|
# |
ODE |
CAS classification |
Solved? |
|
\[
{}y y^{\prime } = x -1
\] |
[_separable] |
✓ |
|
|
\[
{}y y^{\prime } = x -1
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime } = 4 y
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime } = \left (1+y\right )^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x +2 y = 3 x
\] |
[_linear] |
✓ |
|
|
\[
{}3 y^{\prime } x +y = 12 x
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x +y\right ) y^{\prime } = x -y
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x y y^{\prime } = x^{2}+2 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } x = y+2 \sqrt {x y}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (x -y\right ) y^{\prime } = x +y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x \left (x +y\right ) y^{\prime } = \left (x -y\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}\left (x +2 y\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y^{2} y^{\prime } = x^{3}+y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = x y+x^{2} {\mathrm e}^{\frac {y}{x}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = x y+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y y^{\prime } = x^{2}+3 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (x^{2}-y^{2}\right ) y^{\prime } = 2 x y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y y^{\prime } = y^{2}+x \sqrt {4 x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } x = y+\sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x +y y^{\prime } = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (x +y\right ) y^{\prime }+y \left (3 x +y\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}2 x +3 y+\left (3 x +2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}4 x -y+\left (6 y-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 x^{2}+2 y^{2}+\left (4 x y+6 y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\frac {2 x^{{5}/{2}}-3 y^{{5}/{3}}}{2 x^{{5}/{2}} y^{{2}/{3}}}+\frac {\left (3 y^{{5}/{3}}-2 x^{{5}/{2}}\right ) y^{\prime }}{3 x^{{3}/{2}} y^{{5}/{3}}} = 0
\] |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x -y-1}{x +y+3}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y-x +7}{4 x -3 y-18}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y \left (2 x^{3}-y^{3}\right )}{x \left (2 y^{3}-x^{3}\right )}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y+y^{2}-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x y+x^{2} y^{\prime } = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = x y+3 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}6 x y^{3}+2 y^{4}+\left (9 x^{2} y^{2}+8 x y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x^{3} y^{\prime } = x^{2} y-y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x^{2} y-x^{3} y^{\prime } = y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 y+\left (x +1\right ) y^{\prime } = 3 x +3
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {3 x^{2}+2 y^{2}}{4 x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +3 y}{y-3 x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y y^{\prime } = x -1
\] |
[_separable] |
✓ |
|
|
\[
{}y y^{\prime } = x -1
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime } = 4 y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x +2 y = 3 x
\] |
[_linear] |
✓ |
|
|
\[
{}3 y^{\prime } x +y = 12 x
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x +y\right ) y^{\prime } = x -y
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x y y^{\prime } = x^{2}+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } x = y+2 \sqrt {x y}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (x -y\right ) y^{\prime } = x +y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x \left (x +y\right ) y^{\prime } = \left (x -y\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}\left (x +2 y\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y^{2} y^{\prime } = x^{3}+y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = x y+x^{2} {\mathrm e}^{\frac {y}{x}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = x y+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y y^{\prime } = x^{2}+3 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (x^{2}-y^{2}\right ) y^{\prime } = 2 x y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y y^{\prime } = y^{2}+x \sqrt {4 x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } x = y+\sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x +y y^{\prime } = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (x +y\right ) y^{\prime }+y \left (3 x +y\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}2 x +3 y+\left (3 x +2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}4 x -y+\left (6 y-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 x^{2}+2 y^{2}+\left (4 x y+6 y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\frac {2 x^{{5}/{2}}-3 y^{{5}/{3}}}{2 x^{{5}/{2}} y^{{2}/{3}}}+\frac {\left (3 y^{{5}/{3}}-2 x^{{5}/{2}}\right ) y^{\prime }}{3 x^{{3}/{2}} y^{{5}/{3}}} = 0
\] |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
|
|
\[
{}x y+y^{2}-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x y+x^{2} y^{\prime } = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = x y+3 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}6 x y^{3}+2 y^{4}+\left (9 x^{2} y^{2}+8 x y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x^{3} y^{\prime } = x^{2} y-y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x^{2} y-x^{3} y^{\prime } = y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 y+\left (x +1\right ) y^{\prime } = 3 x +3
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-3 x^{2}-2 y^{2}}{4 x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +3 y}{y-3 x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1-2 x}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x}{1+2 y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{2}+x y+y^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{2}+3 y^{2}}{2 x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {4 y-3 x}{2 x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {4 x +3 y}{2 x +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +3 y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2}+3 x y+y^{2}-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{2}-3 y^{2}}{2 x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {3 y^{2}-x^{2}}{2 x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {4 t}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}3+2 x +\left (-2+2 y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 x +4 y+\left (2 x -2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 y+2 x y^{2}+\left (2 x^{2} y+2 x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-a x -b y}{b x +c y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-a x +b y}{b x -c y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 x -y+\left (-x +2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 x y+y^{2}+\left (x y+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x +y+\left (x +2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } x = {\mathrm e}^{\frac {y}{x}} x +y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}3 t +2 y = -t y^{\prime }
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x y+3 y^{2}-\left (x^{2}+2 x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } x +3 y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+\frac {k y}{x} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x -2 y = -1
\] |
[_separable] |
✓ |
|
|
\[
{}\frac {y^{\prime }}{\left (1+y\right )^{2}}-\frac {1}{x \left (1+y\right )} = -\frac {3}{x^{2}}
\] |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x}{1+2 y}
\] |
[_separable] |
✓ |
|
|
\[
{}x +y y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x +3 y}{x -4 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y+x \,{\mathrm e}^{-\frac {y}{x}}}{x}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = y^{2}+x y-x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x y+y^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{3} y^{\prime } = y^{4}+x^{4}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\sec \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = x^{2}+x y+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x y y^{\prime } = x^{2}+2 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y^{2}+x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}}}{2 x y}
\] |
[[_homogeneous, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x y+y^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{3}+y^{3}}{x y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y y^{\prime }+x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}-3 x y-5 x^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = 2 x^{2}+y^{2}+4 x y
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x y y^{\prime } = 3 x^{2}+4 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{3}+2 x y^{2}+x^{2} y+x^{3}}{x \left (x +y\right )^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +2 y}{2 x +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{y-2 x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x y^{2}+2 y^{3}}{x^{3}+x^{2} y+x y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{3}+x^{2} y+3 y^{3}}{x^{3}+3 x y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = y^{2}+x y-4 x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x y y^{\prime } = x^{2}-x y+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y^{2}-x y+2 x^{2}}{x y+2 x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{2}+x y+y^{2}}{x y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-6 x +y-3}{2 x -y-1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x +y+1}{x +2 y-4}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-x +3 y-14}{x +y-2}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}6 x^{2} y^{2}+4 x^{3} y y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}4 x +7 y+\left (4 y+3 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x +y+\left (2 y+2 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}7 x +4 y+\left (4 x +3 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x y y^{\prime }+x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}-y^{2}+x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}3 x^{2} y+2 x^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}27 x y^{2}+8 y^{3}+\left (18 x^{2} y+12 x y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x^{4} y^{4}+x^{5} y^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}t y^{\prime } = y+\sqrt {t^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}2 t y y^{\prime } = 3 y^{2}-t^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (t -\sqrt {t y}\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y+t}{t -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}{\mathrm e}^{\frac {t}{y}} \left (y-t \right ) y^{\prime }+y \left (1+{\mathrm e}^{\frac {t}{y}}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {t +y+1}{t -y+3}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}1+t -2 y+\left (4 t -3 y-6\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 t y^{3}+3 t^{2} y^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}3 t y+y^{2}+\left (t y+t^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y}{t}+\frac {y^{2}}{t^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}t y^{\prime } = y+\sqrt {t^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}2 t y y^{\prime } = 3 y^{2}-t^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (t -\sqrt {t y}\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y+t}{t -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}{\mathrm e}^{\frac {t}{y}} \left (y-t \right ) y^{\prime }+y \left (1+{\mathrm e}^{\frac {t}{y}}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {t +y+1}{t -y+3}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}1+t -2 y+\left (4 t -3 y-6\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 t y^{3}+3 t^{2} y^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}3 t y+y^{2}+\left (t y+t^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y+y^{\prime } x = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime }-1+y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x +2 y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{2}+x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +y\right ) y^{\prime }+x = y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}-y+y^{\prime } x = \sqrt {x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x -y}{x +4 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x +y y^{\prime } = 2 y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } x -y+\sqrt {y^{2}-x^{2}} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x^{2}+y^{2} = x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (x y-x^{2}\right ) y^{\prime }-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y+y^{\prime } x = 2 \sqrt {x y}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x +y+\left (x -y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y \left (x^{2}-x y+y^{2}\right )+x y^{\prime } \left (x^{2}+x y+y^{2}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } x -y-x \sin \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\cosh \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x^{2}+y^{2} = 2 x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (\frac {x}{y}+\frac {y}{x}\right ) y^{\prime }+1 = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{\mathrm e}^{\frac {y}{x}} x +y = y^{\prime } x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (3 x y-2 x^{2}\right ) y^{\prime } = 2 y^{2}-x y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x -k \sqrt {x^{2}+y^{2}}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{2} \left (y y^{\prime }-x \right )+x^{3} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\tanh \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x +y-\left (x -y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x +\left (x -2 y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}2 x -y+1+\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x -y+2+\left (x +y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +y-1}{x -y-1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x +2 y+2 = \left (2 x +y-1\right ) y^{\prime }
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 x -y+1+\left (x -3 y-5\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 x -y+2+\left (x +2 y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x +y+\left (4 x -2 y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x +y+\left (x -2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 x +y+\left (x +3 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}a_{1} x +b_{1} y+c_{1} +\left (b_{1} x +b_{2} y+c_{2} \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x y-\left (x^{2}+y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\frac {x^{2}+3 y^{2}}{x \left (3 x^{2}+4 y^{2}\right )}+\frac {\left (2 x^{2}+y^{2}\right ) y^{\prime }}{y \left (3 x^{2}+4 y^{2}\right )} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\frac {x^{2}-y^{2}}{x \left (2 x^{2}+y^{2}\right )}+\frac {\left (x^{2}+2 y^{2}\right ) y^{\prime }}{y \left (2 x^{2}+y^{2}\right )} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}y+\left (2 x -3 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } x = 5 y+x +1
\] |
[_linear] |
✓ |
|
|
\[
{}x y y^{\prime } = x^{2}-y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{2}+x^{2} y^{\prime } = x y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (1-x \right ) y^{\prime }-1-y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{2}+\left (x y+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}2 x +y-\left (x -2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x -2 y+1+\left (y-2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y+\left (3 x -2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (4 y+3 x \right ) y^{\prime }+2 x +y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x +y+\left (2 x +3 y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
|
|
\[
{}y \sqrt {x^{2}+y^{2}}+x y = x^{2} y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y \cos \left (\frac {x}{y}\right )-\left (y+x \cos \left (\frac {x}{y}\right )\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x +\left (2 x +3 y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}x y-y^{2}-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (-2 x^{2}-3 x y\right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x^{2}+y^{2} = 2 x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}3 x y+\left (3 x^{2}+y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{3}+2 x^{2} y+\left (-3 x^{3}-2 x y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}4 y^{2} = x^{2} {y^{\prime }}^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{2} {y^{\prime }}^{2}+x y y^{\prime }-2 x^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {t}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y}{1+t}
\] |
[_separable] |
✓ |
|
|
\[
{}2 y^{\prime } x +3 x +y = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\left (y-x \right ) y^{\prime }+2 x +3 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y^{2}}{x^{2}} = {\frac {1}{4}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y^{2}}{x^{2}} = {\frac {1}{4}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}\left (5 x +y-7\right ) y^{\prime } = 3 x +3 y+3
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (3 x -y\right ) y^{\prime } = 3 y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\left (x +y\right )^{2}}{2 x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}\sin \left (\frac {y}{x}\right ) \left (-y+y^{\prime } x \right ) = x \cos \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x \left (x^{2}-y^{2}\right )-x \left (x^{2}+y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } x +y \ln \left (x \right ) = y \ln \left (y\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}+2 x y-2 x^{2}}{x^{2}-x y+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}2 x y y^{\prime }-2 y^{2}-x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}} = 0
\] |
[[_homogeneous, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = y^{2}+3 x y+x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}y y^{\prime } = \sqrt {x^{2}+y^{2}}-x
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}2 x \left (2 x +y\right ) y^{\prime } = y \left (4 x -y\right )
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } x = x \tan \left (\frac {y}{x}\right )+y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x \sqrt {x^{2}+y^{2}}+y^{2}}{x y}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{2 x}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime }+\frac {2 x}{4-t} = 5
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{2}+x y+y^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}\left (3 x -y\right ) y^{\prime } = 3 y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\left (x +y\right )^{2}}{2 x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}\sin \left (\frac {y}{x}\right ) \left (-y+y^{\prime } x \right ) = x \cos \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } x +y \ln \left (x \right ) = y \ln \left (y\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}+2 x y-2 x^{2}}{x^{2}-x y+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}2 x y y^{\prime }-2 y^{2}-x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}} = 0
\] |
[[_homogeneous, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = y^{2}+3 x y+x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}y y^{\prime } = \sqrt {x^{2}+y^{2}}-x
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}2 x \left (2 x +y\right ) y^{\prime } = y \left (4 x -y\right )
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } x = x \tan \left (\frac {y}{x}\right )+y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x \sqrt {x^{2}+y^{2}}+y^{2}}{x y}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-2 x +4 y}{x +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x -y}{x +4 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y-\sqrt {x^{2}+y^{2}}}{x}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +a y}{a x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +\frac {y}{2}}{\frac {x}{2}-y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +2 y-1}{2 x -y+3}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\frac {y^{\prime }}{y}-\frac {2 \ln \left (y\right )}{x} = \frac {1-2 \ln \left (x \right )}{x}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}5 x +2 y+1+\left (2 x +y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x -2 y-3+\left (2 x +y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 x -y-6+\left (x +y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = x \left (-1+y\right )+\left (-1+y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
|
|
\[
{}3 y-2 x +\left (3 x -2\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x^{3}+y^{3}-x y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{2}+y^{2}}{2 x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x -y}{2 x +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {3 x -y+1}{3 y-x +5}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y y^{\prime } = x
\] |
[_separable] |
✓ |
|
|
\[
{}y+y^{\prime } x = x
\] |
[_linear] |
✓ |
|
|
\[
{}\left (1-x \right ) y^{\prime } = y
\] |
[_separable] |
✓ |
|
|
\[
{}-y^{2}+x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +y-1\right ) y^{\prime } = x -y+1
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y y^{\prime } = 2 x^{2}-y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2}-y^{2}+x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime }-2 x y-2 y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = 3 \left (x^{2}+y^{2}\right ) \arctan \left (\frac {y}{x}\right )+x y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x \sin \left (\frac {y}{x}\right ) y^{\prime } = y \sin \left (\frac {y}{x}\right )+x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +y+4}{x -y-6}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y+y \cos \left (x y\right )+\left (x +x \cos \left (x y\right )\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (3 x^{2}-y^{2}\right ) y^{\prime }-2 x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x +y\right ) y^{\prime } = y-x
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x +3 y+1+\left (2 y-3 x +5\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } x = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x y-x^{2}\right ) y^{\prime } = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{2}-3 x y-2 x^{2} = \left (x^{2}-x y\right ) y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}2 x y+x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\frac {x}{x^{2}+y^{2}}+\frac {y}{x^{2}}+\left (\frac {y}{x^{2}+y^{2}}-\frac {1}{x}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime }+\frac {x}{y}+2 = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}-y+y^{\prime } x = x \cot \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x \cos \left (\frac {y}{x}\right )^{2}-y+y^{\prime } x = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } x = y \left (1+\ln \left (y\right )-\ln \left (x \right )\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y+\left (x^{2}+y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (1-{\mathrm e}^{-\frac {y}{x}}\right ) y^{\prime }+1-\frac {y}{x} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x^{2}-x y+y^{2}-x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x +y-1}{x -y-2}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y+2 = \left (2 x +y-4\right ) y^{\prime }
