|
# |
ODE |
CAS classification |
Solved? |
|
\[
{}x y^{\prime }+2 y = 3 x
\] |
[_linear] |
✓ |
|
|
\[
{}3 x y^{\prime }+y = 12 x
\] |
[_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] |
✓ |
|
|
\[
{}x y^{\prime } = y+2 \sqrt {x y}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } \left (x -y\right ) = x +y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x \left (x +y\right ) y^{\prime } = y \left (x -y\right )
\] |
[[_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] |
✓ |
|
|
\[
{}x y^{\prime } = y+\sqrt {x^{2}+y^{2}}
\] |
[[_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] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y \left (2 x^{3}-y^{3}\right )}{x \left (2 y^{3}-x^{3}\right )}
\] |
[[_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] |
✓ |
|
|
\[
{}6 x y^{3}+2 y^{4}+\left (9 y^{2} x^{2}+8 x y^{3}\right ) y^{\prime } = 0
\] |
[[_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] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {3 x^{2}+2 y^{2}}{4 x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +3 y}{y-3 x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y^{\prime }+2 y = 3 x
\] |
[_linear] |
✓ |
|
|
\[
{}3 x y^{\prime }+y = 12 x
\] |
[_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] |
✓ |
|
|
\[
{}x y^{\prime } = y+2 \sqrt {x y}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } \left (x -y\right ) = x +y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x \left (x +y\right ) y^{\prime } = y \left (x -y\right )
\] |
[[_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] |
✓ |
|
|
\[
{}x y^{\prime } = y+\sqrt {x^{2}+y^{2}}
\] |
[[_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] |
✓ |
|
|
\[
{}6 x y^{3}+2 y^{4}+\left (9 y^{2} x^{2}+8 x y^{3}\right ) y^{\prime } = 0
\] |
[[_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] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-3 x^{2}-2 y^{2}}{4 x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +3 y}{y-3 x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}+x y+x^{2}}{x^{2}}
\] |
[[_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] |
✓ |
|
|
\[
{}2 x +4 y+\left (2 x -2 y\right ) y^{\prime } = 0
\] |
[[_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‘]] |
✓ |
|
|
\[
{}3 x y+y^{2}+\left (x^{2}+x y\right ) y^{\prime } = 0
\] |
[[_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‘]] |
✓ |
|
|
\[
{}x y^{\prime } = {\mathrm e}^{\frac {y}{x}} x +y
\] |
[[_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‘]] |
✓ |
|
|
\[
{}x y^{\prime }+3 y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+\frac {k y}{x} = 0
\] |
[_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] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}+2 x y}{x^{2}}
\] |
[[_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] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = y^{2}+x y+x^{2}
\] |
[[_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‘]] |
✓ |
|
|
\[
{}\left (-y+x y^{\prime }\right ) \left (\ln \left (y\right )-\ln \left (x \right )\right ) = x
\] |
[[_homogeneous, ‘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‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{-2 x +y}
\] |
[[_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‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}+x y+x^{2}}{x y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}6 y^{2} x^{2}+4 x^{3} y y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}4 x +7 y+\left (3 x +4 y\right ) y^{\prime } = 0
\] |
[[_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‘]] |
✓ |
|
|
\[
{}x^{2}+y^{2}+2 x y y^{\prime } = 0
\] |
[[_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] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y+t}{-y+t}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}{\mathrm e}^{\frac {t}{y}} \left (-t +y\right ) y^{\prime }+y \left (1+{\mathrm e}^{\frac {t}{y}}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}2 t y^{3}+3 t^{2} y^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}3 t y+y^{2}+\left (t^{2}+t y\right ) y^{\prime } = 0
\] |
[[_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] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y+t}{-y+t}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}{\mathrm e}^{\frac {t}{y}} \left (-t +y\right ) y^{\prime }+y \left (1+{\mathrm e}^{\frac {t}{y}}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}2 t y^{3}+3 t^{2} y^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}3 t y+y^{2}+\left (t^{2}+t y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x y^{\prime }+y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime }+2 y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +y\right ) y^{\prime }+x = y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}-y+x y^{\prime } = \sqrt {x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x -y}{x +4 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}-y+x y^{\prime } = \sqrt {x^{2}-y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x +y y^{\prime } = 2 y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y^{\prime }-y+\sqrt {y^{2}-x^{2}} = 0
\] |
[[_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‘]] |
✓ |
|
|
\[
{}x +y+y^{\prime } \left (x -y\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y \left (x^{2}-x y+y^{2}\right )+x y^{\prime } \left (y^{2}+x y+x^{2}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }-y-x \sin \left (\frac {y}{x}\right ) = 0
\] |
[[_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] |
✓ |
|
|
\[
{}{\mathrm e}^{\frac {y}{x}} x +y = x y^{\prime }
\] |
[[_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] |
✓ |
|
|
\[
{}x +y+\left (x -2 y\right ) y^{\prime } = 0
\] |
[[_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‘]] |
✓ |
|
|
\[
{}2 x y-\left (x^{2}+y^{2}\right ) y^{\prime } = 0
\] |
[[_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‘]] |
✓ |
|
|
\[
{}x y y^{\prime } = x^{2}-y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+y^{2} = x y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{2}+\left (x^{2}+x y\right ) y^{\prime } = 0
\] |
[[_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‘]] |
✓ |
|
|
\[
