\prime } x +y&=3 x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
27.390 |
|
| \begin{align*}
x^{2}+y^{2}-2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
63.941 |
|
| \begin{align*}
y y^{\prime }-7 y&=6 x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
88.312 |
|
| \begin{align*}
x +y y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
63.908 |
|
| \begin{align*}
y^{\prime } x +y&=2 x \\
y \left (2\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
28.884 |
|
| \begin{align*}
x +y+\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
91.276 |
|
| \begin{align*}
x^{2}+y^{2}-2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
67.572 |
|
| \begin{align*}
x^{2}+y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
58.340 |
|
| \begin{align*}
x^{2}+y^{2}+2 y y^{\prime } x&=0 \\
y \left (1\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
51.201 |
|
| \begin{align*}
y-\left (x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
72.963 |
|
| \begin{align*}
x^{4}+y^{4}-x y^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
154.262 |
|
| \begin{align*}
5 x -y+3 y^{\prime } x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
30.111 |
|
| \begin{align*}
x^{2}+y^{2}-2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
70.777 |
|
| \begin{align*}
-x^{2} y+\left (x^{3}+y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.181 |
|
| \begin{align*}
3 y+\left (7 x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
110.539 |
|
| \begin{align*}
{\mathrm e}^{\frac {y}{x}}-\frac {y}{x}+y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
37.516 |
|
| \begin{align*}
y x -\left (x^{2}-y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
62.431 |
|
| \begin{align*}
x -y+\left (2 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
99.099 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
50.933 |
|
| \begin{align*}
y^{\prime }&=-\frac {x +2 y}{y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
47.510 |
|
| \begin{align*}
x^{2}+y^{2}-2 y y^{\prime } x&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
60.820 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {2}\, \sqrt {\frac {x +y}{x}}}{2} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
179.802 |
|
| \begin{align*}
y^{\prime } x +y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
20.313 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}-\frac {x}{y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
60.184 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=x -y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
102.849 |
|
| \begin{align*}
2 y^{\prime } x +y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
20.795 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
150.283 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x -y}{x +2 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
108.141 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\sin \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
42.197 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y}{x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
71.427 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{3}+y^{3}}{y^{2} x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
116.934 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2} {\mathrm e}^{\frac {y}{x}}+y^{2}}{y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
44.493 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{3}+x^{2} y-y^{3}}{x^{3}-x y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
427.782 |
|
| \begin{align*}
y^{\prime }&=\frac {y+\sqrt {x^{2}-y^{2}}}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
224.953 |
|
| \begin{align*}
y^{\prime }&=1+\frac {3 y}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
37.758 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
227.815 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
95.862 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=\frac {x^{2}}{y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
193.550 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
128.747 |
|
| \begin{align*}
x^{2} y^{\prime }-y^{2}&=2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
45.063 |
|
| \begin{align*}
3 y^{2}-2 x^{2}&=2 y y^{\prime } x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
142.880 |
|
| \begin{align*}
2 y-3 y^{\prime } x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
29.924 |
|
| \begin{align*}
m y-n x y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
28.629 |
|
| \begin{align*}
v^{\prime }&=-\frac {v}{p} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
24.424 |
|
| \begin{align*}
\left (2 x +y\right ) y^{\prime }+x -2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
69.713 |
|
| \begin{align*}
y x -\left (x^{2}+2 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
72.065 |
|
| \begin{align*}
2 y^{2}+4 x^{2}-y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
83.444 |
|
| \begin{align*}
2 x^{2}+y x -2 y^{2}-\left (x^{2}-4 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
13.026 |
|
| \begin{align*}
x^{2}+2 y^{2}-y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
76.336 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
262.205 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
234.728 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
103.108 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
82.279 |
|
| \begin{align*}
x \left (x^{2}+y^{2}\right )^{2} \left (-y^{\prime } x +y\right )+y^{6} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
38.738 |
|
| \begin{align*}
y y^{\prime } x +x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
80.096 |
|
| \begin{align*}
y x -\left (x +2 y\right )^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
102.868 |
|
| \begin{align*}
v^{2}+x \left (x +v\right ) v^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
212.642 |
|
| \begin{align*}
x \csc \left (\frac {y}{x}\right )-y+y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
33.770 |
|
| \begin{align*}