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x y+\left (x^{2}+2 x y+y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } x = y-{\mathrm e}^{\frac {y}{x}} x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}2 \sqrt {x y}-y-y^{\prime } x = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}-y+y^{\prime } x = x \tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 \left (y+2\right )^{2}}{\left (x +y-1\right )^{2}}
\] |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
|
|
\[
{}\left (y^{\prime }+1\right ) \ln \left (\frac {x +y}{x +3}\right ) = \frac {x +y}{x +3}
\] |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
|
|
\[
{}x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x +\sin \left (\frac {y}{x}\right )^{2} \left (y-y^{\prime } x \right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y+x +y^{\prime } x = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x = a y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x = 1+x +a y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x = a x +b y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x = y+a \sqrt {y^{2}+b^{2} x^{2}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } x +x -y+x \cos \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } x = y-x \cos \left (\frac {y}{x}\right )^{2}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } x -y+x \sec \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } x = y+x \sec \left (\frac {y}{x}\right )^{2}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } x = y+x \sin \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } x = y-x \tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } x = {\mathrm e}^{\frac {y}{x}} x +y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } x = x +y+{\mathrm e}^{\frac {y}{x}} x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } x = \left (1+\ln \left (x \right )-\ln \left (y\right )\right ) y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } x = y-2 x \tanh \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (x +a \right ) y^{\prime } = b +c y
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +a \right ) y^{\prime } = b x +c y
\] |
[_linear] |
✓ |
|
|
\[
{}\left (1-2 x \right ) y^{\prime } = 16+32 x -6 y
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+x^{2}+x y+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = \left (1+2 x -y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = \left (x +a y\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = \left (a x +b y\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+a \,x^{2}+b x y+c y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}\left (x +a \right )^{2} y^{\prime } = 2 \left (x +a \right ) \left (b +y\right )
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x -a \right )^{2} y^{\prime }+k \left (x +y-a \right )^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
|
|
\[
{}a \,x^{2} y^{\prime } = x^{2}+y a x +b^{2} y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x^{3} y^{\prime } = \left (2 x^{2}+y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x^{3} y^{\prime } = \left (x^{2}-y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x^{3} y^{\prime } = \left (3 x^{2}+a y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x +y y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y y^{\prime }+a x +b y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (1+y\right ) y^{\prime } = x +y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x +y\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x -y\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x +y\right ) y^{\prime }+x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x +y\right ) y^{\prime } = x -y
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x -y\right ) y^{\prime } = \left ({\mathrm e}^{-\frac {x}{y}}+1\right ) y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (x +y+1\right ) y^{\prime }+1+4 x +3 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (3-x -y\right ) y^{\prime } = 1+x -3 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (3-x +y\right ) y^{\prime } = 11-4 x +3 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (2 x +y\right ) y^{\prime }+x -2 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (4+2 x -y\right ) y^{\prime }+5+x -2 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (5-2 x -y\right ) y^{\prime }+4-x -2 y = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (1-3 x +y\right ) y^{\prime } = 2 x -2 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (2-3 x +y\right ) y^{\prime }+5-2 x -3 y = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (4 x -y\right ) y^{\prime }+2 x -5 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (6-4 x -y\right ) y^{\prime } = 2 x -y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (1+5 x -y\right ) y^{\prime }+5+x -5 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x -2 y\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x +2 y\right ) y^{\prime }+2 x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x -2 y\right ) y^{\prime }+2 x +y = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (1+x -2 y\right ) y^{\prime } = 1+2 x -y
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x +2 y+1\right ) y^{\prime }+7+x -4 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (3+2 x -2 y\right ) y^{\prime } = 1+6 x -2 y
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (19+9 x +2 y\right ) y^{\prime }+18-2 x -6 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x -3 y\right ) y^{\prime }+4+3 x -y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x +4 y\right ) y^{\prime }+4 x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (5+3 x -4 y\right ) y^{\prime } = 2+7 x -3 y
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}4 \left (1-x -y\right ) y^{\prime }+2-x = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}\left (11-11 x -4 y\right ) y^{\prime } = 62-8 x -25 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (6+3 x +5 y\right ) y^{\prime } = 2+x +7 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (7 x +5 y\right ) y^{\prime }+10 x +8 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (5-x +6 y\right ) y^{\prime } = 3-x +4 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (1+x +9 y\right ) y^{\prime }+1+x +5 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (8+5 x -12 y\right ) y^{\prime } = 3+2 x -5 y
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (140+7 x -16 y\right ) y^{\prime }+25+8 x +y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (3+9 x +21 y\right ) y^{\prime } = 45+7 x -5 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (a x +b y\right ) y^{\prime }+x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}\left (a x +b y\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (a x +b y\right ) y^{\prime }+b x +a y = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (a x +b y\right ) y^{\prime } = b x +a y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y y^{\prime }+x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y y^{\prime } = x^{2}-x y+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x y y^{\prime }+2 x^{2}-2 x y-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x y y^{\prime }+x^{2} \operatorname {arccot}\left (\frac {y}{x}\right )-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y y^{\prime }+x^{2} {\mathrm e}^{-\frac {2 y}{x}}-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x \left (x +y\right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x \left (x -y\right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x \left (x +y\right ) y^{\prime } = x^{2}+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x \left (x -y\right ) y^{\prime }+2 x^{2}+3 x y-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x \left (x +y\right ) y^{\prime }-y \left (x +y\right )+x \sqrt {x^{2}-y^{2}} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x \left (2 x +y\right ) y^{\prime } = x^{2}+x y-y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x \left (4 x -y\right ) y^{\prime }+4 x^{2}-6 x y-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}2 x y y^{\prime }+x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x y y^{\prime } = x^{2}+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x \left (x -2 y\right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x \left (x +2 y\right ) y^{\prime }+\left (2 x -y\right ) y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x \left (x -2 y\right ) y^{\prime }+\left (2 x -y\right ) y = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x \left (2 x +3 y\right ) y^{\prime } = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x \left (2 x +3 y\right ) y^{\prime }+3 \left (x +y\right )^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}a x y y^{\prime } = x^{2}+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}a x y y^{\prime }+x^{2}-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x \left (x -a y\right ) y^{\prime } = y \left (y-a x \right )
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x^{2} \left (x -2 y\right ) y^{\prime } = 2 x^{3}-4 x y^{2}+y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}x^{2} \left (4 x -3 y\right ) y^{\prime } = \left (6 x^{2}-3 x y+2 y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}8 x^{3} y y^{\prime }+3 x^{4}-6 x^{2} y^{2}-y^{4} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y+\left (x^{2}+y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x^{2}+y^{2}\right ) y^{\prime } = x y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x^{2}-y^{2}\right ) y^{\prime } = 2 x y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x^{2}-y^{2}\right ) y^{\prime }+x \left (x +2 y\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x^{2}+y^{2}\right ) y^{\prime }+2 x \left (2 x +y\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (3 x^{2}-y^{2}\right ) y^{\prime } = 2 x y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x^{2}+2 x y-y^{2}\right ) y^{\prime }+x^{2}-2 x y+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x +y\right )^{2} y^{\prime } = x^{2}-2 x y+5 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (a +b +x +y\right )^{2} y^{\prime } = 2 \left (a +y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
|
|
\[
{}\left (2 x^{2}+4 x y-y^{2}\right ) y^{\prime } = x^{2}-4 x y-2 y^{2}
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (3 x +y\right )^{2} y^{\prime } = 4 \left (3 x +2 y\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (1-3 x -y\right )^{2} y^{\prime } = \left (1-2 y\right ) \left (3-6 x -4 y\right )
\] |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
|
|
\[
{}\left (2 x^{2}+3 y^{2}\right ) y^{\prime }+x \left (3 x +y\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (3 x^{2}+2 x y+4 y^{2}\right ) y^{\prime }+y^{2}+6 x y+2 x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (1-3 x +2 y\right )^{2} y^{\prime } = \left (4+2 x -3 y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
|
|
\[