{}x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y+\left (-2 y+3 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (3 x +4 y\right ) y^{\prime }+2 x +y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y^{\prime }-y-\sqrt {x^{2}+y^{2}} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime } = 0
\] |
[[_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] |
✓ |
|
|
\[
{}x y-y^{2}-x^{2} y^{\prime } = 0
\] |
[[_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] |
✓ |
|
|
\[
{}4 y^{2} = {y^{\prime }}^{2} x^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}x \left ({y^{\prime }}^{2}-1\right ) = 2 y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{2} {y^{\prime }}^{2}+x y y^{\prime }-2 x^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+2 y^{2} = x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y = y^{\prime } x \left (1+y^{\prime }\right )
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} y-2 x y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left ({y^{\prime }}^{2}-1\right ) = 2 y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}4 x -2 y y^{\prime }+{y^{\prime }}^{2} x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} y = 3 x y^{\prime }+y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (1+{y^{\prime }}^{2}\right ) x = \left (x +y\right ) y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y+2 x y^{\prime } = {y^{\prime }}^{2} x
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x +2 y y^{\prime } = {y^{\prime }}^{2} x
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}4 x -2 y y^{\prime }+{y^{\prime }}^{2} x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (1+{y^{\prime }}^{2}\right ) y = 2 x y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}2 x +{y^{\prime }}^{2} x = 2 y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}4 {y^{\prime }}^{2} x +2 x y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y = y^{\prime } x \left (1+y^{\prime }\right )
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {t}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}2 x y^{\prime }+3 x +y = 0
\] |
[_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] |
✓ |
|
|
\[
{}\left (3 x -y\right ) y^{\prime } = 3 y
\] |
[[_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] |
✓ |
|
|
\[
{}\sin \left (\frac {y}{x}\right ) \left (-y+x y^{\prime }\right ) = x \cos \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = \sqrt {16 x^{2}-y^{2}}+y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}-y+x y^{\prime } = \sqrt {9 x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (x^{2}-y^{2}\right )-x \left (x^{2}+y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }+y \ln \left (x \right ) = y \ln \left (y\right )
\] |
[[_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‘]] |
✓ |
|
|
\[
{}x y^{\prime } = x \tan \left (\frac {y}{x}\right )+y
\] |
[[_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] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}+x y+x^{2}}{x^{2}}
\] |
[[_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] |
✓ |
|
|
\[
{}\sin \left (\frac {y}{x}\right ) \left (-y+x y^{\prime }\right ) = x \cos \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = \sqrt {16 x^{2}-y^{2}}+y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}-y+x y^{\prime } = \sqrt {9 x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }+y \ln \left (x \right ) = y \ln \left (y\right )
\] |
[[_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‘]] |
✓ |
|
|
\[
{}x y^{\prime } = x \tan \left (\frac {y}{x}\right )+y
\] |
[[_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] |
✓ |
|
|
\[
{}-y+x y^{\prime } = \sqrt {4 x^{2}-y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _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‘]] |
✓ |
|
|
\[
{}\frac {y^{\prime }}{y}-\frac {2 \ln \left (y\right )}{x} = \frac {1-2 \ln \left (x \right )}{x}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x^{3}+y^{3}-x y^{2} y^{\prime } = 0
\] |
[[_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‘]] |
✓ |
|
|
\[
{}y y^{\prime } = x
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime }+y = x
\] |
[_linear] |
✓ |
|
|
\[
{}-y^{2}+x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y y^{\prime } = 2 x^{2}-y^{2}
\] |
[[_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] |
✓ |
|
|
\[
{}y+y \cos \left (x y\right )+\left (x +x \cos \left (x y\right )\right ) y^{\prime } = 0
\] |
[_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‘]] |
✓ |
|
|
\[
{}x y^{\prime } = \sqrt {x^{2}+y^{2}}
\] |
[[_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‘]] |
✓ |
|
|
\[
{}-y+x y^{\prime } = x \cot \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x \cos \left (\frac {y}{x}\right )^{2}-y+x y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = y \left (1+\ln \left (y\right )-\ln \left (x \right )\right )
\] |
[[_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‘]] |
✓ |
|
|
\[
{}2 x y+\left (x^{2}+2 x y+y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x -\sqrt {x^{2}+y^{2}}+\left (y-\sqrt {x^{2}+y^{2}}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } \left (y^{\prime }+2\right ) = y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = y-{\mathrm e}^{\frac {y}{x}} x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{\frac {x y^{\prime }}{y}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}-y+x y^{\prime } = x \tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}4 x -2 y y^{\prime }+{y^{\prime }}^{2} x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = y+\sqrt {x^{2}-y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x +\sin \left (\frac {y}{x}\right )^{2} \left (y-x y^{\prime }\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }+x +y = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime } = a y
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime } = a x +b y