x +\sin \left (\frac {y}{x}\right )^{2} \left (-y^{\prime } x +y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
37.280 |
|
| \begin{align*}
x -y \ln \left (y\right )+y \ln \left (x \right )+x \left (\ln \left (y\right )-\ln \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
85.607 |
|
| \begin{align*}
x -y \arctan \left (\frac {y}{x}\right )+x \arctan \left (\frac {y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
190.945 |
|
| \begin{align*}
y^{2} y^{\prime }&=x \left (-y+y^{\prime } x \right ) {\mathrm e}^{\frac {x}{y}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
83.249 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
87.645 |
|
| \begin{align*}
y-\left (x +\sqrt {y^{2}-x^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
184.507 |
|
| \begin{align*}
x -y+\left (3 x +y\right ) y^{\prime }&=0 \\
y \left (2\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
78.276 |
|
| \begin{align*}
y-\sqrt {x^{2}+y^{2}}-y^{\prime } x&=0 \\
y \left (\sqrt {3}\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
112.382 |
|
| \begin{align*}
y+\sqrt {x^{2}+y^{2}}-y^{\prime } x&=0 \\
y \left (\sqrt {3}\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
106.172 |
|
| \begin{align*}
x \cos \left (\frac {y}{x}\right )^{2}-y+y^{\prime } x&=0 \\
y \left (1\right ) &= \frac {\pi }{4} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
33.947 |
|
| \begin{align*}
y^{2}+7 y x +16 x^{2}+x^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
44.250 |
|
| \begin{align*}
y^{2}+\left (x^{2}+3 y x +4 y^{2}\right ) y^{\prime }&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
77.293 |
|
| \begin{align*}
y \left (2 x^{2}-y x +y^{2}\right )-x^{2} \left (2 x -y\right ) y^{\prime }&=0 \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
152.383 |
|
| \begin{align*}
y \left (9 x -2 y\right )-x \left (6 x -y\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
201.440 |
|
| \begin{align*}
y \left (x^{2}+y^{2}\right )+x \left (3 x^{2}-5 y^{2}\right ) y^{\prime }&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
134.261 |
|
| \begin{align*}
16 x +15 y+\left (3 x +y\right ) y^{\prime }&=0 \\
y \left (1\right ) &= -3 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
260.835 |
|
| \begin{align*}
v \left (3 x +2 v\right )-x^{2} v^{\prime }&=0 \\
v \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
80.262 |
|
| \begin{align*}
x +y+\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
117.799 |
|
| \begin{align*}
2 y x +\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
385.299 |
|
| \begin{align*}
\left (y^{2}-x^{2}\right ) y^{\prime }+2 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
78.253 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
104.873 |
|
| \begin{align*}
y^{\prime } x +x +y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
38.329 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
254.129 |
|
| \begin{align*}
x^{3}+y^{3}+y^{2} \left (3 x +k y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
176.460 |
|
| \begin{align*}
y \left (x +3 y\right )+x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
111.454 |
|
| \begin{align*}
\left (2 x^{3}-x^{2} y+y^{3}\right ) y-x \left (2 x^{3}+y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
129.540 |
|
| \begin{align*}
x -y \cos \left (\frac {y}{x}\right )+x y^{\prime } \cot \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
94.915 |
|
| \begin{align*}
y \left (x^{2}+y^{2}\right )+x \left (3 x^{2}-5 y^{2}\right ) y^{\prime }&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
124.363 |
|
| \begin{align*}
x -y-\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
127.115 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
87.045 |
|
| \begin{align*}
x -y+\left (3 x +y\right ) y^{\prime }&=0 \\
y \left (2\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
86.739 |
|
| \begin{align*}
x^{2}-2 y x -y^{2}-\left (x^{2}+2 y x -y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
72.967 |
|
| \begin{align*}
y \left (y^{2}-3 x^{2}\right )+x^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
176.378 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
185.835 |
|
| \begin{align*}
y^{3}-x^{3}&=x y \left (x +y y^{\prime }\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
74.688 |
|
| \begin{align*}
2 x^{3} y^{\prime }&=y \left (3 x^{2}+y^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
106.843 |
|
| \begin{align*}
-y+y^{\prime } x&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
33.470 |
|
| \begin{align*}
2 y^{3}-x^{3}+3 y^{2} y^{\prime } x&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
115.657 |
|
| \begin{align*}
x^{2}+6 y^{2}-4 y y^{\prime } x&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
80.893 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
178.257 |
|
| \begin{align*}
x^{4}-4 y^{2} x^{2}-y^{4}+4 y y^{\prime } x^{3}&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
149.019 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}-4 t y+6 t^{2}}{t^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
62.419 |
|
| \begin{align*}
\left (t^{2}+3 y^{2}\right ) y^{\prime }&=-2 t y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
411.973 |
|
| \begin{align*}
y y^{\prime }&=t \\
y \left (2\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
92.450 |
|
| \begin{align*}
t^{2} y^{\prime }&=y^{2}+t y+t^{2} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
55.030 |
|
| \begin{align*}
y^{\prime }&=\frac {4 t -3 y}{t -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
115.326 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}-4 t y+6 t^{2}}{t^{2}} \\
y \left (2\right ) &= 4 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
70.671 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+2 t y}{t^{2}+t y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
121.887 |
|
| \begin{align*}
y^{\prime }&=\frac {3 y^{2}-t^{2}}{2 t y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
176.750 |
|
| \begin{align*}
y^{\prime }&=\frac {t^{2}+y^{2}}{t y} \\
