|
# |
ODE |
CAS classification |
Solved? |
|
\[
{}y^{\prime } = 2 x^{2} y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y y^{\prime } = x -1
\] |
[_separable] |
✓ |
|
|
\[
{}y y^{\prime } = x -1
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+2 x y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x y^{3}
\] |
[_separable] |
✓ |
|
|
\[
{}y y^{\prime } = x \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{3} y^{\prime } = \left (1+y^{4}\right ) \cos \left (x \right )
\] |
[_separable] |
✓ |
|
|
\[
{}2 y y^{\prime } = \frac {x}{\sqrt {x^{2}-16}}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 x y^{2}+3 x^{2} y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 2 \sqrt {y}
\] |
[_quadrature] |
✓ |
|
|
\[
{}2 x y y^{\prime } = x^{2}+2 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{2} y^{\prime } = x^{3}+y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = x y+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y y^{\prime } = x^{2}+3 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x y+x^{2} y^{\prime } = 5 y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{2} y^{\prime }+2 x y^{3} = 6 x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y+y^{3}
\] |
[_quadrature] |
✓ |
|
|
\[
{}2 x y+x^{2} y^{\prime } = 5 y^{4}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } x +6 y = 3 x y^{{4}/{3}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 y^{\prime } x +y^{3} {\mathrm e}^{-2 x} = 2 x y
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{2} \left (y+y^{\prime } x \right ) \sqrt {x^{4}+1} = x
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}3 y^{2} y^{\prime }+y^{3} = {\mathrm e}^{-x}
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
|
|
\[
{}3 x y^{2} y^{\prime } = 3 x^{4}+y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+p \left (x \right ) y = q \left (x \right ) y^{n}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}x^{\prime } = x-x^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime } = 10 x-x^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime } = 3 x \left (5-x\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime } = 3 x \left (5-x\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime } = 4 x \left (7-x\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime } = 7 x \left (x-13\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}x y^{2}+3 y^{2}-x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y+y^{2}-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x y^{2}+x^{2} y^{\prime } = y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}2 x y+x^{2} y^{\prime } = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } x +2 y = 6 x^{2} \sqrt {y}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = x y+3 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}4 x y^{2}+y^{\prime } = 5 x^{4} y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{3} y^{\prime } = x^{2} y-y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x^{2} y-x^{3} y^{\prime } = y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}3 x^{5} y^{2}+x^{3} y^{\prime } = 2 y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x = 6 y+12 x^{4} y^{{2}/{3}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}9 x^{2} y^{2}+x^{{3}/{2}} y^{\prime } = y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}3 y+x^{3} y^{4}+3 y^{\prime } x = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = x y^{3}-x y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {3 x^{2}+2 y^{2}}{4 x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}-y}{\tan \left (x \right )}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y^{2} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 2 x^{2} y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y y^{\prime } = x -1
\] |
[_separable] |
✓ |
|
|
\[
{}y y^{\prime } = x -1
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+2 x y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x y^{3}
\] |
[_separable] |
✓ |
|
|
\[
{}y y^{\prime } = x \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
|
|
\[
{}2 y y^{\prime } = \frac {x}{\sqrt {x^{2}-16}}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 x y^{2}+3 x^{2} y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}2 x y y^{\prime } = x^{2}+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{2} y^{\prime } = x^{3}+y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = x y+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y y^{\prime } = x^{2}+3 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x y+x^{2} y^{\prime } = 5 y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{2} y^{\prime }+2 x y^{3} = 6 x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y+y^{3}
\] |
[_quadrature] |
✓ |
|
|
\[
{}2 x y+x^{2} y^{\prime } = 5 y^{4}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } x +6 y = 3 x y^{{4}/{3}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 y^{\prime } x +y^{3} {\mathrm e}^{-2 x} = 2 x y
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{2} \left (y+y^{\prime } x \right ) \sqrt {x^{4}+1} = x
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}3 y^{2} y^{\prime }+y^{3} = {\mathrm e}^{-x}
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
|
|
\[
{}3 x y^{2} y^{\prime } = 3 x^{4}+y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{2}+3 y^{2}-x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y+y^{2}-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x y^{2}+x^{2} y^{\prime } = y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}2 x y+x^{2} y^{\prime } = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } x +2 y = 6 x^{2} \sqrt {y}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = x y+3 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{3} y^{\prime } = x^{2} y-y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x^{2} y-x^{3} y^{\prime } = y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}3 x^{5} y^{2}+x^{3} y^{\prime } = 2 y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x = 6 y+12 x^{4} y^{{2}/{3}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}9 x^{2} y^{2}+x^{{3}/{2}} y^{\prime } = y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}3 y+x^{3} y^{4}+3 y^{\prime } x = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = x y^{3}-x y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-3 x^{2}-2 y^{2}}{4 x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \cot \left (x \right ) \left (\sqrt {y}-y\right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{\left (x^{3}+1\right ) y}
\] |
[_separable] |
✓ |
|
|
\[
{}\sin \left (x \right ) y^{2}+y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \left (1-2 x \right ) y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1-2 x}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}x +y y^{\prime } {\mathrm e}^{-x} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}r^{\prime } = \frac {r^{2}}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x}{y+x^{2} y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x y^{2}}{\sqrt {x^{2}+1}}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x \left (x^{2}+1\right )}{4 y^{3}}
\] |
[_separable] |
✓ |
|
|
\[
{}\sqrt {-x^{2}+1}\, y^{2} y^{\prime } = \arcsin \left (x \right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 y^{2}+x y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {t \left (4-y\right ) y}{3}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {t y \left (4-y\right )}{1+t}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{2}+3 y^{2}}{2 x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{2}-3 y^{2}}{2 x y}
\] |
[[_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] |
✓ |
|
|
\[
{}y^{\prime } = 2 t y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{3}+y^{\prime } = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {t^{2}}{\left (t^{3}+1\right ) y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = t \left (3-y\right ) y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y \left (3-t y\right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = -y \left (3-t y\right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = a y+b y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y \left (1-y^{2}\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = -b \sqrt {y}+a y
\] |
[_quadrature] |
✓ |
|
|
\[
{}\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y \left (1+y\right )}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = a y^{\frac {a -1}{a}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } x +y^{2}+y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+x \left (y^{2}+y\right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 x y \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 y-y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}x +y y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = a y-b y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{{2}/{5}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }-y = x y^{2}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+y = y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}7 y^{\prime } x -2 y = -\frac {x^{2}}{y^{6}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+2 y = 2 \,{\mathrm e}^{\frac {1}{x}} \sqrt {y}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+2 x y = \frac {1}{\left (x^{2}+1\right ) y}
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }-x y = x^{3} y^{3}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }-\frac {\left (x +1\right ) y}{3 x} = y^{4}
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }-2 y = x y^{3}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }-x y = x y^{{3}/{2}}
\] |
[_separable] |
✓ |
|
|
\[
{}y+y^{\prime } x = x^{4} y^{4}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }-2 y = 2 \sqrt {y}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }-4 y = \frac {48 x}{y^{2}}
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x y+x^{2} y^{\prime } = y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }-y = x \sqrt {y}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x y+y^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{3} y^{\prime } = y^{4}+x^{4}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y y^{\prime } = x^{2}+2 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x y+y^{2}}{x^{2}}
\] |
[[_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] |
✓ |
|
|
\[
{}x y y^{\prime } = 3 x^{2}+4 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}3 x y^{2} y^{\prime } = y^{3}+x
