|
# |
ODE |
CAS classification |
Solved? |
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\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = y-x +1
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = x +1-y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = x^{2}-y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = x^{2}-y-2
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = 2 x^{2} y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \sqrt {x -y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \ln \left (1+y^{2}\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = y-x
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+2 x y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y \sin \left (x \right )
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime } = 4 y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 3 \sqrt {x y}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
|
|
\[
{}y^{\prime } = 64^{{1}/{3}} \left (x y\right )^{{1}/{3}}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = 2 y
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime } = \left (y+1\right )^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x y^{3}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 1+x +y+x y
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = 1-x^{2}+y^{2}-x^{2} y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y \,{\mathrm e}^{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 3 x^{2} \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 4 x^{3} y-y
\] |
[_separable] |
✓ |
|
|
\[
{}1+y^{\prime } = 2 y
\] |
[_quadrature] |
✓ |
|
|
\[
{}\tan \left (x \right ) y^{\prime } = y
\] |
[_separable] |
✓ |
|
|
\[
{}-y+x y^{\prime } = 2 x^{2} y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 x y^{2}+3 x^{2} y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 6 \,{\mathrm e}^{2 x -y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y \sqrt {y^{2}-1}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }+y = 2
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }-2 y = 3 \,{\mathrm e}^{2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+3 y = 2 x \,{\mathrm e}^{-3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-2 x y = {\mathrm e}^{x^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime }+2 y = 3 x
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime }+5 y = 7 x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}2 x y^{\prime }+y = 10 \sqrt {x}
\] |
[_linear] |
✓ |
|
|
\[
{}3 x y^{\prime }+y = 12 x
\] |
[_linear] |
✓ |
|
|
\[
{}-y+x y^{\prime } = x
\] |
[_linear] |
✓ |
|
|
\[
{}2 x y^{\prime }-3 y = 9 x^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime }+3 y = 2 x^{5}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}x y^{\prime }-3 y = x^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \left (1-y\right ) \cos \left (x \right )
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime } = 2 y+x^{3} \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = 1+x +y+x y
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime } = 3 y+x^{4} \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = 2 x y+3 x^{2} {\mathrm e}^{x^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime }+\left (2 x -3\right ) y = 4 x^{4}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}+4\right ) y^{\prime }+3 x y = x
\] |
[_separable] |
✓ |
|
|
\[
{}\frac {1-4 x y^{2}}{x^{\prime }} = y^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}\frac {x+y \,{\mathrm e}^{y}}{x^{\prime }} = 1
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}\frac {1+2 x y}{x^{\prime }} = y^{2}+1
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+p \left (x \right ) y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +y\right ) y^{\prime } = x -y
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x y y^{\prime } = x^{2}+2 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{\prime } = y+2 \sqrt {x y}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (x -y\right ) y^{\prime } = x +y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x \left (x +y\right ) y^{\prime } = \left (x -y\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}\left (x +2 y\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y^{2} y^{\prime } = x^{3}+y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = x y+x^{2} {\mathrm e}^{\frac {y}{x}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = x y+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y y^{\prime } = x^{2}+3 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (x^{2}-y^{2}\right ) y^{\prime } = 2 x y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y y^{\prime } = y^{2}+x \sqrt {4 x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = y+\sqrt {y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } y+x = \sqrt {y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (x +y\right ) y^{\prime }+y \left (3 x +y\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } = \sqrt {x +y+1}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \left (4 x +y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
|
|
\[
{}\left (x +y\right ) y^{\prime } = 1
\] |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+2 x y = 5 y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = y+y^{3}
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+2 x y = 5 y^{4}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{\prime }+6 y = 3 x y^{{4}/{3}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x y^{\prime }+y^{3} {\mathrm e}^{-2 x} = 2 x y
\] |
[_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] |
✓ |
|
|
\[
{}\left ({\mathrm e}^{y}+x \right ) y^{\prime } = x \,{\mathrm e}^{-y}-1
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x +3 y+\left (3 x +2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}4 x -y+\left (6 y-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 x^{2}+2 y^{2}+\left (4 x y+6 y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\frac {2 x^{{5}/{2}}-3 y^{{5}/{3}}}{2 x^{{5}/{2}} y^{{2}/{3}}}+\frac {\left (3 y^{{5}/{3}}-2 x^{{5}/{2}}\right ) y^{\prime }}{3 x^{{3}/{2}} y^{{5}/{3}}} = 0
\] |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
|
|
\[