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime } = y+\sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = y+\sqrt {x^{2}-y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }+x -y+x \cos \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = y-x \cos \left (\frac {y}{x}\right )^{2}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }-y+x \sec \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = y+x \sec \left (\frac {y}{x}\right )^{2}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = y+x \sin \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = y-x \tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = {\mathrm e}^{\frac {y}{x}} x +y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = x +y+{\mathrm e}^{\frac {y}{x}} x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = \left (1+\ln \left (x \right )-\ln \left (y\right )\right ) y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = y-2 x \tanh \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+x^{2}+x y+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _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] |
✓ |
|
|
\[
{}a \,x^{2} y^{\prime } = x^{2}+y a x +b^{2} y^{2}
\] |
[[_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‘]] |
✓ |
|
|
\[
{}\left (x +y\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } \left (x -y\right ) = y
\] |
[[_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‘]] |
✓ |
|
|
\[
{}y^{\prime } \left (x -y\right ) = \left ({\mathrm e}^{-\frac {x}{y}}+1\right ) y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (2 x +y\right ) y^{\prime }+x -2 y = 0
\] |
[[_homogeneous, ‘class A‘], _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‘]] |
✓ |
|
|
\[
{}\left (x -2 y\right ) y^{\prime } = y
\] |
[[_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‘]] |
✓ |
|
|
\[
{}\left (x +4 y\right ) y^{\prime }+4 x -y = 0
\] |
[[_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‘]] |
✓ |
|
|
\[
{}\left (a x +b y\right ) y^{\prime }+x = 0
\] |
[[_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‘]] |
✓ |
|
|
\[
{}x^{2}+y^{2}+2 x y y^{\prime } = 0
\] |
[[_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] |
✓ |
|
|
\[
{}8 x^{3} y y^{\prime }+3 x^{4}-6 y^{2} x^{2}-y^{4} = 0
\] |
[[_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] |
✓ |
|
|
\[
{}\left (2 x^{2}+4 x y-y^{2}\right ) y^{\prime } = x^{2}-4 x y-2 y^{2}
\] |
[[_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] |
✓ |
|
|
\[
{}\left (2 x^{2}+3 y^{2}\right ) y^{\prime }+x \left (3 x +y\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (3 x^{2}+2 x y+4 y^{2}\right ) y^{\prime }+2 x^{2}+6 x y+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x^{2}+a y^{2}\right ) y^{\prime } = x y
\] |
[[_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] |
✓ |
|
|
\[
{}x \left (x^{2}-x y+y^{2}\right ) y^{\prime }+\left (y^{2}+x y+x^{2}\right ) y = 0
\] |
[[_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] |
✓ |
|
|
\[
{}\left (3 x^{2}+y^{2}\right ) y y^{\prime }+x \left (x^{2}+3 y^{2}\right ) = 0
\] |
[[_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] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x = y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x +x -2 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x +x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x -y y^{\prime }+a x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x -y y^{\prime }+a y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x -\left (3 x -y\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x -2 y y^{\prime }+a x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x -2 y y^{\prime }+x +2 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x +a y y^{\prime }+b x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}3 {y^{\prime }}^{2} x -6 y y^{\prime }+x +2 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}4 {y^{\prime }}^{2} x +2 x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x^{2} = y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x^{2}+x^{2}-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x^{2} = \left (x -y\right )^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x^{2}-x \left (x -2 y\right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x^{2}+3 x y y^{\prime }+2 y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x^{2}+4 x y y^{\prime }-5 y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x^{2}-5 x y y^{\prime }+6 y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x^{2}+\left (2 x +y\right ) y y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x^{2}+\left (2 x -y\right ) y y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}a \,x^{2} {y^{\prime }}^{2}-2 a x y y^{\prime }+a \left (1-a \right ) x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (-a^{2}+1\right ) x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-a^{2} x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} y = a^{2} x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} y+2 a x y^{\prime }-a y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} y-4 a^{2} x y^{\prime }+a^{2} y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} y+a x y^{\prime }+b y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} y-\left (x +y\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x +y\right ) {y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}\right ) y^{\prime }+x y = 0
\] |
[_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] |
✓ |
|
|
\[
{}x \left (x -2 y\right ) {y^{\prime }}^{2}-2 x y y^{\prime }-2 x y+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (x -2 y\right ) {y^{\prime }}^{2}+6 x y y^{\prime }-2 x y+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{2} {y^{\prime }}^{2}+2 x y y^{\prime }+x^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2}+2 y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (\left (1-a \right ) x^{2}+y^{2}\right ) {y^{\prime }}^{2}+2 a x y y^{\prime }+x^{2}+\left (1-a \right ) y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (\left (-4 a^{2}+1\right ) x^{2}+y^{2}\right ) {y^{\prime }}^{2}-8 a^{2} x y y^{\prime }+x^{2}+\left (-4 a^{2}+1\right ) y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (\left (-a^{2}+1\right ) x^{2}+y^{2}\right ) {y^{\prime }}^{2}+2 a^{2} x y y^{\prime }+x^{2}+\left (-a^{2}+1\right ) y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x +y\right )^{2} {y^{\prime }}^{2} = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x +y\right )^{2} {y^{\prime }}^{2}-\left (x^{2}-x y-2 y^{2}\right ) y^{\prime }-y \left (x -y\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2}+4 y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (x^{2}-4 y^{2}\right ) {y^{\prime }}^{2}+6 x y y^{\prime }-4 x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (-a^{2}+1\right ) y^{2} {y^{\prime }}^{2}-3 a^{2} x y y^{\prime }-a^{2} x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}4 x^{2} y^{2} {y^{\prime }}^{2} = \left (x^{2}+y^{2}\right )^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x y}{x^{2}-y^{2}}