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y y^{\prime } = 3 x^{6}+6 y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (y^{3}-1\right ) {\mathrm e}^{x}+3 y^{2} \left ({\mathrm e}^{x}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}{\mathrm e}^{x} \left (x^{4} y^{2}+4 x^{3} y^{2}+1\right )+\left (2 x^{4} y \,{\mathrm e}^{x}+2 y\right ) y^{\prime } = 0
\] |
[_exact, _Bernoulli] |
✓ |
|
|
\[
{}2 x y y^{\prime }+x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime }-y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}3 x^{2} y^{2}+2 y+2 y^{\prime } x = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}t^{2} \left (1+y^{2}\right )+2 y y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 t}{y+t^{2} y}
\] |
[_separable] |
✓ |
|
|
\[
{}\sqrt {t^{2}+1}\, y^{\prime } = \frac {t y^{3}}{\sqrt {t^{2}+1}}
\] |
[_separable] |
✓ |
|
|
\[
{}2 t y y^{\prime } = 3 y^{2}-t^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\left (1+\cos \left (4 t \right )\right ) y}{4}-\frac {\left (1-\cos \left (4 t \right )\right ) y^{2}}{800}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}t^{2} \left (1+y^{2}\right )+2 y y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 t}{y+t^{2} y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y}{t}+\frac {y^{2}}{t^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 t y y^{\prime } = 3 y^{2}-t^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\left (1+\cos \left (4 t \right )\right ) y}{4}-\frac {\left (1-\cos \left (4 t \right )\right ) y^{2}}{800}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = t y^{a}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{t} y^{2}-2 y
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = t y^{3}-y
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}x^{\prime } = x \left (-x+1\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime } = -x \left (-x+1\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime } = x^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}x y^{2}+x +\left (y-x^{2} y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{2}+x +\left (x^{2} y-y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y+y^{\prime } x = y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{2}+y y^{\prime }+x^{2} y y^{\prime }-1 = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{2}+x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2}+y^{2} = x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2}+y^{2} = 2 x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y+y^{2}+x^{3} y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{3}-1+x^{2} y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y \left (y-x^{2}\right )+x^{3} y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}{\mathrm e}^{x} y^{\prime } = 2 x y^{2}+y \,{\mathrm e}^{x}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}2 x^{2} y y^{\prime }+x^{4} {\mathrm e}^{x}-2 x y^{2} = 0
\] |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
|
|
\[
{}y \left (1-x^{4} y^{2}\right )+y^{\prime } x = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}3 y^{2} y^{\prime }-x y^{3} = {\mathrm e}^{\frac {x^{2}}{2}} \cos \left (x \right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{3} y^{\prime }+x y^{4} = x \,{\mathrm e}^{-x^{2}}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}x y y^{\prime } = x^{2}-y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }-x y = \sqrt {y}\, x \,{\mathrm e}^{x^{2}}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}t x^{\prime }+x \left (1-x^{2} t^{4}\right ) = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{2}+x^{2} y^{\prime } = x y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }-x y = \frac {x}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y+y^{\prime } x = y^{2} x^{2} \cos \left (x \right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}r^{\prime }+\left (r-\frac {1}{r}\right ) \theta = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x +2 y = 3 x^{3} y^{{4}/{3}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}3 y^{\prime }+\frac {2 y}{x +1} = \frac {x}{y^{2}}
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = y^{3} \sin \left (x \right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+y = y^{2} {\mathrm e}^{-t}
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
|
|
\[
{}y-y^{\prime } x = 2 y^{\prime }+2 y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}2 x^{3}-y^{3}-3 x +3 x y^{2} y^{\prime } = 0
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}3 x -6 = x y y^{\prime }
\] |
[_separable] |
✓ |
|
|
\[
{}2 y^{\prime } x -y+\frac {x^{2}}{y^{2}} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } x +y \left (1+y^{2}\right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x -5 y-x \sqrt {y} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y-y^{2}-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } x -2 y-2 x^{4} y^{3} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y+y^{\prime } x = x^{3} y^{6}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{\prime } = x+x^{2} {\mathrm e}^{\theta }
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
|
|
\[
{}x^{2}+y^{2} = 2 x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}4 x y^{2}+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 \left (x^{2}+1\right ) y^{\prime } = \left (2 y^{2}-1\right ) x y
\] |
[_separable] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1 = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{2} {y^{\prime }}^{2}+x y y^{\prime }-2 x^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y {y^{\prime }}^{2}+\left (y^{2}-x^{3}-x y^{2}\right ) y^{\prime }-x y \left (x^{2}+y^{2}\right ) = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = x^{2} y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -y^{3}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{t}}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {t}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}-y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }-x y^{3} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+x y^{2} = 4 y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {2 x^{2}+y^{2}+x}{x y}
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {4 y^{2}}{x^{2}}-y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x +y-\frac {y^{2}}{x^{{3}/{2}}} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}}{x^{2}+1}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y^{3} \sin \left (x \right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\cos \left (x \right )-2 x y^{2}}{2 x^{2} y}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}}{x^{2}+1}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y^{3} \sin \left (x \right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{x} = \frac {4 x^{2} \cos \left (x \right )}{y}
\] |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+\frac {\tan \left (x \right ) y}{2} = 2 y^{3} \sin \left (x \right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }-\frac {3 y}{2 x} = 6 y^{{1}/{3}} x^{2} \ln \left (x \right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = 6 \sqrt {x^{2}+1}\, \sqrt {y}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = 6 x^{4} y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x \left (y^{\prime }+y^{3} x^{2}\right )+y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (x -a \right ) \left (x -b \right ) \left (y^{\prime }-\sqrt {y}\right ) = 2 \left (b -a \right ) y
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+\frac {6 y}{x} = \frac {3 y^{{2}/{3}} \cos \left (x \right )}{x}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+4 x y = 4 x^{3} \sqrt {y}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{2 x \ln \left (x \right )} = 2 x y^{3}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{\left (\pi -1\right ) x} = \frac {3 x y^{\pi }}{1-\pi }
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 y^{\prime }+y \cot \left (x \right ) = \frac {8 \cos \left (x \right )^{3}}{y}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}\left (1-\sqrt {3}\right ) y^{\prime }+y \sec \left (x \right ) = y^{\sqrt {3}} \sec \left (x \right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+\frac {2 x y}{x^{2}+1} = x y^{2}
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = y^{3} \sin \left (x \right )^{3}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}x^{2}+x -1+\left (2 x y+y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime }-x^{2} y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{3}+y^{3}-x y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y y^{\prime } = x
\] |
[_separable] |
✓ |
|
|
\[
{}3 y^{2} y^{\prime } = 2 x -1
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 6 x y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{\prime }-y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x = 2 y \left (-1+y\right )
\] |
[_separable] |
✓ |
|
|
\[
{}{\mathrm e}^{2 x} y y^{\prime }+2 x = 0
\] |
[_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] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x \left (1+y^{2}\right )}{y \left (x^{2}+1\right )}
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{3}+{\mathrm e}^{x^{2}} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2+y^{2}+2 x +2 y y^{\prime } = 0
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}1-\left (y-2 x y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}3 y^{\prime } x -3 x y^{4} \ln \left (x \right )-y = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y \left (6 y^{2}-x -1\right )+2 y^{\prime } x = 0
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (x +1\right ) \left (y^{\prime }+y^{2}\right )-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y y^{\prime }+y^{2}-\sin \left (x \right ) = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}2 x^{3}-y^{4}+x y^{3} y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }-\tan \left (x \right ) y+y^{2} \cos \left (x \right ) = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}x y^{2} \left (y+y^{\prime } x \right ) = 1
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}1+y^{2} \sin \left (2 x \right )-2 y \cos \left (x \right )^{2} y^{\prime } = 0
\] |
[_exact, _Bernoulli] |
✓ |
|
|
\[
{}{\mathrm e}^{x}+3 y^{2}+2 x y y^{\prime } = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}2 x^{3} y y^{\prime }+3 x^{2} y^{2}+7 = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} \left (-y+y^{\prime } x \right ) = \left (x +y\right ) y
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x^{{3}/{2}}+x^{2}+y^{2}+2 y \sqrt {x}\, y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y \left (6 y^{2}-x -1\right )+2 y^{\prime } x = 0
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{3}-1+x^{2} y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = x y \left (3+y\right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = a x y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \left (a +b y \cos \left (k x \right )\right ) y