y \left ({\mathrm e}\right ) &= 2 \,{\mathrm e} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
106.819 |
|
| \begin{align*}
y^{\prime } t&=y+\sqrt {t^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
✗ |
277.501 |
|
| \begin{align*}
t^{2} y^{\prime }&=t y+y \sqrt {t^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
325.988 |
|
| \begin{align*}
y-t +\left (t +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
173.610 |
|
| \begin{align*}
y^{2}+2 t y y^{\prime }+3 t^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
112.467 |
|
| \begin{align*}
3 y-5 t +2 y y^{\prime }-y^{\prime } t&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
205.878 |
|
| \begin{align*}
\left (t^{2}+3 y^{2}\right ) y^{\prime }+2 t y&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✗ |
✗ |
16.764 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
280.133 |
|
| \begin{align*}
y^{\prime }&=\frac {t -y}{y+t} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
147.617 |
|
| \begin{align*}
y^{\prime } t&=2 y-t \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
32.241 |
|
| \begin{align*}
y^{\prime }&=\frac {c t -a y}{A t +b y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
276.683 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{t^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
66.892 |
|
| \begin{align*}
y^{\prime }&=\frac {-3 t^{2}-2 y^{2}}{4 t y+6 y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
517.423 |
|
| \begin{align*}
y^{\prime }&=\frac {4 t -y}{t -6 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
147.808 |
|
| \begin{align*}
y^{\prime }&=-\frac {3 t^{2}+2 y^{2}}{4 t y+6 y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
487.855 |
|
| \begin{align*}
y^{\prime } x -2 y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
47.565 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
90.290 |
|
| \begin{align*}
y^{\prime } x&=2 y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
37.892 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
149.244 |
|
| \begin{align*}
\left (-x +y\right ) y^{\prime }&=x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
182.529 |
|
| \begin{align*}
y y^{\prime }&=3 x \\
y \left (-2\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
87.531 |
|
| \begin{align*}
y y^{\prime }&=3 x \\
y \left (2\right ) &= -4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
75.425 |
|
| \begin{align*}
y^{\prime } x&=2 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
42.446 |
|
| \begin{align*}
y^{\prime } x&=2 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
35.318 |
|
| \begin{align*}
3 y^{\prime } x -2 y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
44.375 |
|
| \begin{align*}
y^{\prime } x +y&=2 x \\
y \left (x_{0} \right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
87.957 |
|
| \begin{align*}
y y^{\prime }&=-x \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
81.240 |
|
| \begin{align*}
y^{\prime }&=1-\frac {y}{x} \\
y \left (-\frac {1}{2}\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
62.326 |
|
| \begin{align*}
y^{\prime }&=1-\frac {y}{x} \\
y \left (\frac {3}{2}\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
52.546 |
|
| \begin{align*}
y^{\prime } x&=4 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
46.790 |
|
| \begin{align*}
y+3 x +y^{\prime } x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
49.141 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y}{x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
121.635 |
|
| \begin{align*}
y^{\prime }&=\frac {6 x^{2}-7 y^{2}}{14 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
120.070 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{3}+y^{3}}{y^{2} x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
216.221 |
|
| \begin{align*}
y^{\prime }&=\frac {y+\sqrt {x^{2}-y^{2}}}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
376.621 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\sin \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
73.428 |
|
| \begin{align*}
x^{2}-y^{2}-\frac {2 y^{3} y^{\prime }}{x}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
224.323 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
156.749 |
|
| \begin{align*}
y^{2}+\left (y x +x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
271.408 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
214.160 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
55.598 |
|
| \begin{align*}
y^{\prime } x +x +y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
63.201 |
|
| \begin{align*}
y^{\prime } x&={\mathrm e}^{\frac {y}{x}} x +y \\
y \left (1\right ) &= \ln \left (2\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
99.905 |
|
| \begin{align*}
y^{\prime } x&=y+\sqrt {y^{2}-x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
236.115 |
|
| \begin{align*}
y y^{\prime } x&=2 y^{2}-3 x^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
175.082 |
|
| \begin{align*}
x +y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
98.447 |
|
| \begin{align*}
x^{2}+y^{2}-2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
151.000 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{\left (\ln \left (x \right )-\ln \left (y\right )\right ) x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
251.501 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
122.017 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
508.468 |
|
| \begin{align*}
x +y-\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
88.885 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
114.757 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
37.507 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
214.434 |
|
| \begin{align*}
y^{\prime } x&=y+\sqrt {y^{2}-x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
237.704 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
247.782 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
281.368 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y}{3 x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