{}\left (x^{2}+a y^{2}\right ) y^{\prime } = x y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x^{2}+x y+a y^{2}\right ) y^{\prime } = a \,x^{2}+x y+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (a \,x^{2}+2 x y-a y^{2}\right ) y^{\prime }+x^{2}-2 y a x -y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (a \,x^{2}+2 b x y+c y^{2}\right ) y^{\prime }+k \,x^{2}+2 y a x +b y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (2 x^{2}+y^{2}\right ) y^{\prime } = \left (2 x^{2}+3 y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (x^{2}-x y+y^{2}\right ) y^{\prime }+\left (x^{2}+x y+y^{2}\right ) y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (x^{2}-x y-y^{2}\right ) y^{\prime } = \left (x^{2}+x y-y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (x^{2}+y a x +y^{2}\right ) y^{\prime } = \left (x^{2}+b x y+y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (x^{2}-2 y^{2}\right ) y^{\prime } = \left (2 x^{2}-y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (x^{2}+2 y^{2}\right ) y^{\prime } = \left (2 x^{2}+3 y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}2 x \left (5 x^{2}+y^{2}\right ) y^{\prime } = x^{2} y-y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (x^{2}+y a x +2 y^{2}\right ) y^{\prime } = \left (a x +2 y\right ) y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (x^{2}-6 y^{2}\right ) y^{\prime } = 4 \left (x^{2}+3 y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x^{3}-y^{3}\right ) y^{\prime }+x^{2} y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x^{3}+y^{3}\right ) y^{\prime }+x^{2} \left (a x +3 y\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}y \left (3 x^{2}+y^{2}\right ) y^{\prime }+x \left (x^{2}+3 y^{2}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}2 y^{3} y^{\prime } = x^{3}-x y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (3 x^{2}+2 y^{2}\right ) y y^{\prime }+x^{3} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (5 x^{2}+2 y^{2}\right ) y y^{\prime }+x \left (x^{2}+5 y^{2}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (3 x^{3}+6 x^{2} y-3 x y^{2}+20 y^{3}\right ) y^{\prime }+4 x^{3}+9 x^{2} y+6 x y^{2}-y^{3} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x^{3}+a y^{3}\right ) y^{\prime } = x^{2} y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (2 x^{3}+y^{3}\right ) y^{\prime } = \left (2 x^{3}-x^{2} y+y^{3}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (2 x^{3}-y^{3}\right ) y^{\prime } = \left (x^{3}-2 y^{3}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (x^{3}+3 x^{2} y+y^{3}\right ) y^{\prime } = \left (3 x^{2}+y^{2}\right ) y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (x^{3}-2 y^{3}\right ) y^{\prime } = \left (2 x^{3}-y^{3}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (a \,x^{3}+\left (a x +b y\right )^{3}\right ) y y^{\prime }+x \left (\left (a x +b y\right )^{3}+b y^{3}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } \sqrt {y} = \sqrt {x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } \sqrt {x y}+x -y = \sqrt {x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x -2 \sqrt {x y}\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (x -\sqrt {x^{2}+y^{2}}\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (x +\sqrt {x^{2}+y^{2}}\right ) y^{\prime }+y \sqrt {x^{2}+y^{2}} = 0
\] |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
|
|
\[
{}x y \left (x +\sqrt {x^{2}-y^{2}}\right ) y^{\prime } = x y^{2}-\left (x^{2}-y^{2}\right )^{{3}/{2}}
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
|
|
\[
{}x \left (x -y \tan \left (\frac {y}{x}\right )\right ) y^{\prime }+\left (x +y \tan \left (\frac {y}{x}\right )\right ) y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x {y^{\prime }}^{2}-\left (2 x +3 y\right ) y^{\prime }+6 y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}x {y^{\prime }}^{2}+\left (1-x \right ) y y^{\prime }-y^{2} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2} = y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2} = \left (x -y\right )^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-y^{\prime } x +y \left (1-y\right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+3 x y y^{\prime }+2 y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+4 x y y^{\prime }-5 y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-5 x y y^{\prime }+6 y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }-y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-x y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}\right ) y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x^{2}-y^{2}\right ) y^{\prime }-x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}-\left (x^{2}-y^{2}\right ) y^{\prime }-x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (3 x^{2}-2 y^{2}\right ) y^{\prime }-6 x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-\left (x +1\right ) y y^{\prime }+x = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}\left (x +y\right )^{2} {y^{\prime }}^{2} = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x +y\right )^{2} {y^{\prime }}^{2}-\left (x^{2}-x y-2 y^{2}\right ) y^{\prime }-\left (x -y\right ) y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}4 y^{2} {y^{\prime }}^{2}+2 y^{\prime } x y \left (3 x +1\right )+3 x^{3} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{2}-4 y^{2}\right ) {y^{\prime }}^{2}+6 x y y^{\prime }-4 x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}4 x^{2} y^{2} {y^{\prime }}^{2} = \left (x^{2}+y^{2}\right )^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (x +2 y\right ) {y^{\prime }}^{3}+3 \left (x +y\right ) {y^{\prime }}^{2}+\left (2 x +y\right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x y}{x^{2}-y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +y-3}{x -y-1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (y-x \right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (2 \sqrt {x y}-x \right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (7 x +5 y\right ) y^{\prime }+10 x +8 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x -y+1+\left (2 y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (7 x +5 y\right ) y^{\prime }+10 x +8 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2}+2 x y-y^{2}+\left (y^{2}+2 x y-x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{2}+\left (x y+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}2 x y+\left (x^{2}+y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x +\sqrt {y^{2}-x y}\right ) y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x +y-\left (x -y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } x -y-x \sin \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}2 x^{2} y+y^{3}+\left (x y^{2}-2 x^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{2}+\left (x \sqrt {y^{2}-x^{2}}-x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
|
|
\[
{}\frac {y \cos \left (\frac {y}{x}\right )}{x}-\left (\frac {x \sin \left (\frac {y}{x}\right )}{y}+\cos \left (\frac {y}{x}\right )\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y+x \ln \left (\frac {y}{x}\right ) y^{\prime }-2 y^{\prime } x = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}2 y \,{\mathrm e}^{\frac {x}{y}}+\left (y-2 x \,{\mathrm e}^{\frac {x}{y}}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}{\mathrm e}^{\frac {y}{x}} x -y \sin \left (\frac {y}{x}\right )+x \sin \left (\frac {y}{x}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x^{2}+y^{2} = 2 x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}{\mathrm e}^{\frac {y}{x}} x +y = y^{\prime } x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{x}+\csc \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y-y^{2}-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x +2 y-4-\left (2 x -4 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x +y-1-\left (x -y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}7 y-3+\left (2 x +1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x +2 y+\left (-1+y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 x -2 y+4-\left (2 x +7 y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 x +2 y+3-\left (x +2 y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y+7+\left (2 x +y+3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x +y+2-\left (x -y-4\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = 1+\frac {y}{x}-\frac {y^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}\left (3 x +2 y+1\right ) y^{\prime }+4 x +3 y+2 = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x^{2}-y^{2}\right ) y^{\prime } = 2 x y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } x = x +y+{\mathrm e}^{\frac {y}{x}} x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } x -y-x \sin \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (x y-x^{2}\right ) y^{\prime }+y^{2}-3 x y-2 x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+x^{2}+x y+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x y y^{\prime }+x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x y y^{\prime }+3 x^{2}-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (2 x y^{3}-x^{4}\right ) y^{\prime }+2 x^{3} y-y^{4} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x^{2}+y^{2}\right ) y^{\prime }+2 x \left (2 x +y\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}2 y^{3} y^{\prime }+x y^{2}-x^{3} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x -y\right ) y^{\prime }+x +y+1 = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+y^{2}-x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y y^{\prime } = -x +\sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y+\left (y^{2}-x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{2}-x y+\left (x y+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x}-\tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (2 x +y\right ) y^{\prime }-x +2 y = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 x^{2} y+x^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{3}+x y^{2}\right ) y^{\prime } = 2 y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (2 y-x \right ) y^{\prime } = 2 x +y
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y+y^{2}+\left (x^{2}-x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x^{3}+y^{3} = 3 x y^{2} y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y-3 x +\left (4 y+3 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x^{3}+3 x y^{2}\right ) y^{\prime } = 3 x^{2} y+y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x -y-1+\left (4 y+x -1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2}-2 x y+5 y^{2} = \left (x^{2}+2 x y+y^{2}\right ) y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x y+y^{2}}{x^{2}+2 x y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } x +2 y = 3 x -1
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = y^{2}-x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{2}+x^{2} y^{\prime } = x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}2 x y y^{\prime } = x^{2}-y^{2}
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } x = 2 y
\] |
[_separable] |
✓ |
|
|
\[
{}x +y y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 x^{3} y^{\prime } = y \left (3 x^{2}+y^{2}\right )
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}4 y+y^{\prime } x = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{2}-x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x \sin \left (\frac {y}{x}\right )-y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y \sqrt {x^{2}+y^{2}}-x \left (x +\sqrt {x^{2}+y^{2}}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
|
|
\[
{}1+2 y-\left (4-x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x +2 y+\left (2 x +3 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{2}-x^{2}+x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{3}+y^{3}+3 x y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } x +2 y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y y^{\prime }+x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y \left (x -2 y\right )-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y y^{\prime }+x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x y y^{\prime }+x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}x +y+1-\left (x -y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+x y y^{\prime }-6 y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x {y^{\prime }}^{2}+\left (y-1-x^{2}\right ) y^{\prime }-x \left (-1+y\right ) = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } x = 1-x +2 y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x -2 y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {x}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}3 y^{\prime } x +5 y = 10