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = y \left (a +b y^{2}\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = x y^{3}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y \left (1-x y^{2}\right ) = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+2 x y \left (1+a x y^{2}\right ) = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+\left (\tan \left (x \right )+y^{2} \sec \left (x \right )\right ) y = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+y^{3} \sec \left (x \right ) \tan \left (x \right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = f \left (x \right ) y+g \left (x \right ) y^{k}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+2 y \left (1-x \sqrt {y}\right ) = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } x +\left (1-x y\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } x = \left (1-x y\right ) y
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } x = \left (1+x y\right ) y
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } x = a \,x^{3} \left (1-x y\right ) y
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } x = y \left (1+2 x y\right )
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } x +\left (a +b \,x^{n} y\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } x +\left (1-a y \ln \left (x \right )\right ) y = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } x = y \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x +y \left (1-x y^{2}\right ) = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y+y^{\prime } x = a \left (x^{2}+1\right ) y^{3}
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } x = a y+b \left (x^{2}+1\right ) y^{3}
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } x +2 y = a \,x^{2 k} y^{k}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } x = 4 y-4 \sqrt {y}
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime } = a y+b x y^{2}
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime }+y+\left (x +1\right )^{4} y^{3} = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime } = \left (1-x y^{3}\right ) y
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (x +a \right ) y^{\prime } = y \left (1-a y\right )
\] |
[_separable] |
✓ |
|
|
\[
{}\left (a -x \right ) y^{\prime } = y+\left (c x +b \right ) y^{3}
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}2 y^{\prime } x = y \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
|
|
\[
{}2 y^{\prime } x +y \left (1+y^{2}\right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 y^{\prime } x = \left (1+x -6 y^{2}\right ) y
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}2 \left (x +1\right ) y^{\prime }+2 y+\left (x +1\right )^{4} y^{3} = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
|
|
\[
{}3 y^{\prime } x = \left (2+x y^{3}\right ) y
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}3 y^{\prime } x = \left (1+3 x y^{3} \ln \left (x \right )\right ) y
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = \left (x +a y\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = \left (a x +b y\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+\left (x^{2}+y^{2}-x \right ) y = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = 2 y \left (x -y^{2}\right )
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = \left (a x +b y^{3}\right ) y
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+x y+\sqrt {y} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x y \left (1-y\right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = x y \left (1+a y\right )
\] |
[_separable] |
✓ |
|
|
\[
{}\left (-x^{2}+4\right ) y^{\prime }+4 y = \left (x +2\right ) y^{2}
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (a^{2}+x^{2}\right ) y^{\prime }+\left (x -y\right ) y = 0
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (a^{2}+x^{2}\right ) y^{\prime }+x y+b x y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x \left (x +a \right ) y^{\prime } = \left (b +c y\right ) y
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime } = c y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{3} y^{\prime } = y \left (y+x^{2}\right )
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{3} y^{\prime } = \left (x +1\right ) y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{3} y^{\prime } = \left (2 x^{2}+y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} \left (1-x \right ) y^{\prime } = \left (2-x \right ) x y-y^{2}
\] |
[[_homogeneous, ‘class D‘], _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] |
✓ |
|
|
\[
{}6 x^{3} y^{\prime } = 4 x^{2} y+\left (1-3 x \right ) y^{4}
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{4} y^{\prime } = \left (x^{3}+y\right ) y
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} \left (-x^{2}+1\right ) y^{\prime } = \left (x -3 x^{3} y\right ) y
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } \left (a +\cos \left (\frac {x}{2}\right )^{2}\right ) = y \tan \left (\frac {x}{2}\right ) \left (1+a +\cos \left (\frac {x}{2}\right )^{2}-y\right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}x +y y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y y^{\prime }+x \,{\mathrm e}^{x^{2}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y y^{\prime }+4 \left (x +1\right ) x +y^{2} = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y y^{\prime } = a x +b y^{2}
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}y y^{\prime } = b \cos \left (x +c \right )+a y^{2}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y y^{\prime } = a x +b x y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y y^{\prime } = \csc \left (x \right )^{2}-y^{2} \cot \left (x \right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}2 y y^{\prime }+2 x +x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 y y^{\prime } = x y^{2}+x^{3}
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}x y y^{\prime }+1+y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y y^{\prime } = x +y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y y^{\prime }+x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y y^{\prime }+x^{4}-y^{2} = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y y^{\prime } = a \,x^{3} \cos \left (x \right )+y^{2}
\] |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
|
|
\[
{}x y y^{\prime } = a +b y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}x y y^{\prime } = a \,x^{n}+b y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y y^{\prime } = \left (x^{2}+1\right ) \left (1-y^{2}\right )
\] |
[_separable] |
✓ |
|
|
\[
{}2 x y y^{\prime }+1-2 x^{3}-y^{2} = 0
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x y y^{\prime }+a +y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 x y y^{\prime } = a x +y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x y y^{\prime }+x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x y y^{\prime } = x^{2}+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x y y^{\prime } = 4 x^{2} \left (2 x +1\right )+y^{2}
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x y y^{\prime }+x^{2} \left (a \,x^{3}+1\right ) = 6 y^{2}
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}2 \left (x +1\right ) y y^{\prime }+2 x -3 x^{2}+y^{2} = 0
\] |
[_exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}a x y y^{\prime } = x^{2}+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}a x y y^{\prime }+x^{2}-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y y^{\prime }+x \left (1-y^{2}\right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y y^{\prime }+2 x^{2}+x y^{2} = 0
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x^{2} y y^{\prime } = x^{2} \left (2 x +1\right )-y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 \left (x +1\right ) x y y^{\prime } = 1+y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}3 x^{2} y y^{\prime }+1+2 x y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x^{3} y y^{\prime }+a +3 x^{2} y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y \left (b \,x^{2}+a \right ) y^{\prime } = A +B y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}3 x^{4} y y^{\prime } = 1-2 x^{3} y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}3 y^{2} y^{\prime } = 1+x +a y^{3}
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}3 x y^{2} y^{\prime } = 2 x -y^{3}
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}6 x y^{2} y^{\prime }+x +2 y^{3} = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{2} y^{\prime }+1-x +x^{3} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } \sqrt {y} = \sqrt {x}
\] |
[_separable] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-\left (x -y\right ) y y^{\prime }-x y^{3} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-x y \left (x^{2}+y^{2}\right ) y^{\prime }+x^{4} y^{4} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+\left (a +b \,x^{2} y^{3}\right ) y^{\prime }+a b y^{3} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y {y^{\prime }}^{2}-\left (1+x y\right ) y^{\prime }+x = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-x y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1 = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}\right ) y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x^{2}-y^{2}\right ) y^{\prime }-x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}-\left (x^{2}-y^{2}\right ) y^{\prime }-x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}+y^{\prime } \left (3 x^{2}-2 y^{2}\right )-6 x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{2} {y^{\prime }}^{2} = a^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-\left (x +1\right ) y y^{\prime }+x = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}4 y^{2} {y^{\prime }}^{2}+2 \left (3 x +1\right ) x y y^{\prime }+3 x^{3} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}4 x^{2} y^{2} {y^{\prime }}^{2} = \left (x^{2}+y^{2}\right )^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}+\left (2 x -y^{2}\right ) {y^{\prime }}^{2}-2 x y^{2} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}-\left (2 x +y^{2}\right ) {y^{\prime }}^{2}+\left (x^{2}-y^{2}+2 x y^{2}\right ) y^{\prime }-\left (x^{2}-y^{2}\right ) y^{2} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}-\left (x^{2}+x y+y^{2}\right ) {y^{\prime }}^{2}+x y \left (x^{2}+x y+y^{2}\right ) y^{\prime }-x^{3} y^{3} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}-\left (x^{2}+x y^{2}+y^{4}\right ) {y^{\prime }}^{2}+x y^{2} \left (x^{2}+x y^{2}+y^{4}\right ) y^{\prime }-x^{3} y^{6} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }+x y = x^{3} y^{3}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y+x y^{2}-y^{\prime } x = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y \left (x^{2}+1\right ) y^{\prime }-1-y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) z^{\prime }-x z = a x z^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}3 z^{2} z^{\prime }-a z^{3} = x +1