\] |
[[_homogeneous, ‘class A‘], _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] |
✓ |
|
|
\[
{}\left (y-x \right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (2 \sqrt {x y}-x \right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }-y-\sqrt {x^{2}+y^{2}} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _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‘]] |
✓ |
|
|
\[
{}-y+x y^{\prime } = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (7 x +5 y\right ) y^{\prime }+10 x +8 y = 0
\] |
[[_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] |
✓ |
|
|
\[
{}y^{2}+\left (x^{2}+x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}+\frac {2 x y^{\prime }}{y}-1 = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y = x y^{\prime }+x \sqrt {1+{y^{\prime }}^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y-2 x y^{\prime } = {y^{\prime }}^{2} x
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}2 x y+\left (x^{2}+y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x +\sqrt {y^{2}-x y}\right ) y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x +y-y^{\prime } \left (x -y\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y^{\prime }-y-x \sin \left (\frac {y}{x}\right ) = 0
\] |
[[_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] |
✓ |
|
|
\[
{}y+x \ln \left (\frac {y}{x}\right ) y^{\prime }-2 x y^{\prime } = 0
\] |
[[_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] |
✓ |
|
|
\[
{}{\mathrm e}^{\frac {y}{x}} x +y = x y^{\prime }
\] |
[[_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] |
✓ |
|
|
\[
{}y^{\prime } = 1+\frac {y}{x}-\frac {y^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}-y+x y^{\prime } = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x^{2}-y^{2}\right ) y^{\prime } = 2 x y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = x +y+{\mathrm e}^{\frac {y}{x}} x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }-y-x \sin \left (\frac {y}{x}\right ) = 0
\] |
[[_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] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} y+2 x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+y^{2}-x y = 0
\] |
[[_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] |
✓ |
|
|
\[
{}y^{2}-x y+\left (x^{2}+x y\right ) y^{\prime } = 0
\] |
[[_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] |
✓ |
|
|
\[
{}\left (-x +2 y\right ) y^{\prime } = 2 x +y
\] |
[[_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] |
✓ |
|
|
\[
{}y-3 x +\left (3 x +4 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x^{3}+3 x y^{2}\right ) y^{\prime } = y^{3}+3 x^{2} y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x^{2}-2 x y+5 y^{2} = \left (x^{2}+2 x y+y^{2}\right ) y^{\prime }
\] |
[[_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‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = y^{2}-x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+y^{2} = x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}2 x y y^{\prime } = x^{2}-y^{2}
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{\prime } = 2 y
\] |
[_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] |
✓ |
|
|
\[
{}4 y+x y^{\prime } = 0
\] |
[_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] |
✓ |
|
|
\[
{}x +2 y+\left (2 x +3 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x y^{\prime }-2 y = \sqrt {4 y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{2}-x^{2}+x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{3}+y^{3}+3 x y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{\prime }+2 y = 0
\] |
[_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] |
✓ |
|
|
\[
{}x^{2}+y^{2}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x^{2}+x y y^{\prime }-6 y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x -2 y y^{\prime }+4 x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}8 {y^{\prime }}^{2} y-2 x y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x -y y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} y-x y^{\prime }+3 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x -2 y y^{\prime }+4 x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x -2 y y^{\prime }+x +2 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (1+{y^{\prime }}^{2}\right ) \left (x -y\right )^{2} = \left (x +y y^{\prime }\right )^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }-2 y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {x}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime } = 2 y
\] |
[_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] |
✓ |
|
|
\[
{}3 x y^{\prime }-2 y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime }+y = 2 x
\] |
[_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] |
✓ |
|
|
\[
{}x y^{\prime } = 4 y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {x}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +y\right ) y^{\prime }+x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+y^{2} = x y y^{\prime }
\] |
[[_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] |
✓ |
|
|
\[
{}-y+x y^{\prime } = x \tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = y-{\mathrm e}^{\frac {y}{x}} x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}-y+x y^{\prime } = \left (x +y\right ) \ln \left (\frac {x +y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = y \cos \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y+\sqrt {x y}-x y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }-\sqrt {x^{2}-y^{2}}-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x +y-y^{\prime } \left (x -y\right ) = 0
\] |
[[_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] |
✓ |
|
|
\[
{}-y+x y^{\prime } = y y^{\prime }