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x = 2 y
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{2}+y^{2}\right ) y^{\prime } = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (y-x \right ) y^{\prime } = x +y
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y y^{\prime } = 3 x
\] |
[_separable] |
✓ |
|
|
\[
{}y y^{\prime } = 3 x
\] |
[_separable] |
✓ |
|
|
\[
{}y y^{\prime } = 3 x
\] |
[_separable] |
✓ |
|
|
\[
{}3 y^{\prime } x -2 y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (2 y-2\right ) y^{\prime } = 2 x -1
\] |
[_separable] |
✓ |
|
|
\[
{}y+y^{\prime } x = 2 x
\] |
[_linear] |
✓ |
|
|
\[
{}y y^{\prime } = -x
\] |
[_separable] |
✓ |
|
|
\[
{}y y^{\prime } = -x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 1-\frac {y}{x}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = 1-\frac {y}{x}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x = 4 y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\left (2 y+3\right )^{2}}{\left (4 x +5\right )^{2}}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {3 x +1}{2 y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {x}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x +2 y = 3
\] |
[_separable] |
✓ |
|
|
\[
{}y+y^{\prime } x = 4 x +1
\] |
[_linear] |
✓ |
|
|
\[
{}2 x -1+\left (3 y+7\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\frac {1}{\sqrt {x}}+\frac {y^{\prime }}{\sqrt {y}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{\sqrt {x}}
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +y\right ) y^{\prime }+x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{2}+x^{2} y^{\prime } = x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}\left (x^{2}+y^{2}\right ) y^{\prime } = 2 x y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}-y+y^{\prime } x = x \tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } x = y-{\mathrm e}^{\frac {y}{x}} x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}-y+y^{\prime } x = \left (x +y\right ) \ln \left (\frac {x +y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } x = y \cos \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y+\sqrt {x y}-y^{\prime } x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x +y-\left (x -y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2}+2 x y-y^{2}+\left (y^{2}+2 x y-x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}-y+y^{\prime } x = y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{2}+\left (x^{2}-x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x^{2}+x y+y^{2} = x^{2} y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}\frac {1}{x^{2}-x y+y^{2}} = \frac {y^{\prime }}{2 y^{2}-x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x y}{3 x^{2}-y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x}{y}+\frac {y}{x}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } x = y+\sqrt {y^{2}-x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (2 \sqrt {x y}-x \right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } x = y \ln \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-3 x y y^{\prime }+2 y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+\frac {x +2 y}{x} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } x = x +\frac {y}{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +y-2}{y-x -4}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x -4 y+6+\left (x +y-2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y-x +5}{2 x -y-4}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {4 x +3 y+15}{2 x +y+7}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +3 y-5}{x -y-1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 \left (y+2\right )^{2}}{\left (x +y+1\right )^{2}}
\] |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
|
|
\[
{}\left (x +4 y\right ) y^{\prime } = 2 x +3 y-5
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y+2 = \left (2 x +y-4\right ) y^{\prime }
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (y^{\prime }+1\right ) \ln \left (\frac {x +y}{x +3}\right ) = \frac {x +y}{x +3}
\] |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x -2 y+5}{y-2 x -4}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {3 x -y+1}{2 x +y+4}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x +3+\left (2 y-2\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 x +4 y+\left (2 x -2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } x -2 \sqrt {x y} = y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +y-1}{x -y+3}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+y^{2}-x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x +y-\left (x -y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y \,{\mathrm e}^{x y}+x \,{\mathrm e}^{x y} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2}+y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2}-y^{2}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x +y y^{\prime }+y-y^{\prime } x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y y^{\prime } = x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}}{x y+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{2}+x y+y^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y+x \,{\mathrm e}^{-\frac {2 y}{x}}}{x}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x -y+2}{x +y-1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x +3 y+1}{x -2 y-1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\left (x +y-1\right )^{2}}{2 \left (x +2\right )^{2}}
\] |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
|
|
\[
{}y^{\prime } x = 2 y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x y}{x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}2 x y y^{\prime } = x^{2}+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}}{x y-x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x^{5} y^{\prime }+y^{5} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y y^{\prime } = x +1
\] |
[_separable] |
✓ |
|
|
\[
{}y+y \cos \left (x y\right )+\left (x +x \cos \left (x y\right )\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2}-2 y^{2}+x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime }-3 x y-2 y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = 3 \left (x^{2}+y^{2}\right ) \arctan \left (\frac {y}{x}\right )+x y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x \sin \left (\frac {y}{x}\right ) y^{\prime } = y \sin \left (\frac {y}{x}\right )+x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } x = y+2 x \,{\mathrm e}^{-\frac {y}{x}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x -y-\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } x = 2 x -6 y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = 2 x y+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{3}+y^{3}-x y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +y+4}{x -y-6}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x -2 y+\left (-1+y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +y-1}{x +4 y+2}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x +3 y-1-4 \left (x +1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}{\mathrm e}^{\frac {x}{y}}-\frac {y y^{\prime }}{x} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{2}-x y}{y^{2} \cos \left (\frac {x}{y}\right )}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y \tan \left (\frac {y}{x}\right )}{x}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y+y^{\prime } x = x
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{2}+y^{2}}{x^{2}-y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +2 y}{2 x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x y+x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{2}+2 y^{2}}{x^{2}-2 y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x {y^{\prime }}^{2}-\left (2 x +3 y\right ) y^{\prime }+6 y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-5 x y y^{\prime }+6 y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+y^{\prime } x -y^{2}-y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +y\right )^{2} {y^{\prime }}^{2} = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-x y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}\left (4 x -y\right ) {y^{\prime }}^{2}+6 \left (x -y\right ) y^{\prime }+2 x -5 y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}\left (x -y\right )^{2} {y^{\prime }}^{2} = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x^{2}+y^{2}\right )^{2} {y^{\prime }}^{2} = 4 x^{2} y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x +y\right )^{2} {y^{\prime }}^{2}+\left (2 y^{2}+x y-x^{2}\right ) y^{\prime }+y \left (y-x \right ) = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y \left (x^{2}+y^{2}\right ) \left (-1+{y^{\prime }}^{2}\right ) = y^{\prime } \left (x^{4}+x^{2} y^{2}+y^{4}\right )
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}6 x {y^{\prime }}^{2}-\left (3 x +2 y\right ) y^{\prime }+y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-\left (x +1\right ) y y^{\prime }+x = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2} = \left (x -y\right )^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}x {y^{\prime }}^{2}+\left (1-x \right ) y y^{\prime }-y^{2} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x -y}{x +4 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{2}+x^{2} y^{\prime } = x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {5 x^{2}-x y+y^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}2 t +3 x+\left (x+2\right ) x^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y y^{\prime }-y = x
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } x +a \sqrt {x^{2}+y^{2}}-y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } x -{\mathrm e}^{\frac {y}{x}} x -y-x = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } x -y-x \sin \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } x +x -y+x \cos \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } x +x \tan \left (\frac {y}{x}\right )-y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+x^{2}+x y+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x^{2} y^{\prime }-y^{2}-x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime }-y^{2}-x y-x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}3 x^{2} y^{\prime }-7 y^{2}-3 x y-x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}y y^{\prime }+a y+x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y y^{\prime }-x \,{\mathrm e}^{\frac {x}{y}} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (1+y\right ) y^{\prime }-y-x = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x +y-1\right ) y^{\prime }-y+2 x +3 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (y+2 x -2\right ) y^{\prime }-y+x +1 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (y-2 x +1\right ) y^{\prime }+y+x = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (2 y+x +7\right ) y^{\prime }-y+2 x +4 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (2 y-x \right ) y^{\prime }-y-2 x = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (4 y-3 x -5\right ) y^{\prime }-3 y+7 x +2 = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (4 y+11 x -11\right ) y^{\prime }-25 y-8 x +62 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (12 y-5 x -8\right ) y^{\prime }-5 y+2 x +3 = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (a y+b x +c \right ) y^{\prime }+\alpha y+\beta x +\gamma = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y y^{\prime }+x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (x y-x^{2}\right ) y^{\prime }+y^{2}-3 x y-2 x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}2 x y y^{\prime }-y^{2}+a \,x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x \left (2 x +3 y\right ) y^{\prime }+3 \left (x +y\right )^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}\left (3 x +2\right ) \left (y-2 x -1\right ) y^{\prime }-y^{2}+x y-7 x^{2}-9 x -3 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}\left (2 x^{2} y-x^{3}\right ) y^{\prime }+y^{3}-4 x y^{2}+2 x^{3} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}\left (x^{2}+y^{2}\right ) y^{\prime }+2 x \left (2 x +y\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x^{2}+y^{2}\right ) y^{\prime }-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (y^{2}-x^{2}\right ) y^{\prime }+2 x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x^{2}+2 x y-y^{2}+\left (y^{2}+2 x y-x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (y+3 x -1\right )^{2} y^{\prime }-\left (2 y-1\right ) \left (4 y+6 x -3\right ) = 0