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}z^{\prime }+2 x z = 2 a \,x^{3} z^{3}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}z^{\prime }+z \cos \left (x \right ) = z^{n} \sin \left (2 x \right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y+y^{\prime } x = y^{2} \ln \left (x \right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}x^{2}+y^{2} = 2 x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y-y^{2}-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y+y^{\prime } x = y^{2} \ln \left (x \right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+y = x y^{3}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}\left (-x^{3}+1\right ) y^{\prime }-2 \left (x +1\right ) y = y^{{5}/{2}}
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } x +x y^{2}-y = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } x -y \left (-1+2 y \ln \left (x \right )\right ) = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}x^{2} \left (x -1\right ) y^{\prime }-y^{2}-x \left (x -2\right ) y = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{x} = \frac {y^{2}}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}2 \cos \left (x \right ) y^{\prime } = y \sin \left (x \right )-y^{3}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}2 x y y^{\prime }+\left (x +1\right ) y^{2} = {\mathrm e}^{x}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}x^{2} y+y^{2}+x^{3} y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y+y^{\prime } x = x^{2} \left ({\mathrm e}^{x}+1\right ) y^{2}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+8 x^{3} y^{3}+2 x y = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}x^{3} y^{\prime }-y^{2}-x^{2} y = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+x y-3 x y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y y^{\prime }+x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x y y^{\prime }+3 x^{2}-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}3 x y^{2} y^{\prime }+y^{3}-2 x = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = a x y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}x y \left (x^{2}+1\right ) y^{\prime } = 1+y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}x y y^{\prime }+1+y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x y^{2}+x}{x^{2} y-y}
\] |
[_separable] |
✓ |
|
|
\[
{}y y^{\prime }+x y^{2}-8 x = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+2 x y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y = x y^{{2}/{3}}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{x} = 2 x^{{3}/{2}} \sqrt {y}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}3 x y^{2} y^{\prime }+3 y^{3} = 1
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+y^{2}-x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}3 x^{3} y^{2} y^{\prime }-y^{3} x^{2} = 1
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }-2 y-y^{2} {\mathrm e}^{3 x} = 0
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+x y = \frac {x}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x y^{2}+3 y^{2}\right ) y^{\prime }-2 x = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x = \frac {1}{y^{3}}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x}{y^{2} \sqrt {x +1}}
\] |
[_separable] |
✓ |
|
|
\[
{}x v^{\prime } = \frac {1-4 v^{2}}{3 v}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime }-x^{3} = x
\] |
[_quadrature] |
✓ |
|
|
\[
{}x +x y^{2}+{\mathrm e}^{x^{2}} y y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\frac {y^{\prime }}{y}+y \,{\mathrm e}^{\cos \left (x \right )} \sin \left (x \right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2}+2 y y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\sqrt {y}+\left (x +1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{x^{2}}}{y^{2}}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = x y^{3}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x y^{3}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x y^{3}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x y^{3}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+2 y = \frac {x}{y^{2}}
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x y^{3}-\left (-x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}t^{3} y^{2}+\frac {t^{4} y^{\prime }}{y^{6}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+x y = x y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}3 y^{\prime } x +y+x^{2} y^{4} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{x} = y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } x +3 y = x^{2} y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{3}+y^{3} = 3 x y^{2} y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+y = x y^{3}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+y = y^{4} {\mathrm e}^{x}
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
|
|
\[
{}2 y^{\prime }+y = y^{3} \left (x -1\right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }-2 \tan \left (x \right ) y = y^{2} \tan \left (x \right )^{2}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+\tan \left (x \right ) y = y^{3} \sec \left (x \right )^{4}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }-y \cot \left (x \right ) = y^{2} \sec \left (x \right )^{2}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}2 x y y^{\prime } = x^{2}-y^{2}
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}x \left (1+y^{2}\right )-\left (x^{2}+1\right ) y y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\frac {r \tan \left (\theta \right ) r^{\prime }}{a^{2}-r^{2}} = 1
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{x} = x y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x +y y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 x^{3} y^{\prime } = y \left (3 x^{2}+y^{2}\right )
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{2}-x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{2}-x^{2}+x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{3}+y^{3}+3 x y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y y^{\prime }+x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{2}+x y-y^{\prime } x = 0
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}y \left (x -2 y\right )-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y y^{\prime }+x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x y y^{\prime }+x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+y = y^{2} {\mathrm e}^{x}
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } x +y-x^{3} y^{6} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y y^{\prime }-x y^{2}+x = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 x^{\prime }-\frac {x}{y}+x^{3} \cos \left (y \right ) = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}2 x y^{5}-y+2 y^{\prime } x = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{3}-y^{3}-x^{2} {\mathrm e}^{x}+3 x y^{2} y^{\prime } = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = 2 x y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}2 y^{\prime } = y^{3} \cos \left (x \right )
\] |
[_separable] |
✓ |
|
|
\[
{}p^{\prime } = p \left (1-p\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {x}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y-y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y-y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }+2 x y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+2 x y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+2 x y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+2 x y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 3 y^{{2}/{3}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{{2}/{3}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y y^{\prime } = 3 x
\] |
[_separable] |
✓ |
|
|
\[
{}y y^{\prime } = 3 x
\] |
[_separable] |
✓ |
|
|
\[
{}y y^{\prime } = 3 x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x \sqrt {y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y \left (y-3\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y+y^{\prime } x = \frac {1}{y^{2}}
\] |
[_separable] |
✓ |
|
|
\[
{}y y^{\prime } = -x
\] |
[_separable] |
✓ |
|
|
\[
{}y y^{\prime } = -x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1}{y}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1}{y}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y-y^{3}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}-3 y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }+2 x y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\sin \left (3 x \right )+2 y \cos \left (3 x \right )^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}p^{\prime } = p-p^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}\left ({\mathrm e}^{x}+{\mathrm e}^{-x}\right ) y^{\prime } = y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y^{2} \sin \left (x^{2}\right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {3 x +1}{2 y}
\] |
[_separable] |
✓ |
|
|
\[
{}\sin \left (x \right )+y y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x = y^{2}-y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x = y^{2}-y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x = y^{2}-y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x = y^{2}-y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y-y^{3}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y-y^{3}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y-y^{3}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y-y^{3}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\sin \left (\sqrt {x}\right )}{\sqrt {y}}
\] |
[_separable] |
✓ |
|
|
\[
{}\left (\sqrt {x}+x \right ) y^{\prime } = \sqrt {y}+y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y^{{2}/{3}}-y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{\sqrt {x}}}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x \arctan \left (x \right )}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {x}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x \sqrt {y}
\] |
[_separable] |
✓ |
|
|
\[
{}m^{\prime } = -\frac {k}{m^{2}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y y^{\prime }-x = 2 y^{2}
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{y \left (x^{3}+1\right )}