\] |
[[_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‘]] |
✓ |
|
|
\[
{}y^{2}+x y+x^{2} = x^{2} y^{\prime }
\] |
[[_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] |
✓ |
|
|
\[
{}\left (2 \sqrt {x y}-x \right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = y \ln \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (x y^{\prime }+y\right )^{2} = y^{2} y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x^{2}-3 x y y^{\prime }+2 y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}-y+x y^{\prime } = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} y+2 x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime }+\frac {x +2 y}{x} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y^{\prime } = x +\frac {y}{2}
\] |
[_linear] |
✓ |
|
|
\[
{}2 x +4 y+\left (2 x -2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y^{\prime }-2 \sqrt {x y} = y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+y^{2}-x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x +y-y^{\prime } \left (x -y\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y+\sqrt {x^{2}+y^{2}}-x y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y \,{\mathrm e}^{x y}+x \,{\mathrm e}^{x y} y^{\prime } = 0
\] |
[_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] |
✓ |
|
|
\[
{}x +y y^{\prime }+y-x y^{\prime } = 0
\] |
[[_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‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}}{x^{2}+x y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}+x y+x^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y+x \,{\mathrm e}^{-\frac {2 y}{x}}}{x}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = 2 y
\] |
[_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] |
✓ |
|
|
\[
{}y+y \cos \left (x y\right )+\left (x +x \cos \left (x y\right )\right ) y^{\prime } = 0
\] |
[_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] |
✓ |
|
|
\[
{}x y^{\prime } = y+2 x \,{\mathrm e}^{-\frac {y}{x}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x -y-\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y^{\prime } = 2 x -6 y
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime } = \sqrt {x^{2}+y^{2}}
\] |
[[_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] |
✓ |
|
|
\[
{}y^{\prime } = \sin \left (\frac {y}{x}\right )-\cos \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}{\mathrm e}^{\frac {x}{y}}-\frac {y y^{\prime }}{x} = 0
\] |
[[_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] |
✓ |
|
|
\[
{}x y^{\prime }+y = x
\] |
[_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] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x^{2}-y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x^{2}-5 x y y^{\prime }+6 y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +y\right )^{2} {y^{\prime }}^{2} = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x -y\right )^{2} {y^{\prime }}^{2} = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x^{2}+y^{2}\right )^{2} {y^{\prime }}^{2} = 4 y^{2} x^{2}
\] |
[[_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‘]] |
✓ |
|
|
\[
{}x y \left (x^{2}+y^{2}\right ) \left ({y^{\prime }}^{2}-1\right ) = y^{\prime } \left (x^{4}+y^{2} x^{2}+y^{4}\right )
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x -2 y y^{\prime }+4 x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x -2 y y^{\prime }+4 x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x^{2} = \left (x -y\right )^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} y-\left (x +y\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x -y}{x +4 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+y^{2} = x y y^{\prime }
\] |
[[_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] |
✓ |
|
|
\[
{}y y^{\prime }-y = x
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y = {y^{\prime }}^{2} x
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-\frac {y}{x}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} = \frac {y}{x}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }-y-\sqrt {x^{2}+y^{2}} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }+a \sqrt {x^{2}+y^{2}}-y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }-{\mathrm e}^{\frac {y}{x}} x -y-x = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }-y-x \sin \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }+x -y+x \cos \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }+x \tan \left (\frac {y}{x}\right )-y = 0
\] |
[[_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] |
✓ |
|
|
\[
{}\left (-x +2 y\right ) y^{\prime }-y-2 x = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _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‘]] |
✓ |
|
|
\[
{}\left (2 x^{2} y-x^{3}\right ) y^{\prime }+y^{3}-4 x y^{2}+2 x^{3} = 0
\] |
[[_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] |
✓ |
|
|
\[
{}\left (4 y^{2}+x^{2}\right ) y^{\prime }-x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (3 x^{2}+2 x y+4 y^{2}\right ) y^{\prime }+2 x^{2}+6 x y+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (a y^{2}+2 b x y+c \,x^{2}\right ) y^{\prime }+b y^{2}+2 c x y+d \,x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (y^{2}+x y-x^{2}\right ) y^{\prime }-y^{3}+x y^{2}+x^{2} y = 0
\] |
[[_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‘]] |
✓ |
|
|
\[
{}\left (-y+x y^{\prime }\right ) \cos \left (\frac {y}{x}\right )^{2}+x = 0
\] |