\] |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
|
|
\[
{}\left (4 y^{2}+x^{2}\right ) y^{\prime }-x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (3 x^{2}+2 x y+4 y^{2}\right ) y^{\prime }+y^{2}+6 x y+2 x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (1-3 x +2 y\right )^{2} y^{\prime }-\left (3 y-2 x -4\right )^{2} = 0
\] |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
|
|
\[
{}\left (a y^{2}+2 b x y+c \,x^{2}\right ) y^{\prime }+b y^{2}+2 c x y+d \,x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (a y+b x +c \right )^{2} y^{\prime }+\left (\alpha y+\beta x +\gamma \right )^{2} = 0
\] |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
|
|
\[
{}x \left (y^{2}+x y-x^{2}\right ) y^{\prime }-y^{3}+x y^{2}+x^{2} y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}2 x \left (5 x^{2}+y^{2}\right ) y^{\prime }+y^{3}-x^{2} y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (y^{3}-x^{3}\right ) y^{\prime }-x^{2} y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}2 y^{3} y^{\prime }+x y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (2 y^{3}+5 x^{2} y\right ) y^{\prime }+5 x y^{2}+x^{3} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (3 x^{3}+6 x^{2} y-3 x y^{2}+20 y^{3}\right ) y^{\prime }+4 x^{3}+9 x^{2} y+6 x y^{2}-y^{3} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (2 x y^{3}-x^{4}\right ) y^{\prime }+2 x^{3} y-y^{4} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y \left (y^{3}-2 x^{3}\right ) y^{\prime }+\left (2 y^{3}-x^{3}\right ) x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y \left (\left (b x +a y\right )^{3}+b \,x^{3}\right ) y^{\prime }+x \left (\left (b x +a y\right )^{3}+a y^{3}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x +\sqrt {x^{2}+y^{2}}\right ) y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (y \sqrt {x^{2}+y^{2}}+\left (y^{2}-x^{2}\right ) \sin \left (\alpha \right )-2 x y \cos \left (\alpha \right )\right ) y^{\prime }+x \sqrt {x^{2}+y^{2}}+2 x y \sin \left (\alpha \right )+\left (y^{2}-x^{2}\right ) \cos \left (\alpha \right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } \cot \left (\frac {y}{x}\right )+2 x \sin \left (\frac {y}{x}\right )-y \cot \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘]] |
✓ |
|
|
\[
{}\left (-y+y^{\prime } x \right ) \cos \left (\frac {y}{x}\right )^{2}+x = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (y \sin \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right )\right ) x y^{\prime }-\left (x \cos \left (\frac {y}{x}\right )+y \sin \left (\frac {y}{x}\right )\right ) y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+3 x y y^{\prime }+2 y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+4 x y y^{\prime }-5 y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y {y^{\prime }}^{2}-\left (y-x \right ) y^{\prime }-x = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}\right ) y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{2} {y^{\prime }}^{2}-2 y^{3} y^{\prime }+2 x y^{2}-x^{3} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{3}+3 a \,x^{2}+3 a^{2} x +a^{3}+x y^{2}+a y^{2}+y^{3}}{\left (x +a \right )^{3}}
\] |
[[_homogeneous, ‘class C‘], _rational, _Abel] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-b^{3}+6 b^{2} x -12 b \,x^{2}+8 x^{3}-4 b y^{2}+8 x y^{2}+8 y^{3}}{\left (2 x -b \right )^{3}}
\] |
[[_homogeneous, ‘class C‘], _rational, _Abel] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-125+300 x -240 x^{2}+64 x^{3}-80 y^{2}+64 x y^{2}+64 y^{3}}{\left (4 x -5\right )^{3}}
\] |
[[_homogeneous, ‘class C‘], _rational, _Abel] |
✓ |
|
|
\[
{}y y^{\prime }-y = A x +B
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (A y+B x +a \right ) y^{\prime }+B y+k x +b = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (y+a x +b \right ) y^{\prime } = \alpha y+\beta x +\gamma
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\frac {y^{2}-2 x^{2}}{x y^{2}-x^{3}}+\frac {\left (2 y^{2}-x^{2}\right ) y^{\prime }}{y^{3}-x^{2} y} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\frac {1}{\sqrt {x^{2}+y^{2}}}+\left (\frac {1}{y}-\frac {x}{y \sqrt {x^{2}+y^{2}}}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}y+x +y^{\prime } x = 0
\] |
[_linear] |
✓ |
|
|
\[
{}6 x -2 y+1+\left (2 y-2 x -3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}{\mathrm e}^{\frac {y}{x}} x +y-y^{\prime } x = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}2 x^{2} y+3 y^{3}-\left (x^{3}+2 x y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+y^{2}-x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x^{2} y+y^{3}-x^{3} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{3}+x^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x +y \cos \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}4 x +3 y+1+\left (x +y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}4 x -y+2+\left (x +y+3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{2} \left (3 y-6 y^{\prime } x \right )-x \left (y-2 y^{\prime } x \right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+y^{2}-x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x +y-\left (x -y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2}+y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}3 x^{2}+6 x y+3 y^{2}+\left (2 x^{2}+3 x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{2}-x^{2}+2 m x y+\left (m y^{2}-m \,x^{2}-2 x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x +y y^{\prime }+y-y^{\prime } x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (y-x \right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x \sin \left (\frac {y}{x}\right )-y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x -2 y+5+\left (2 x -y+4\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{3}-2 x^{2} y+\left (2 x y^{2}-x^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}1+{\mathrm e}^{\frac {y}{x}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (2 \sqrt {x y}-x \right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x^{\prime } = \frac {2 x}{t}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime } = -\frac {t}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}2 t x^{\prime } = x
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime } = \frac {2 x}{1+t}
\] |
[_separable] |
✓ |
|
|
\[
{}\left (2 u+1\right ) u^{\prime }-1-t = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime } = \frac {4 t^{2}+3 x^{2}}{2 t x}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}+2 t y}{t^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{\prime } = \frac {2 x}{3 t}+\frac {2 t}{x}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}t^{2} y^{\prime }+2 t y-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{3}+3 t x^{2} x^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2}-t^{2} x^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 x y y^{\prime }+x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}3 x +2 y+\left (2 x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{2}+2 x y-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x y+3 y^{2}-\left (x^{2}+2 x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}v^{3}+\left (u^{3}-u v^{2}\right ) v^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \tan \left (\frac {y}{x}\right )+y-y^{\prime } x = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (2 s^{2}+2 s t +t^{2}\right ) s^{\prime }+s^{2}+2 s t -t^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}x^{3}+y^{2} \sqrt {x^{2}+y^{2}}-x y \sqrt {x^{2}+y^{2}}\, y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\sqrt {x +y}+\sqrt {x -y}+\left (\sqrt {x -y}-\sqrt {x +y}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}x^{2}+3 y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (4 x -y\right ) y^{\prime }+2 x -5 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 x^{2}+9 x y+5 y^{2}-\left (6 x^{2}+4 x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x +2 y+\left (2 x -y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 x -y-\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2}+2 y^{2}+\left (4 x y-y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}2 x^{2}+2 x y+y^{2}+\left (x^{2}+2 x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}3 x -5 y+\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x^{2}+x y+y^{2}+2 x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x -7 y}{3 y-8 x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x^{2}+y^{2}}{2 x y-x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x^{2}+y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x +7 y}{2 x -2 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+x y = \frac {y^{3}}{x}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}5 x +2 y+1+\left (2 x +y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x -2 y-3+\left (2 x +y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}10 x -4 y+12-\left (x +5 y+3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 x -y-6+\left (x +y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}4 x +3 y+1+\left (x +y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } x = k y
\] |
[_separable] |
✓ |
|
|
\[
{}x y+y^{2}+x^{2}-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x^{\prime } = \frac {x^{2}+t \sqrt {t^{2}+x^{2}}}{t x}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}12 x +6 y-9+\left (5 x +2 y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x \left (\ln \left (x \right )-\ln \left (y\right )\right ) y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}-\left (x^{2}+y^{2}\right ) y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime } = {\mathrm e}^{\frac {x}{t}}+\frac {x}{t}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y-x -4}{2 x -y+5}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x -y\right ) y-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (x -y\right ) y-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +y-3}{-x +y+1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (y^{2}-x^{2}\right ) y^{\prime }+2 x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}1+y-\left (1-x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y-x +\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y+x +y^{\prime } x = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x +y+\left (y-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (7 x +5 y\right ) y^{\prime }+10 x +8 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 \sqrt {s t}-s+t s^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{2} y^{\prime } = x^{3}+y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x \cos \left (\frac {y}{x}\right ) \left (y+y^{\prime } x \right ) = y \sin \left (\frac {y}{x}\right ) \left (-y+y^{\prime } x \right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\frac {y-y^{\prime } x}{\sqrt {x^{2}+y^{2}}} = m