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+2 x y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 3 y^{{2}/{3}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y+y^{\prime } x = y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}2 x^{2} y y^{\prime }+y^{2} = 2
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-x y^{2} = 2 x y
\] |
[_separable] |
✓ |
|
|
\[
{}{\mathrm e}^{x}-\left ({\mathrm e}^{x}+1\right ) y y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\frac {y}{x -1}+\frac {x y^{\prime }}{1+y} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\frac {1}{\sqrt {x}}+\frac {y^{\prime }}{\sqrt {y}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{\sqrt {x}}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}2 y^{\prime } x = y \left (2 x^{2}-y^{2}\right )
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x}{y}+\frac {y}{x}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 y^{\prime } x +\left (x^{2} y^{4}+1\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+y^{2}-x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{2 x}+\frac {x^{2}}{2 y}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\phi ^{\prime }-\frac {\phi ^{2}}{2}-\phi \cot \left (\theta \right ) = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}x^{2}+y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2}-y^{2}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y y^{\prime } = x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 2 \sqrt {y}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 2 \sqrt {y}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y y^{\prime } = {\mathrm e}^{2 x}
\] |
[_separable] |
✓ |
|
|
\[
{}2 x y y^{\prime } = x^{2}+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{5} y^{\prime }+y^{5} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{2}-x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y y^{\prime } = x +1
\] |
[_separable] |
✓ |
|
|
\[
{}\frac {y^{\prime }}{x^{2}+1} = \frac {x}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{2} y^{\prime } = x +2
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x^{2} y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y+y^{\prime } x = x^{4} y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{2} y^{\prime }+y^{3} = x \cos \left (x \right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y+y^{\prime } x = x y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+x y = x y^{4}
\] |
[_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] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = 2 x y+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{3}+y^{3}-x y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1-x y^{2}}{2 x^{2} y}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2+3 x y^{2}}{4 x^{2} y}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{2} y^{\prime } = x
\] |
[_separable] |
✓ |
|
|
\[
{}y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-x y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-x y \left (x +y\right ) y^{\prime }+x^{3} y^{3} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x y^{2}-1\right ) y^{\prime }-y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}x y \left (x^{2}+y^{2}\right ) \left (-1+{y^{\prime }}^{2}\right ) = y^{\prime } \left (x^{4}+x^{2} y^{2}+y^{4}\right )
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1 = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-\left (x +1\right ) y y^{\prime }+x = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = 6 x^{4} y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{3} = \frac {\left (1-2 x \right ) y^{4}}{3}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}p^{\prime } = a p-b p^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{2}+\frac {2}{x}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}f^{\prime } = \frac {1}{f}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 2 \sqrt {y}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 2 y \left (x \sqrt {y}-1\right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}v v^{\prime } = \frac {2 v^{2}}{r^{3}}+\frac {\lambda r}{3}
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = y \left (1-y^{2}\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}c y^{\prime } = \frac {a x +b y^{2}}{y}
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }-x y^{2}-3 x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+f \left (x \right ) y^{2}+g \left (x \right ) y = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+2 a \,x^{3} y^{3}+2 x y = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } x +x y^{2}-y = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } x -y^{2} \ln \left (x \right )+y = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } x -y \left (-1+2 y \ln \left (x \right )\right ) = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime }+y \left (y-x \right ) = 0
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}3 y^{\prime } x -3 x \ln \left (x \right ) y^{4}-y = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime }-y^{2}-x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }-y \left (y-x \right ) = 0
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+a x y^{2}+x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{2}-4\right ) y^{\prime }+\left (x +2\right ) y^{2}-4 y = 0
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{3} y^{\prime }-y^{2}-x^{2} y = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} \left (x -1\right ) y^{\prime }-y^{2}-x \left (x -2\right ) y = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\cos \left (x \right ) y^{\prime }-y^{4}-y \sin \left (x \right ) = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y y^{\prime }+y^{2}+4 \left (x +1\right ) x = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y y^{\prime }+a y^{2}-b \cos \left (x +c \right ) = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y y^{\prime }+x y^{2}-4 x = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 y y^{\prime }-x y^{2}-x^{3} = 0
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}a y y^{\prime }+b y^{2}+f \left (x \right ) = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}x y y^{\prime }+x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y y^{\prime }-y^{2}+a \,x^{3} \cos \left (x \right ) = 0
\] |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
|
|
\[
{}2 x y y^{\prime }-y^{2}+a x = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x y y^{\prime }-y^{2}+a \,x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x y y^{\prime }+2 y^{2}+1 = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 x^{2} y y^{\prime }+y^{2}-2 x^{3}-x^{2} = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x^{2} y y^{\prime }-y^{2}-x^{2} {\mathrm e}^{x -\frac {1}{x}} = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}2 x^{3}+y y^{\prime }+3 x^{2} y^{2}+7 = 0
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}y y^{\prime } \sin \left (x \right )^{2}+y^{2} \cos \left (x \right ) \sin \left (x \right )-1 = 0
\] |
[_exact, _Bernoulli] |
✓ |
|
|
\[
{}f \left (x \right ) y y^{\prime }+g \left (x \right ) y^{2}+h \left (x \right ) = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}3 x y^{2} y^{\prime }+y^{3}-2 x = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}6 x y^{2} y^{\prime }+x +2 y^{3} = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 y^{3} y^{\prime }+x y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{3} y^{\prime }+y^{4}-x \sin \left (x \right ) = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}+y \left (y-x \right ) y^{\prime }-x y^{3} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+\left (a \,x^{2} y^{3}+b \right ) y^{\prime }+a b y^{3} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y {y^{\prime }}^{2}-\left (y-x \right ) y^{\prime }-x = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}\right ) y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{2} {y^{\prime }}^{2}-2 y^{3} y^{\prime }+2 x y^{2}-x^{3} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}-\left (x^{2}+x y+y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+x^{2} y^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y \left (-1+\ln \left (\left (x +1\right ) x \right ) y x^{4}-\ln \left (\left (x +1\right ) x \right ) x^{3}\right )}{x}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y \left (1-x +y x^{2} \ln \left (x \right )+x^{3} y-x \ln \left (x \right )-x^{2}\right )}{\left (x -1\right ) x}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y \left (-\ln \left (\frac {1}{x}\right )+{\mathrm e}^{x}+y x^{2} \ln \left (x \right )+x^{3} y-x \ln \left (x \right )-x^{2}\right )}{\left (-\ln \left (\frac {1}{x}\right )+{\mathrm e}^{x}\right ) x}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y \left (-{\mathrm e}^{x}+\ln \left (2 x \right ) x^{2} y-\ln \left (2 x \right ) x \right ) {\mathrm e}^{-x}}{x}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y \left (\tan \left (x \right )+\ln \left (2 x \right ) x -\ln \left (2 x \right ) x^{2} y\right )}{x \tan \left (x \right )}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y \left (-1-\ln \left (\frac {\left (x -1\right ) \left (x +1\right )}{x}\right )+\ln \left (\frac {\left (x -1\right ) \left (x +1\right )}{x}\right ) x y\right )}{x}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y \left (-\ln \left (x \right )-x \ln \left (\frac {\left (x -1\right ) \left (x +1\right )}{x}\right )+\ln \left (\frac {\left (x -1\right ) \left (x +1\right )}{x}\right ) x^{2} y\right )}{x \ln \left (x \right )}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y \left (-\ln \left (\frac {1}{x}\right )-\ln \left (\frac {x^{2}+1}{x}\right ) x +\ln \left (\frac {x^{2}+1}{x}\right ) x^{2} y\right )}{x \ln \left (\frac {1}{x}\right )}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y \left (-\tanh \left (\frac {1}{x}\right )-\ln \left (\frac {x^{2}+1}{x}\right ) x +\ln \left (\frac {x^{2}+1}{x}\right ) x^{2} y\right )}{x \tanh \left (\frac {1}{x}\right )}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y \left (\tanh \left (x \right )+\ln \left (2 x \right ) x -\ln \left (2 x \right ) x^{2} y\right )}{x \tanh \left (x \right )}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y \left (\ln \left (x -1\right )+\coth \left (x +1\right ) x -\coth \left (x +1\right ) x^{2} y\right )}{x \ln \left (x -1\right )}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y \left (-\cosh \left (\frac {1}{x +1}\right ) x +\cosh \left (\frac {1}{x +1}\right )-x +x^{2} y-x^{2}+x^{3} y\right )}{x \left (x -1\right ) \cosh \left (\frac {1}{x +1}\right )}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y \left (-1-\cosh \left (\frac {x +1}{x -1}\right ) x +\cosh \left (\frac {x +1}{x -1}\right ) x^{2} y-\cosh \left (\frac {x +1}{x -1}\right ) x^{2}+\cosh \left (\frac {x +1}{x -1}\right ) x^{3} y\right )}{x}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y \left (-1-x \,{\mathrm e}^{\frac {x +1}{x -1}}+x^{2} {\mathrm e}^{\frac {x +1}{x -1}} y-x^{2} {\mathrm e}^{\frac {x +1}{x -1}}+x^{3} {\mathrm e}^{\frac {x +1}{x -1}} y\right )}{x}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}g \left (x \right ) y^{\prime } = f_{1} \left (x \right ) y+f_{n} \left (x \right ) y^{n}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{2}-x^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+y^{2}-x y = 0