[[_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] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x -2 y+x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x +x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x +\left (y-3 x \right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x -y y^{\prime }+a y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x +2 y y^{\prime }-x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x -2 y y^{\prime }-x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x -2 y y^{\prime }+4 x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x -2 y y^{\prime }+x +2 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x +a y y^{\prime }+b x = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x^{2}+3 x y y^{\prime }+2 y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x^{2}+4 x y y^{\prime }-5 y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x^{2}-y \left (-2 x +y\right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (a^{2}-1\right ) x^{2} {y^{\prime }}^{2}+2 x y y^{\prime }-y^{2}+a^{2} x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}a \,x^{2} {y^{\prime }}^{2}-2 a x y y^{\prime }+y^{2}-a \left (a -1\right ) x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} y+2 x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} y+2 x y^{\prime }-9 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} y-2 x y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} y-4 x y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} y-4 a^{2} x y^{\prime }+a^{2} y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} y+a x y^{\prime }+b y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x +y\right ) {y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}4 {y^{\prime }}^{2} y+2 x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}\right ) y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (2 x y-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+2 x y-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (2 x y-x^{2}\right ) {y^{\prime }}^{2}-6 x y y^{\prime }-y^{2}+2 x y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (y^{2}-a^{2} x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+\left (-a^{2}+1\right ) x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (\left (1-a \right ) x^{2}+y^{2}\right ) {y^{\prime }}^{2}+2 a x y y^{\prime }+\left (1-a \right ) y^{2}+x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}3 y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+4 y^{2}-x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (-a^{2}+1\right ) y^{2} {y^{\prime }}^{2}-2 a^{2} x y y^{\prime }+y^{2}-a^{2} x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y^{2} {y^{\prime }}^{2}-2 y^{3} y^{\prime }+2 x y^{2}-x^{3} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{2}+y^{2}\right ) f \left (\frac {x}{\sqrt {x^{2}+y^{2}}}\right ) \left (1+{y^{\prime }}^{2}\right )-\left (-y+x y^{\prime }\right )^{2} = 0
\] |
[[_homogeneous, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x^{2}+y^{2}\right ) f \left (\frac {y}{\sqrt {x^{2}+y^{2}}}\right ) \left (1+{y^{\prime }}^{2}\right )-\left (-y+x y^{\prime }\right )^{2} = 0
\] |
[[_homogeneous, ‘class A‘]] |
✓ |
|
|
\[
{}x \left (\sqrt {1+{y^{\prime }}^{2}}+y^{\prime }\right )-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y \sqrt {1+{y^{\prime }}^{2}}-a y y^{\prime }-a x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = f \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\frac {-2 x^{2}+y^{2}}{x y^{2}-x^{3}}+\frac {\left (2 y^{2}-x^{2}\right ) y^{\prime }}{y^{3}-x^{2} y} = 0
\] |
[[_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] |
✓ |
|
|
\[
{}y+x +x y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}{\mathrm e}^{\frac {y}{x}} x +y-x y^{\prime } = 0
\] |
[[_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] |
✓ |
|
|
\[
{}y^{2} \left (3 y-6 x y^{\prime }\right )-x \left (y-2 x y^{\prime }\right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+y^{2}-x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x +y-y^{\prime } \left (x -y\right ) = 0
\] |
[[_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] |
✓ |
|
|
\[
{}x +y y^{\prime }+y-x y^{\prime } = 0
\] |
[[_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‘]] |
✓ |
|
|
\[
{}-y+x y^{\prime } = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}-y+x y^{\prime } = \sqrt {x^{2}-y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \sin \left (\frac {y}{x}\right )-y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{3}-2 x^{2} y+\left (2 x y^{2}-x^{3}\right ) y^{\prime } = 0
\] |
[[_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] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x -2 y y^{\prime }-x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}4 {y^{\prime }}^{2} x +2 x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x -2 y y^{\prime }-x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x +y^{\prime } y \left (2 {y^{\prime }}^{2}+3\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}a^{2} y {y^{\prime }}^{2}-2 x y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x -2 y y^{\prime }-x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x^{2}+y^{2}\right ) \left (1+y^{\prime }\right )^{2}-2 \left (x +y\right ) \left (1+y^{\prime }\right ) \left (x +y y^{\prime }\right )+\left (x +y y^{\prime }\right )^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}a^{2} y {y^{\prime }}^{2}-2 x y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}3 {y^{\prime }}^{2} x -6 y y^{\prime }+x +2 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x -2 y y^{\prime }-x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x^{\prime } = \frac {2 x}{t}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime } = -\frac {t}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}2 t x^{\prime } = x
\] |
[_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] |
✓ |
|
|
\[
{}x^{2}+y^{2}+2 x y y^{\prime } = 0
\] |
[[_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] |
✓ |
|
|
\[
{}x \tan \left (\frac {y}{x}\right )+y-x y^{\prime } = 0
\] |
[[_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] |
✓ |
|
|
\[
{}2 x -5 y+\left (4 x -y\right ) y^{\prime } = 0
\] |
[[_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] |
✓ |
|
|
\[
{}x y^{\prime } = k y
\] |
[_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] |
✓ |
|
|
\[
{}x y^{\prime } = y+\sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (\ln \left (x \right )-\ln \left (y\right )\right ) y^{\prime }-y = 0
\] |
[[_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] |
✓ |
|
|
\[
{}y \left (x -y\right )-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y \left (x -y\right )-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (y^{2}-x^{2}\right ) y^{\prime }+2 x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} y+2 x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y-x +\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y+x +x y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x +y+\left (y-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}-y+x y^{\prime } = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}8 y+10 x +\left (7 x +5 y\right ) y^{\prime } = 0