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\frac {x +y y^{\prime }}{\sqrt {x^{2}+y^{2}}} = m
\] |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
|
|
\[
{}y y^{\prime } = -x +\sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime }-\frac {a y}{x} = \frac {x +1}{x}
\] |
[_linear] |
✓ |
|
|
\[
{}\frac {x}{\left (x +y\right )^{2}}+\frac {\left (2 x +y\right ) y^{\prime }}{\left (x +y\right )^{2}} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}\frac {1}{x^{2}}+\frac {3 y^{2}}{x^{4}} = \frac {2 y y^{\prime }}{x^{3}}
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}\frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y}{x}-\sqrt {3}
\] |
[_linear] |
✓ |
|
|
\[
{}\frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x \cos \left (\frac {y}{x}\right ) y^{\prime } = y \cos \left (\frac {y}{x}\right )-x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}2 x y+x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 y^{\prime } x -y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x -y}{x +3 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x y}{x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{y-x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y \left (2 x +y\right )}{x \left (x +2 y\right )}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x -y y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{y-x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{y-x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{y-x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{y-x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x y}{x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {t}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y+1}{t}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {t}{y-2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y}{t}+2
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y}{1+t}+2
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y}{t}+2
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\left (1+t \right )^{2}}{\left (y+1\right )^{2}}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y+1}{t}
\] |
[_separable] |
✓ |
|
|
\[
{}y y^{\prime } = 2 x
\] |
[_separable] |
✓ |
|
|
\[
{}\left (y-2\right ) y^{\prime } = x -3
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{\prime }-x y = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x}{y}+\frac {y}{x}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\cos \left (\frac {y}{x}\right ) \left (y^{\prime }-\frac {y}{x}\right ) = 1+\sin \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x -y}{x +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-\frac {3 y}{x} = \frac {y^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\frac {x^{2}}{y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (x +y\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (2 x y+2 x^{2}\right ) y^{\prime } = x^{2}+2 x y+2 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}-y+y^{\prime } x = \sqrt {x y+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}2 x y+y^{2}+\left (x^{2}+2 x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}4 x^{3} y+\left (x^{4}-y^{4}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}x y y^{\prime }-y^{2} = \sqrt {x^{4}+x^{2} y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x^{3}+y^{3}+x y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y y^{\prime } = 2 x^{2}+2 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +2 y}{2 x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y y^{\prime } = x^{2}+x y+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}2 y-6 x +\left (x +1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}2 x -y-y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {x}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {2 y}{x}-3
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x y+y^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x -3 y+\left (2 y-3 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {t}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2+y}{2 t +1}
\] |
[_separable] |
✓ |
|
|
\[
{}4 \left (x -1\right )^{2} y^{\prime }-3 \left (3+y\right )^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {3+y}{3 x +1}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {3 y+1}{x +3}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y-2}{x -2}
\] |
[_separable] |
✓ |
|
|
\[
{}t y^{\prime }+y = t
\] |
[_linear] |
✓ |
|
|
\[
{}\frac {t}{\sqrt {t^{2}+y^{2}}}+\frac {y y^{\prime }}{\sqrt {t^{2}+y^{2}}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y \cos \left (t y\right )+t \cos \left (t y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}3 t y^{2}+y^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}{\mathrm e}^{t y}+\frac {t \,{\mathrm e}^{t y} y^{\prime }}{y} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{2}+2 t y y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\frac {3 t^{2}}{y}-\frac {t^{3} y^{\prime }}{y^{2}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 t y+\left (t^{2}+y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}3 t^{2}+3 y^{2}+6 t y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}-\frac {y^{2} {\mathrm e}^{\frac {y}{t}}}{t^{2}}+1+{\mathrm e}^{\frac {y}{t}} \left (1+\frac {y}{t}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
|
|
\[
{}2 t \sin \left (\frac {y}{t}\right )-y \cos \left (\frac {y}{t}\right )+t \cos \left (\frac {y}{t}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
|
|
\[
{}2 t y^{2}+2 t^{2} y y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}1+5 t -y-\left (t +2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}t^{2} y+t^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 t y+y^{2}-t^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\frac {9 t}{5}+2 y+\left (2 t +2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 t +\frac {19 y}{10}+\left (\frac {19 t}{10}+2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{t} = \frac {y^{2}}{t^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\cos \left (\frac {t}{y+t}\right )+{\mathrm e}^{\frac {2 y}{t}} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y \ln \left (\frac {t}{y}\right )+\frac {t^{2} y^{\prime }}{y+t} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\frac {2}{t}+\frac {1}{y}+\frac {t y^{\prime }}{y^{2}} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 t +\left (y-3 t \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}2 y-3 t +t y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}t y-y^{2}+t \left (t -3 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}t^{2}+t y+y^{2}-t y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}t^{3}+y^{3}-t y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {t +4 y}{4 t +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y+\left (y+t \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 t^{2}-7 t y+5 y^{2}+t y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{2} = \left (t y-4 t^{2}\right ) y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y-\left (3 \sqrt {t y}+t \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (t^{2}-y^{2}\right ) y^{\prime }+y^{2}+t y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}t y y^{\prime }-t^{2} {\mathrm e}^{-\frac {y}{t}}-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1}{\frac {2 y \,{\mathrm e}^{-\frac {t}{y}}}{t}+\frac {t}{y}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}t \left (\ln \left (t \right )-\ln \left (y\right )\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {4 y^{2}-t^{2}}{2 t y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}t y^{\prime }-y-\sqrt {t^{2}+y^{2}} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}t^{3}+y^{2} \sqrt {t^{2}+y^{2}}-t y \sqrt {t^{2}+y^{2}}\, y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{3}-t^{3}-t y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}t y^{3}-\left (t^{4}+y^{4}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}1+t -2 y+\left (4 t -3 y-6\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}5 t +2 y+1+\left (2 t +y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}-t^{2}}{t y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y \sin \left (\frac {t}{y}\right )-\left (t +t \sin \left (\frac {t}{y}\right )\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}3 t +\left (t -4 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y-t +\left (y+t \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{2}+\left (t y+t^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}r^{\prime } = \frac {r^{2}+t^{2}}{r t}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{\prime } = \frac {5 t x}{t^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}2 x -y-2+\left (2 y-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y}{t -2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1+y}{x -y}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x = 2 x -y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x = y+x \cos \left (\frac {y}{x}\right )^{2}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } x = y \left (\ln \left (y\right )-\ln \left (x \right )\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = x^{2}-x y+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}y^{\prime } x = y+\sqrt {y^{2}-x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime } = x^{2}+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}4 x -3 y+\left (2 y-3 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y-x +\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x +y-2+\left (x -y+4\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x +y+\left (x -y-2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x +3 y-5+\left (3 x +2 y-5\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y+y^{\prime } x = 2 x
\] |
[_linear] |
✓ |
|
|
\[
{}3 x y^{2} y^{\prime }-2 y^{3} = x^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x \left (2 x^{2}+y^{2}\right )+y \left (x^{2}+2 y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}3 x^{2} y+y^{3}+\left (x^{3}+3 x y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+3 x y y^{\prime }+2 y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{3}-3 x y^{2}+\left (y^{3}-3 x^{2} y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}5 x y-4 y^{2}-6 x^{2}+\left (y^{2}-8 x y+\frac {5 x^{2}}{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\frac {1}{x^{2}-x y+y^{2}} = \frac {y^{\prime }}{2 y^{2}-x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x -y+3+\left (3 x +y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
|
|
\[
{}x^{2}+y^{2}-x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (5 x -7 y+1\right ) y^{\prime }+x +y-1 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 \left (y+2\right )^{2}}{\left (x +y-1\right )^{2}}
\] |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
|
|
\[
{}y^{\prime } = \frac {3-2 x}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x}{1+2 y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {t -y}{2 t +5 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {4 t}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}2 x +3+\left (2 y-2\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 x +4 y+\left (2 x -2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x y^{2}+2 y+\left (2 x^{2} y+2 x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {4 x +2 y}{2 x +3 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {4 x -2 y}{2 x -3 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 x -y+\left (2 y-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 x y+y^{2}+\left (x y+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y y^{\prime } = x +1
\] |
[_separable] |
✓ |
|
|
\[