\] |
[[_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] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }-2 \left (x +1\right ) y = y^{{5}/{2}}
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}y y^{\prime }+x y^{2} = x
\] |
[_separable] |
✓ |
|
|
\[
{}4 y^{\prime } x +3 y+{\mathrm e}^{x} x^{4} y^{5} = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+y^{2}-x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2}+y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x -y^{2}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } x +y+x^{4} y^{4} {\mathrm e}^{x} = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }-x y = a x y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{2}+y-y^{\prime } x = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } x -y^{2} \ln \left (x \right )+y = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}-\left (2 x +y^{2}\right ) {y^{\prime }}^{2}+\left (x^{2}-y^{2}+2 x y^{2}\right ) y^{\prime }-\left (x^{2}-y^{2}\right ) y^{2} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime } = -\frac {t}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime } = -x^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime } = x \left (1-\frac {x}{4}\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime } = \sqrt {x}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }+y+\frac {1}{y} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}\left (1+t \right ) x^{\prime }+x^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime } = 2 t x^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime } = x \left (x+4\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 t y^{2}}{t^{2}+1}
\] |
[_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] |
✓ |
|
|
\[
{}y^{\prime } = -y^{2} {\mathrm e}^{-t^{2}}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime } = \frac {2 x}{3 t}+\frac {2 t}{x}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{\prime } = x \left (1+x \,{\mathrm e}^{t}\right )
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
|
|
\[
{}x^{\prime } = -\frac {x}{t}+\frac {1}{t x^{2}}
\] |
[_separable] |
✓ |
|
|
\[
{}t^{2} y^{\prime }+2 t y-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{\prime } = a x+b x^{3}
\] |
[_quadrature] |
✓ |
|
|
\[
{}w^{\prime } = t w+t^{3} w^{3}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}x+3 t x^{2} x^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2}-t^{2} x^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 x y y^{\prime }+x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}y+y^{\prime } x = x^{3} y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}}{x -2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}4 x +3 y^{2}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{2}+2 x y-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (x +4\right ) \left (1+y^{2}\right )+y \left (x^{2}+3 x +2\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (3 x +8\right ) \left (y^{2}+4\right )-4 y \left (x^{2}+5 x +6\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2}+3 y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{x} = -\frac {y^{2}}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y+y^{\prime } x = -2 x^{6} y^{4}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+\left (4 y-\frac {8}{y^{3}}\right ) x = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime }+\frac {\left (1+t \right ) x}{2 t} = \frac {1+t}{t x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{2 x} = \frac {x}{y^{3}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+x y = x y^{3}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2}+y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 y^{2}+8+\left (-x^{2}+1\right ) y y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}{\mathrm e}^{2 x} y^{2}-2 x +{\mathrm e}^{2 x} y y^{\prime } = 0
\] |
[_exact, _Bernoulli] |
✓ |
|
|
\[
{}4 x y y^{\prime } = 1+y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+x y = \frac {y^{3}}{x}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{\prime } = x \left (2-x\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime } = -x^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{2} {\mathrm e}^{-t^{2}}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime } = k x-x^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime } = -x \left (k^{2}+x^{2}\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}V^{\prime }\left (x \right )+2 y y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime } = k x-x^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}-\left (x^{2}+y^{2}\right ) y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} = 9 y^{4}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y = y^{\prime } x +\frac {1}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{x +1}+y^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (x -y\right ) y-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{\prime } = \frac {x}{t}+\frac {x^{2}}{t^{3}}
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }-\frac {3 y}{x}+x^{3} y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (x -y\right ) y-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } x -y^{2} \ln \left (x \right )+y = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}3 x y^{2} y^{\prime }+y^{3}-2 x = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}y+y^{\prime } x = x y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y y^{\prime } = 1
\] |
[_quadrature] |
✓ |
|
|
\[
{}x -x y^{2}+\left (y-x^{2} y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{2} y^{\prime } = x^{3}+y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+x y = x^{3} y^{3}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }-x y+a x y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}3 y^{2} y^{\prime }-a y^{3}-x -1 = 0
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } x = \left (y \ln \left (x \right )-2\right ) y
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y-\cos \left (x \right ) y^{\prime } = y^{2} \cos \left (x \right ) \left (1-\sin \left (x \right )\right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}\frac {1}{x^{2}}+\frac {3 y^{2}}{x^{4}} = \frac {2 y y^{\prime }}{x^{3}}
\] |
[[_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] |
✓ |
|
|
\[
{}\frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x -y^{2} \ln \left (x \right )+y = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+\frac {1}{2 y} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = x \sqrt {y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 3 y^{{2}/{3}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}-3 y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1}{x y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x}{y^{2}}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y}{x}+y^{{1}/{4}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -2 y+y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}2 y y^{\prime } = 1
\] |
[_quadrature] |
✓ |
|
|
\[
{}2 x y y^{\prime }+y^{2} = -1
\] |
[_separable] |
✓ |
|
|
\[
{}x -y y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y \left (1-y\right )-2 y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x \left (1-y^{3}\right )-3 y^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{3}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{3}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{3}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {3 x^{2}}{2 y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {3 x^{2}}{2 y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {3 x^{2}}{2 y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {3 x^{2}}{2 y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 3 x y^{{1}/{3}}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 3 x y^{{1}/{3}}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 3 x y^{{1}/{3}}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 3 x y^{{1}/{3}}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 3 x y^{{1}/{3}}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = t^{2} y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 t y^{2}+3 y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {t}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {t}{y+t^{2} y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = t y^{{1}/{3}}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y \left (1-y\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = -y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = t^{2} y^{3}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {t}{y-t^{2} y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = t y^{2}+2 y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime } = \frac {t^{2}}{x+t^{3} x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1-y^{2}}{y}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 2 t y^{2}+3 t^{2} y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}+5}{y}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 4 y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 2 y \left (1-y\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 3 y \left (1-y\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}+y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}-y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = t y+t y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \sqrt {y}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = -y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{3}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 3 y \left (y-2\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 3 y \left (y-2\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 3 y \left (y-2\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 3 y \left (y-2\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y-y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}-y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 2 y-y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = t^{2} y^{3}+y^{3}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 t y^{2}+3 t^{2} y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {t^{2}}{y+t^{3} y}