217.142 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
152.142 |
|
| \begin{align*}
y^{\prime } x&=\sqrt {y^{2}-x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
376.083 |
|
| \begin{align*}
a \,x^{2}+2 b x y+c y^{2}+y^{\prime } \left (b \,x^{2}+2 c x y+f y^{2}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
289.253 |
|
| \begin{align*}
x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
65.401 |
|
| \begin{align*}
y^{3} y^{\prime }+3 x y^{2}+2 x^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
290.239 |
|
| \begin{align*}
\left (2 \sqrt {y x}-x \right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
286.885 |
|
| \begin{align*}
3 y^{\prime } x -2 y&=\frac {x^{3}}{y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
236.564 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
322.510 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{\frac {x y^{\prime }}{y}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
212.090 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
275.585 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
241.415 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
331.839 |
|
| \begin{align*}
1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
157.473 |
|
| \begin{align*}
x^{2}+y^{2}-y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
112.602 |
|
| \begin{align*}
y \left (\left (a y+b x \right )^{3}+b \,x^{3}\right ) y^{\prime }+x \left (\left (a y+b x \right )^{3}+a y^{3}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
226.874 |
|
| \begin{align*}
y^{\prime } x&=x -y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
75.003 |
|
| \begin{align*}
y^{\prime } x +y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
48.231 |
|
| \begin{align*}
1+{\mathrm e}^{\frac {y}{x}}-\frac {y \,{\mathrm e}^{\frac {y}{x}}}{x}+{\mathrm e}^{\frac {y}{x}} y^{\prime }&=0 \\
y \left (1\right ) &= -5 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
107.917 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
420.175 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{x^{2}}-\frac {y}{x}+1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
73.217 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
126.088 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
162.158 |
|
| \begin{align*}
\left (x -2 y\right ) y^{\prime }&=2 x -y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
230.818 |
|
| \begin{align*}
y^{\prime } x&=x \cos \left (\frac {y}{x}\right )+y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
90.317 |
|
| \begin{align*}
x^{2} y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
84.682 |
|
| \begin{align*}
x^{3} y^{\prime }&=x^{2} y-y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
231.137 |
|
| \begin{align*}
x +y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
121.511 |
|
| \begin{align*}
y^{\prime } x&=2 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
58.622 |
|
| \begin{align*}
y^{\prime } x +y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
47.941 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
146.290 |
|
| \begin{align*}
y^{\prime }&=\frac {-3 x +y}{x +3 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
148.675 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
157.329 |
|
| \begin{align*}
x +2 y-y^{\prime } x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
43.328 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
115.789 |
|
| \begin{align*}
y^{2}-2 y x +x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
119.084 |
|
| \begin{align*}
2 x^{3} y^{\prime }&=\left (2 x^{2}-y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
195.714 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=y y^{\prime } x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
263.822 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }&=2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
250.362 |
|
| \begin{align*}
-y+y^{\prime } x&=x \tan \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
91.054 |
|
| \begin{align*}
y^{\prime } x&=y-{\mathrm e}^{\frac {y}{x}} x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
82.054 |
|
| \begin{align*}
-y+y^{\prime } x&=\left (x +y\right ) \ln \left (\frac {x +y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
150.953 |
|
| \begin{align*}
y^{\prime } x&=y \cos \left (\ln \left (\frac {y}{x}\right )\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✗ |
✓ |
✓ |
358.454 |
|
| \begin{align*}
y+\sqrt {y x}&=y^{\prime } x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
304.402 |
|
| \begin{align*}
y^{\prime } x&=y+\sqrt {x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
389.586 |
|
| \begin{align*}
2 y x +\left (x^{2}-y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
569.703 |
|
| \begin{align*}
y^{\prime } x&=y+\sqrt {y^{2}-x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
305.900 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{\frac {x y^{\prime }}{y}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
236.644 |
|
| \begin{align*}
x^{2} y^{\prime }&=y \left (x +y\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
66.950 |
|
| \begin{align*}
\frac {-y^{\prime } x +y}{x +y y^{\prime }}&=2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
135.825 |
|
| \begin{align*}
y \left (-y^{\prime } x +y\right )&=\sqrt {y^{4}+x^{4}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
405.686 |
|
| \begin{align*}
x^{2} \left (y^{\prime }-1\right )&=y \left (x +y\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
88.211 |
|
| \begin{align*}
\sqrt {x}\, y^{\prime }&=\sqrt {-x +y}+\sqrt {x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
440.903 |
|
| \begin{align*}
y^{2} \left (-y^{\prime } x +y\right )&=x^{3} y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
256.652 |
|
| \begin{align*}
x \left (\ln \left (y\right )-\ln \left (x \right )\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
244.315 |
|
| \begin{align*}
x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
89.399 |
|