{}\frac {\left (3 x^{3}-x y^{2}\right ) y^{\prime }}{3 x^{2} y+y^{3}} = 1
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y y^{\prime } = \left (x +y\right )^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {4 y-7 x}{5 x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } x -4 \sqrt {y^{2}-x^{2}} = y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{4}+2 x y^{3}-3 x^{2} y^{2}-2 x^{3} y}{2 x^{2} y^{2}-2 x^{3} y-2 x^{4}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (y+x \,{\mathrm e}^{\frac {x}{y}}\right ) y^{\prime } = y \,{\mathrm e}^{\frac {x}{y}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y y^{\prime } = x^{2}+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (3 x-y \right ) x^{\prime }+9 y -2 x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}5 x y^{2}+5 y+\left (5 x^{2} y+5 x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime } = \frac {2 x y +x^{2}}{3 y^{2}+2 x y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}4 x y y^{\prime } = 8 x^{2}+5 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x y}{x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y \left (1+\ln \left (y\right )-\ln \left (x \right )\right )}{x}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{2}+x^{2} y^{\prime } = x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}\left (x +y\right ) y^{\prime } = y-x
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}3 y-7 x +7 = \left (3 x -7 y-3\right ) y^{\prime }
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 \left (y+2\right )^{2}}{\left (x +y-1\right )^{2}}
\] |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
|
|
\[
{}\frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } x = 2 y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x y}{x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}2 x y y^{\prime } = x^{2}+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}}{x y-x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x^{5} y^{\prime }+y^{5} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2}-2 y^{2}+x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime }-3 x y-2 y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = 3 \left (x^{2}+y^{2}\right ) \arctan \left (\frac {y}{x}\right )+x y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x \sin \left (\frac {y}{x}\right ) y^{\prime } = y \sin \left (\frac {y}{x}\right )+x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } x = y+2 x \,{\mathrm e}^{-\frac {y}{x}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x -y-\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } x = 2 x +3 y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = 2 x y+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{3}+y^{3}-x y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +y+4}{x -y-6}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x -2 y+\left (-1+y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +y-1}{x +4 y+2}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x +3 y-1-4 \left (x +1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y+y \cos \left (x y\right )+\left (x +x \cos \left (x y\right )\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\frac {4 y^{2}-2 x^{2}}{4 x y^{2}-x^{3}}+\frac {\left (8 y^{2}-x^{2}\right ) y^{\prime }}{4 y^{3}-x^{2} y} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (3 x^{2}-y^{2}\right ) y^{\prime }-2 x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x +y\right ) y^{\prime } = y-x
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y+y^{\prime } x = \sqrt {x y}\, y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}2 x +3 y+1+\left (2 y-3 x +5\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } x = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y y^{\prime } = y^{2}+x^{2} y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{2}-3 x y-2 x^{2} = \left (x^{2}-x y\right ) y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x^{2} y^{4}+x^{6}-x^{3} y^{3} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = 1+\frac {y}{x}-\frac {y^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x y \,{\mathrm e}^{\frac {x^{2}}{y^{2}}}}{y^{2}+y^{2} {\mathrm e}^{\frac {x^{2}}{y^{2}}}+2 x^{2} {\mathrm e}^{\frac {x^{2}}{y^{2}}}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +2 y+2}{y-2 x}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\frac {y-x}{\left (x +y\right )^{3}}-\frac {2 x y^{\prime }}{\left (x +y\right )^{3}} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}3 x^{2} y-y^{3}-\left (3 x y^{2}-x^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-3 x -2 y-1}{2 x +3 y-1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 x y+y^{2}+\left (3 x y+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = x^{2}+x y+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x^{2} y^{\prime }-y^{2} = 2 x y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (t^{2}-x^{2}\right ) x^{\prime } = t x
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}v^{\prime }+\frac {2 v}{u} = 3
\] |
[_linear] |
✓ |
|
|
\[
{}y^{2} = x \left (y-x \right ) y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}2 x^{2} y+y^{3}-x^{3} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 a x +b y+\left (2 c y+b x +e \right ) y^{\prime } = g
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x +y y^{\prime } = m y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\frac {2 x}{y^{3}}+\left (\frac {1}{y^{2}}-\frac {3 x^{2}}{y^{4}}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = 1+\frac {2 y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x \left (x -2 y\right ) y^{\prime }+x^{2}+2 y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}5 x y y^{\prime }-x^{2}-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (x^{2}+3 x y-y^{2}\right ) y^{\prime }-3 y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x^{2}+2 x y\right ) y^{\prime }-3 x^{2}+2 x y-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}5 x y y^{\prime }-4 x^{2}-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}3 x^{2} y^{\prime }+2 x^{2}-3 y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}\left (3 x +2 y-7\right ) y^{\prime } = 2 x -3 y+6
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (6 x -5 y+4\right ) y^{\prime } = 1+2 x -y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (5 x -2 y+7\right ) y^{\prime } = x -3 y+2
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x -3 y+4\right ) y^{\prime } = 5 x -7 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (1-x \right ) y^{\prime }-1-y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2}+y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{2}+\left (x y+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (4 y+3 x \right ) y^{\prime }+y-2 x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (y-3 x +3\right ) y^{\prime } = 2 y-x -4
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2}-4 x y-2 y^{2}+\left (y^{2}-4 x y-2 x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}2 a x +b y+g +\left (2 c y+b x +e \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2} y-2 x y^{2}-\left (x^{3}-3 x^{2} y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{3}-2 x^{2} y+\left (2 x y^{2}-x^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } x -a y = x +1
\] |
[_linear] |
✓ |
|
|
\[
{}2 x -y+1+\left (2 y-x -1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } x +\frac {y^{2}}{x} = y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x +y y^{\prime } = m \left (-y+y^{\prime } x \right )
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y y^{\prime } = a x
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +y\right ) y^{\prime }+x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (y^{2}-x^{2}\right ) y^{\prime }+2 x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{2}+x^{2} y^{\prime } = x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}\left (x +2 y\right ) {y^{\prime }}^{3}+3 {y^{\prime }}^{2} \left (x +y\right )+\left (2 x +y\right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}4 y^{2} {y^{\prime }}^{2}+2 y^{\prime } x y \left (3 x +1\right )+3 x^{3} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{2} \left ({y^{\prime }}^{2}+2\right ) = 2 y^{3} y^{\prime }+x^{3}
\] |
[_separable] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}+y^{\prime } \left (3 x^{2}-2 y^{2}\right )-6 x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } \sqrt {x} = \sqrt {y}
\] |
[_separable] |
✓ |
|
|
\[
{}y+x +y^{\prime } x = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y-x +\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x^{3}+3 x y^{2}+\left (3 x^{2} y+y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}x +y y^{\prime } = m \left (-y+y^{\prime } x \right )
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x^{2}+y^{2}\right ) y^{\prime } = x y+x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x \cos \left (\frac {y}{x}\right )+y \sin \left (\frac {y}{x}\right )\right ) y-\left (y \sin \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right )\right ) x y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x^{2}-y^{2}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{2} = \left (x y-x^{2}\right ) y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x \sin \left (\frac {y}{x}\right ) y^{\prime } = y \sin \left (\frac {y}{x}\right )-x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (x^{2}+y^{2}\right ) y^{\prime } = x y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+y \left (x +y\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 y^{\prime } = \frac {y}{x}+\frac {y^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (6 x -5 y+4\right ) y^{\prime }+y-2 x -1 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x -3 y+4\right ) y^{\prime }+7 y-5 x = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x \left (x^{2}+3 y^{2}\right )+y \left (3 x^{2}+y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}x^{2}+3 y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1+2 x -y}{x +2 y-3}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x -y\right ) y^{\prime } = x +y+1
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2} y-2 x y^{2}-\left (x^{3}-3 x^{2} y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x^{2}+y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x +y y^{\prime } = m \left (-y+y^{\prime } x \right )
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{2}+x^{2} y^{\prime } = x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime }+\frac {a x +b y+c}{b x +f y+e} = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}x {y^{\prime }}^{2}+\left (y-x \right ) y^{\prime }-y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}\left (y^{\prime }+y+x \right ) \left (y+x +y^{\prime } x \right ) \left (y^{\prime }+2 x \right ) = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+x y y^{\prime }-6 y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y-y^{\prime } x = x +y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}+y^{\prime } \left (3 x^{2}-2 y^{2}\right )-6 x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x \cos \left (\frac {y}{x}\right )+y \sin \left (\frac {y}{x}\right )\right ) y = \left (y \sin \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right )\right ) x y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{2}+\left (x y+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {6 x -2 y-7}{2 x +3 y-6}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{3}-2 x^{2} y+\left (2 x y^{2}-x^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x +2 y\right ) {y^{\prime }}^{3}+3 {y^{\prime }}^{2} \left (x +y\right )+\left (2 x +y\right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}x y^{2} \left ({y^{\prime }}^{2}+2\right ) = 2 y^{3} y^{\prime }+x^{3}
\] |
[_separable] |
✓ |
|