\] |
[_separable] |
✓ |
|
|
\[
{}y y^{\prime } = 2 x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{3}-25 y+y^{\prime } = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 2 \sqrt {y}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 3 y^{2}-\sin \left (x \right ) y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}x y y^{\prime } = y^{2}+9
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y y^{\prime } = x y^{2}+x
\] |
[_separable] |
✓ |
|
|
\[
{}y y^{\prime } = x y^{2}-9 x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 200 y-2 y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 3 y^{2}-\sin \left (x \right ) y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 3 x y^{3}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 200 y-2 y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y y^{\prime } = \sin \left (x \right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x = y^{2}-y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x = y^{2}-y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}-1}{x y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+4 y = y^{3}
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{2} y^{\prime }-x y = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\frac {x}{y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+3 y = 3 y^{3}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }-\frac {3 y}{x} = \frac {y^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+3 y \cot \left (x \right ) = 6 \cos \left (x \right ) y^{{2}/{3}}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{x} = \frac {1}{y}
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\frac {x^{2}}{y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}3 y^{\prime }+\frac {2 y}{x} = 4 \sqrt {y}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{x} = y^{3} x^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+3 y = \frac {28 \,{\mathrm e}^{2 x}}{y^{3}}
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1}{y}-\frac {y}{2 x}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}{\mathrm e}^{x y^{2}-x^{2}} \left (y^{2}-2 x \right )+2 \,{\mathrm e}^{x y^{2}-x^{2}} x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x y^{3}+4 x^{3}+3 x^{2} y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}2-2 x +3 y^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}1+3 x^{2} y^{2}+\left (2 x^{3} y+6 y\right ) y^{\prime } = 0
\] |
[_exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}1+y^{4}+x y^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x = 2 y^{2}-6 y
\] |
[_separable] |
✓ |
|
|
\[
{}4 y^{2}-x^{2} y^{2}+y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{2}-6+x^{2} y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{3}+y^{3}+x y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}1+2 x y^{2}+\left (2 x^{2} y+2 y\right ) y^{\prime } = 0
\] |
[_exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}3 x y^{3}-y+y^{\prime } x = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {3 y}{x +1}-y^{2}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y y^{\prime } = 2 x^{2}+2 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{3} y^{\prime } = y^{4}-x^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = 4 y-\frac {16 \,{\mathrm e}^{4 x}}{y^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
|
|
\[
{}y y^{\prime }-x y^{2} = 6 x \,{\mathrm e}^{4 x^{2}}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{2}-y^{2} \cos \left (x \right )+y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y^{3}-y^{3} \cos \left (x \right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {x}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x y+y^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = y^{{1}/{5}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}\frac {y^{\prime }}{t} = \sqrt {y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 6 y^{{2}/{3}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = t y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {t}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -y^{3}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x}{y^{2}}
\] |
[_separable] |
✓ |
|
|
\[
{}\frac {1}{2 \sqrt {t}}+y^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x^{2}}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1+y^{2}}{y}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {5^{-t}}{y^{2}}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y^{3}+y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{3}-y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{3}+y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\sqrt {t}}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y^{2} \cos \left (t \right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \sqrt {y}\, \cos \left (t \right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}-y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 16 y-8 y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}\frac {t}{\sqrt {t^{2}+y^{2}}}+\frac {y y^{\prime }}{\sqrt {t^{2}+y^{2}}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}3 t y^{2}+y^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}-1+3 y^{2} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}3 t^{2}+3 y^{2}+6 t y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 t y+y^{2}-t^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}5 t y^{2}+y+\left (2 t^{3}-t \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{2} = \frac {t}{y}
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+y = t y^{2}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}2 t y^{\prime }-y = 2 t y^{3} \cos \left (t \right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}t y^{\prime }-y = t y^{3} \sin \left (t \right )
\] |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }-2 y = \frac {\cos \left (t \right )}{\sqrt {y}}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+3 y = \sqrt {y}\, \sin \left (t \right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{t} = t y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{t} = \frac {y^{2}}{t^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{t} = \frac {y^{2}}{t}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{t} = t^{2} y^{{3}/{2}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\frac {2}{t}+\frac {1}{y}+\frac {t y^{\prime }}{y^{2}} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\sqrt {t^{2}+1}+y y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}t^{3}+y^{3}-t y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+2 y = t^{2} \sqrt {y}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }-2 y = t^{2} \sqrt {y}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {4 y^{2}-t^{2}}{2 t y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{3}-t^{3}-t y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = y^{4}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}-t^{2}}{t y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 t^{5}}{5 y^{2}}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{t} = \frac {y^{2}}{t}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{5 t}}{y^{4}}
\] |
[_separable] |
✓ |
|
|
\[
{}r^{\prime } = \frac {r^{2}+t^{2}}{r t}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }-y = t y^{3}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+y = \frac {{\mathrm e}^{t}}{y^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
|
|
\[
{}y-t y^{\prime } = 2 y^{2} \ln \left (t \right )
\] |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = t y^{3}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {t}{y^{3}}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y+3 y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}x y y^{\prime }+1+y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}4 y^{6}+x^{3} = 6 x y^{5} y^{\prime }
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = 2 x y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}3 x y^{2} y^{\prime }-2 y^{3} = x^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 y^{\prime } \ln \left (x \right )+\frac {y}{x} = \frac {\cos \left (x \right )}{y}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}2 y^{\prime } \sin \left (x \right )+y \cos \left (x \right ) = y^{3} \sin \left (x \right )^{2}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }-y \cos \left (x \right ) = y^{2} \cos \left (x \right )
\] |
[_separable] |
✓ |
|
|
\[
{}x +y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{4} \ln \left (x \right )-2 x y^{3}+3 x^{2} y^{2} y^{\prime } = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}x^{2}+y^{2}+1-2 x y y^{\prime } = 0
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = y^{n} \sin \left (2 x \right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y-x y^{2} \ln \left (x \right )+y^{\prime } x = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}x y y^{\prime }-y^{2} = x^{4}
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{2} y^{\prime }-y^{3} = \frac {x^{4}}{3}
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2}+y^{2}-x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{2}+y-y^{\prime } x = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2}+y^{2}+2 x +2 y y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x -y^{2}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y+y^{\prime } x = y^{2} \ln \left (x \right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{4}}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{2} \left (x^{3}+1\right )}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y^{3} \sin \left (x \right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y y^{\prime } = \left (x y^{2}+x \right ) {\mathrm e}^{x^{2}}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x \left (y-y^{2}\right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \left (1-12 x \right ) y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {3-2 x}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}x +y y^{\prime } {\mathrm e}^{-x} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}r^{\prime } = \frac {r^{2}}{\theta }
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {3 x}{y+x^{2} y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 x y^{2}+4 x^{3} y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x \left (x^{2}+1\right ) y^{5}}{6}
\] |
[_separable] |
✓ |
|
|
\[