\] |
[[_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] |
✓ |
|
|
\[
{}x \cos \left (\frac {y}{x}\right ) \left (x y^{\prime }+y\right ) = y \sin \left (\frac {y}{x}\right ) \left (-y+x y^{\prime }\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\frac {y-x y^{\prime }}{\sqrt {x^{2}+y^{2}}} = m
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\frac {x +y y^{\prime }}{\sqrt {x^{2}+y^{2}}} = m
\] |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
|
|
\[
{}y+\frac {x}{y^{\prime }} = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y y^{\prime } = -x +\sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\frac {x}{\left (x +y\right )^{2}}+\frac {\left (2 x +y\right ) y^{\prime }}{\left (x +y\right )^{2}} = 0
\] |
[[_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] |
✓ |
|
|
\[
{}y = {y^{\prime }}^{2} y+2 x y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y}{x}-\sqrt {3}
\] |
[_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] |
✓ |
|
|
\[
{}2 x y^{\prime }-y = 0
\] |
[_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] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y}{t}+2
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y}{t}+2
\] |
[_linear] |
✓ |
|
|
\[
{}y y^{\prime } = 2 x
\] |
[_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‘]] |
✓ |
|
|
\[
{}-y+x y^{\prime } = \sqrt {x^{2}+x y}
\] |
[[_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] |
✓ |
|
|
\[
{}x y y^{\prime }-y^{2} = \sqrt {x^{4}+y^{2} x^{2}}
\] |
[[_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] |
✓ |
|
|
\[
{}x y y^{\prime } = y^{2}+x y+x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}2 x -y-y y^{\prime } = 0
\] |
[[_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] |
✓ |
|
|
\[
{}y^{\prime } = \sqrt {\frac {y}{t}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}t y^{\prime }+y = t
\] |
[_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] |
✓ |
|
|
\[
{}t^{2} y+t^{3} y^{\prime } = 0
\] |
[_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‘]] |
✓ |
|
|
\[
{}y+2 \sqrt {t^{2}+y^{2}}-t y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{2} = \left (t y-4 t^{2}\right ) y^{\prime }
\] |
[[_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] |
✓ |
|
|
\[
{}y^{4}+\left (t^{4}-t y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}t^{{1}/{3}} y^{{2}/{3}}+t +\left (t^{{2}/{3}} y^{{1}/{3}}+y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}-t^{2}}{t y}
\] |
[[_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‘]] |
✓ |
|
|
\[
{}y^{2}+\left (t^{2}+t y\right ) y^{\prime } = 0
\] |
[[_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] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime } = 2 x -y
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime } = y+x \cos \left (\frac {y}{x}\right )^{2}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = y \left (\ln \left (y\right )-\ln \left (x \right )\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = x^{2}-x y+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime } = x^{2}+y^{2}
\] |
[[_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‘]] |
✓ |
|
|
\[
{}x y^{\prime }+y = 2 x
\] |
[_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] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x^{2}+3 x y y^{\prime }+2 y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x y^{\prime }+y\right )^{2} = y^{2} y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}3 {y^{\prime }}^{2} x -6 y y^{\prime }+x +2 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x^{3}-3 x y^{2}+\left (y^{3}-3 x^{2} y\right ) y^{\prime } = 0
\] |
[[_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] |
✓ |
|
|
\[
{}1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
|
|
\[
{}x^{2}+y^{2}-x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-y+t}{2 t +5 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {4 t}{y}
\] |
[_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] |
✓ |
|
|
\[
{}2 x -y+\left (-x +2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 x y+y^{2}+\left (x^{2}+x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}\frac {\left (3 x^{3}-x y^{2}\right ) y^{\prime }}{3 x^{2} y+y^{3}} = 1
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\sqrt {x^{2}-y^{2}}+y = x y^{\prime }
\] |
[[_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‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{4}+2 x y^{3}-3 y^{2} x^{2}-2 x^{3} y}{2 y^{2} x^{2}-2 x^{3} y-2 x^{4}}
\] |
[[_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] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+y^{2} = x y y^{\prime }
\] |
[[_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] |
✓ |
|
|
\[
{}\frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x +2 x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y = \frac {k \left (x +y y^{\prime }\right )}{\sqrt {1+{y^{\prime }}^{2}}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x -2 y y^{\prime }+4 x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x +2 x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x^{2}-2 x y y^{\prime }+2 x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = 2 y
\] |
[_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] |
✓ |
|
|
\[
{}x y^{\prime } = y+2 x \,{\mathrm e}^{-\frac {y}{x}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x -y-\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y^{\prime } = 2 x +3 y
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime } = \sqrt {x^{2}+y^{2}}
\] |
[[_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] |
✓ |
|
|
\[
{}y+y \cos \left (x y\right )+\left (x +x \cos \left (x y\right )\right ) y^{\prime } = 0
\] |
[_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‘]] |
✓ |
|
|
\[
{}x y^{\prime }+y = \sqrt {x y}\, y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y y^{\prime } = x^{2} y^{\prime }+y^{2}
\] |
[[_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‘]] |
✓ |
|
|
\[
{}x^{2} y^{4}+x^{6}-x^{3} y^{3} y^{\prime } = 0
\] |
[[_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] |
✓ |
|
|
\[
{}\frac {y-x}{\left (x +y\right )^{3}}-\frac {2 x y^{\prime }}{\left (x +y\right )^{3}} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}3 x^{2} y-y^{3}-\left (3 x y^{2}-x^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}3 x y+y^{2}+\left (3 x y+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = y^{2}+x y+x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x^{2} y^{\prime }-y^{2} = 2 x y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{\prime } = \cos \left (\frac {x}{t}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (t^{2}-x^{2}\right ) x^{\prime } = t x
\] |
[[_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] |
✓ |
|
|
\[
{}x +y y^{\prime } = m y
\] |
[[_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‘]] |
✓ |
|
|
\[
{}y-2 x y^{\prime }-{y^{\prime }}^{2} y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (x -2 y\right ) y^{\prime }+x^{2}+2 y^{2} = 0
\] |
[[_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] |
✓ |
|
|
\[
{}x^{2}+y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{2}+\left (x^{2}+x y\right ) y^{\prime } = 0
\] |
[[_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‘]] |
✓ |
|
|
\[
{}x^{2}-4 x y-2 y^{2}+\left (y^{2}-4 x y-2 x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}x^{2} y-2 x y^{2}-\left (x^{3}-3 x^{2} y\right ) y^{\prime } = 0
\] |
[[_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] |
✓ |
|
|
\[
{}-y+x y^{\prime } = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }+\frac {y^{2}}{x} = y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x +y y^{\prime } = m \left (-y+x y^{\prime }\right )
\] |
[[_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] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+y^{2} = x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x -2 y y^{\prime }+a x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{2}+x y y^{\prime }-{y^{\prime }}^{2} x^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y = {y^{\prime }}^{2} y+2 x y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x^{2}-2 x y y^{\prime }+2 y^{2}-x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y^{2} \left ({y^{\prime }}^{2}+2\right ) = 2 y^{3} y^{\prime }+x^{3}
\] |
[_separable] |
✓ |
|
|
\[
{}3 y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+4 y^{2}-x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (x^{2}+y^{2}\right ) \left (1+y^{\prime }\right )^{2}-2 \left (x +y\right ) \left (1+y^{\prime }\right ) \left (x +y y^{\prime }\right )+\left (x +y y^{\prime }\right )^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (y y^{\prime }+n x \right )^{2} = \left (y^{2}+n \,x^{2}\right ) \left (1+{y^{\prime }}^{2}\right )
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (3 x^{2}-2 y^{2}\right ) y^{\prime }-6 x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x -2 y y^{\prime }+a x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y+x +x y^{\prime } = 0
\] |
[_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] |
✓ |
|
|
\[
{}x +y y^{\prime } = m \left (-y+x y^{\prime }\right )
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x^{2}+y^{2}\right ) y^{\prime } = x^{2}+x y
\] |
[[_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] |
✓ |
|
|
\[
{}-y+x y^{\prime } = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (3 x^{2}+y^{2}\right ) y y^{\prime }+x \left (x^{2}+3 y^{2}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}x^{2}+3 y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y-2 x y^{2}-\left (x^{3}-3 x^{2} y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x^{2}+y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}-y+x y^{\prime } = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x +y y^{\prime } = m \left (-y+x y^{\prime }\right )
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+y^{2} = x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x^{2}+x y y^{\prime }-6 y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x +a x = 2 y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} y+2 x y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}4 {y^{\prime }}^{2} y+2 x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} y+2 x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x^{2}-2 x y y^{\prime }+2 y^{2} = x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y = x y^{\prime }+x \sqrt {1+{y^{\prime }}^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x +y^{\prime } y \left (2 {y^{\prime }}^{2}+3\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y-x y^{\prime } = x +y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}a^{2} y {y^{\prime }}^{2}-4 x y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (3 x^{2}-2 y^{2}\right ) y^{\prime }-6 x y = 0
\] |
[_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] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x -2 y y^{\prime }+a x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} y-2 x y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}3 {y^{\prime }}^{2} x -6 y y^{\prime }+x +2 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{2}+\left (x^{2}+x y\right ) y^{\prime } = 0
\] |
[[_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] |
✓ |
|
|
\[
{}y^{3}-2 x^{2} y+\left (2 x y^{2}-x^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y-2 x y^{\prime }+a y {y^{\prime }}^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y^{2} \left ({y^{\prime }}^{2}+2\right ) = 2 y^{3} y^{\prime }+x^{3}
\] |
[_separable] |
✓ |
|
|
\[
{}\left (y y^{\prime }+n x \right )^{2} = \left (y^{2}+n \,x^{2}\right ) \left (1+{y^{\prime }}^{2}\right )
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x^{2}+y^{2}\right ) \left (1+y^{\prime }\right )^{2}-2 \left (x +y\right ) \left (1+y^{\prime }\right ) \left (x +y y^{\prime }\right )+\left (x +y y^{\prime }\right )^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x -2 y y^{\prime }+x +2 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} y^{2} \cos \left (a \right )^{2}-2 y^{\prime } x y \sin \left (a \right )^{2}+y^{2}-x^{2} \sin \left (a \right )^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|