{}2 y y^{\prime } = \frac {x}{\sqrt {x^{2}-4}}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{2} \sqrt {-x^{2}+1}\, y^{\prime } = \arcsin \left (x \right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 y^{2}+x y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {t \left (4-y\right ) y}{3}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {t y \left (4-y\right )}{1+t}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {4 t}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 t y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y^{3} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {t^{2}}{y \left (t^{3}+1\right )}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = t \left (3-y\right ) y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y \left (3-t y\right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = -y \left (3-t y\right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y y^{\prime } = x +1
\] |
[_separable] |
✓ |
|
|
\[
{}x \left (x -1\right ) y^{\prime } = y \left (1+y\right )
\] |
[_separable] |
✓ |
|
|
\[
{}x y y^{\prime } = x^{2}+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}t y^{\prime }+y = t^{2} y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = y \left (t y^{3}-1\right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+\frac {3 y}{t} = t^{2} y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}t^{2} y^{\prime }+2 t y-y^{3} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}5 \left (t^{2}+1\right ) y^{\prime } = 4 t y \left (y^{3}-1\right )
\] |
[_separable] |
✓ |
|
|
\[
{}3 t y^{\prime }+9 y = 2 t y^{{5}/{3}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = y+\sqrt {y}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = r y-k^{2} y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = a y+b y^{3}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }-4 y^{2} {\mathrm e}^{x} = y
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x y^{2}-\frac {\sin \left (2 x \right )}{2}}{\left (-x^{2}+1\right ) y}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}2 x y y^{\prime }+\ln \left (x \right ) = -y^{2}-1
\] |
[_exact, _Bernoulli] |
✓ |
|
|
\[
{}4 x y y^{\prime } = 8 x^{2}+5 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+y-y^{{1}/{4}} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } x -4 y = x^{2} \sqrt {y}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y+y^{\prime } x = x y^{2} \ln \left (x \right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }-\frac {x y}{2 x^{2}-2}-\frac {x}{2 y} = 0
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}x -y^{2}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y-x y^{2} \ln \left (x \right )+y^{\prime } x = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} y+y^{\prime } \left (x -y\right )-x = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}-\left (x^{2}+x y+y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+x^{2} y^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \sqrt {y}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y y^{\prime } = {\mathrm e}^{2 x}
\] |
[_separable] |
✓ |
|
|
\[
{}2 x y y^{\prime } = x^{2}+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{5} y^{\prime }+y^{5} = 0
\] |
[_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] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = 2 x y+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{3}+y^{3}-x y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1-x y^{2}}{2 x^{2} y}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2+3 x y^{2}}{4 x^{2} y}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}1+y^{2} \sin \left (2 x \right )-2 y \cos \left (x \right )^{2} y^{\prime } = 0
\] |
[_exact, _Bernoulli] |
✓ |
|
|
\[
{}\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x +3 y^{2}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{3}+x y^{3}+3 y^{2} y^{\prime } = 0
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{2}-y+y^{\prime } x = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 x y^{2}-y+y^{\prime } x = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y+y^{\prime } x = x^{4} y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{2} y^{\prime }+y^{3} = x \cos \left (x \right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y+y^{\prime } x = x y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y+y^{\prime } x = x^{2} y^{\prime }+y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{4}+x^{6}-x^{3} y^{3} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{2}+y+y^{\prime } x = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y+y^{\prime } x = y^{2} \ln \left (x \right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime }-y^{2} = 2 x y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{\prime } = 2 \sqrt {x}
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime }+2 t x+t x^{4} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 x^{2} y+y^{3}-x^{3} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{x} = \frac {\sin \left (x \right )}{y^{3}}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}\left (T \ln \left (t \right )-1\right ) T = t T^{\prime }
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y-\cos \left (x \right ) y^{\prime } = y^{2} \cos \left (x \right ) \left (1-\sin \left (x \right )\right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}1+v^{2}+\left (u^{2}+1\right ) v v^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y \sin \left (x \right ) = \sin \left (x \right ) y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }-x y = a x y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = y^{n} \sin \left (2 x \right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}3 y^{2} y^{\prime }+y^{3} = x -1
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }-\tan \left (x \right ) y = y^{4} \sec \left (x \right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}5 x y y^{\prime }-x^{2}-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}5 x y y^{\prime }-4 x^{2}-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y-y^{\prime } x = a \left (y^{\prime }+y^{2}\right )
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2}+y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{4} {\mathrm e}^{x}-2 m x y^{2}+2 m \,x^{2} y y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
|
|
\[
{}y \left (2 x y+{\mathrm e}^{x}\right )-{\mathrm e}^{x} y^{\prime } = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}x^{2}+y^{2}+2 x +2 y y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2}+y^{2}-x^{2} y y^{\prime } = 0
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{x} = x^{2} y^{6}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = 3 x^{2} y^{{1}/{3}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+\frac {x y}{-x^{2}+1} = x \sqrt {y}
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}3 x \left (-x^{2}+1\right ) y^{2} y^{\prime }+\left (2 x^{2}-1\right ) y^{3} = a \,x^{3}
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}3 y^{\prime }+\frac {2 y}{x +1} = \frac {x^{3}}{y^{2}}
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } x +\frac {y^{2}}{x} = y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2}+y^{2}+1-2 x y y^{\prime } = 0
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = y^{n} \sin \left (2 x \right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = x^{3} y^{3}-x y
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y y^{\prime } = a x
\] |
[_separable] |
✓ |
|
|
\[
{}y y^{\prime }+b y^{2} = a \cos \left (x \right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}+2 x {y^{\prime }}^{2}-y^{2} {y^{\prime }}^{2}-2 x y^{2} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}4 y^{2} {y^{\prime }}^{2}+2 y^{\prime } x y \left (3 x +1\right )+3 x^{3} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y \left (y-y^{\prime } x \right ) = x +y y^{\prime }
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{2} \left ({y^{\prime }}^{2}+2\right ) = 2 y^{3} y^{\prime }+x^{3}
\] |
[_separable] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}+y^{\prime } \left (3 x^{2}-2 y^{2}\right )-6 x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}-\left (x^{2}+x y+y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+x^{2} y^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } \sqrt {x} = \sqrt {y}
\] |
[_separable] |
✓ |
|
|
\[
{}\left (1+x y\right ) y-y^{\prime } x = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } \sin \left (x \right )-y \cos \left (x \right )+y^{2} = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y+y^{\prime } x = y^{2} \ln \left (x \right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}x y^{2}+x +\left (y+x^{2} y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y-y^{\prime } x = a \left (y^{\prime }+y^{2}\right )
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2}-y^{2}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+y \left (x +y\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 y^{\prime } = \frac {y}{x}+\frac {y^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2}+3 y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y \left (2 x y+{\mathrm e}^{x}\right )-{\mathrm e}^{x} y^{\prime } = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}2 y^{\prime }-y \sec \left (x \right ) = y^{3} \tan \left (x \right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = y^{n} \sin \left (2 x \right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}x^{2}+y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1+x^{2}+y^{2}}{2 x y}
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}y y^{\prime }+b y^{2} = a \cos \left (x \right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y \left (2 x y+{\mathrm e}^{x}\right )-{\mathrm e}^{x} y^{\prime } = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} y+y^{\prime } \left (x -y\right )-x = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}x +{y^{\prime }}^{2} y = y^{\prime } \left (1+x y\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}+2 x {y^{\prime }}^{2}-y^{2} {y^{\prime }}^{2}-2 x y^{2} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}+y^{\prime } \left (3 x^{2}-2 y^{2}\right )-6 x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{2}-3 x y y^{\prime } = 2 y^{2}+x^{3}
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}y-y^{\prime } x = a \left (y^{\prime }+y^{2}\right )
\] |
[_separable] |
✓ |
|
|
\[
{}1+y^{2}-x y y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+p \left (x \right ) y = q \left (x \right ) y^{n}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}-\left (x^{2}+x y+y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+x^{2} y^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}x y \left (y-y^{\prime } x \right ) = x +y y^{\prime }
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{2} \left ({y^{\prime }}^{2}+2\right ) = 2 y^{3} y^{\prime }+x^{3}
\] |
[_separable] |
✓ |
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