{}y^{\prime } = f \left (a x +b y+c \right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }-4 x^{2} y+2 y \ln \left (y\right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x -y-1}{x +y+3}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y-x +7}{4 x -3 y-18}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \sin \left (x -y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y \left (2 x^{3}-y^{3}\right )}{x \left (2 y^{3}-x^{3}\right )}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = x^{2}+y^{2}+1
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
|
|
\[
{}x^{\prime } = x-x^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime } = 10 x-x^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime } = 1-x^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime } = 9-4 x^{2}
\] |
[_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] |
✓ |
|
|
\[
{}x^{3}+3 y-x y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{2}+3 y^{2}-x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y+y^{2}-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}3 y+x^{4} y^{\prime } = 2 x y
\] |
[_separable] |
✓ |
|
|
\[
{}2 x y^{2}+x^{2} y^{\prime } = y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}2 x^{2} y+x^{3} y^{\prime } = 1
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+2 x y = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{\prime }+2 y = 6 x^{2} \sqrt {y}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = 1+x^{2}+y^{2}+x^{2} y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = x y+3 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}6 x y^{3}+2 y^{4}+\left (9 x^{2} y^{2}+8 x y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}4 x y^{2}+y^{\prime } = 5 x^{4} y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{3} y^{\prime } = x^{2} y-y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+3 y = 3 x^{2} {\mathrm e}^{-3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = x^{2}-2 x y+y^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
|
|
\[
{}2 x^{2} y-x^{3} y^{\prime } = y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}3 x^{5} y^{2}+x^{3} y^{\prime } = 2 y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime }+3 y = \frac {3}{x^{{3}/{2}}}
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime } = 6 y+12 x^{4} y^{{2}/{3}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}9 x^{2} y^{2}+x^{{3}/{2}} y^{\prime } = y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}2 y+\left (x +1\right ) y^{\prime } = 3 x +3
\] |
[_linear] |
✓ |
|
|
\[
{}9 \sqrt {x}\, y^{{4}/{3}}-12 x^{{1}/{5}} y^{{3}/{2}}+\left (8 x^{{3}/{2}} y^{{1}/{3}}-15 x^{{6}/{5}} \sqrt {y}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
|
|
\[
{}3 y+x^{3} y^{4}+3 x y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (2 x +1\right ) y^{\prime }+y = \left (2 x +1\right )^{{3}/{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \sqrt {x +y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = 3 \left (y+7\right ) x^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x y^{3}-x y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {3 x^{2}+2 y^{2}}{4 x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {3 y+x}{y-3 x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x y+2 x}{x^{2}+1}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y^{2} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = y-x +1
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = x +1-y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = x^{2}-y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = x^{2}-y-2
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = 2 x^{2} y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \ln \left (1+y^{2}\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+2 x y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y \sin \left (x \right )
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime } = 4 y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 3 \sqrt {x y}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
|
|
\[
{}y^{\prime } = 4 \left (x y\right )^{{1}/{3}}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = 2 y
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = \left (y+1\right )^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x y^{3}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 1+x +y+x y
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = 1-x^{2}+y^{2}-x^{2} y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y \,{\mathrm e}^{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 3 x^{2} \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 4 x^{3} y-y
\] |
[_separable] |
✓ |
|
|
\[
{}1+y^{\prime } = 2 y
\] |
[_quadrature] |
✓ |
|
|
\[
{}\tan \left (x \right ) y^{\prime } = y
\] |
[_separable] |
✓ |
|
|
\[
{}-y+x y^{\prime } = 2 x^{2} y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 x y^{2}+3 x^{2} y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 6 \,{\mathrm e}^{2 x -y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y = 2
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }-2 y = 3 \,{\mathrm e}^{2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+3 y = 2 x \,{\mathrm e}^{-3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-2 x y = {\mathrm e}^{x^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime }+2 y = 3 x
\] |
[_linear] |
✓ |
|
|
\[
{}2 x y^{\prime }+y = 10 \sqrt {x}
\] |
[_linear] |
✓ |
|
|
\[
{}2 x y^{\prime }+y = 10 \sqrt {x}
\] |
[_linear] |
✓ |
|
|
\[
{}3 x y^{\prime }+y = 12 x
\] |
[_linear] |
✓ |
|
|
\[
{}-y+x y^{\prime } = x
\] |
[_linear] |
✓ |
|
|
\[
{}2 x y^{\prime }-3 y = 9 x^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime }+3 y = 2 x^{5}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}x y^{\prime }-3 y = x^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \left (1-y\right ) \cos \left (x \right )
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime } = 2 y+x^{3} \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = 1+x +y+x y
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime } = 3 y+x^{4} \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = 2 x y+3 x^{2} {\mathrm e}^{x^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime }+\left (2 x -3\right ) y = 4 x^{4}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}+4\right ) y^{\prime }+3 x y = x
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +y\right ) y^{\prime } = x -y
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x y y^{\prime } = y^{2}+x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{\prime } = y+2 \sqrt {x y}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (x -y\right ) y^{\prime } = x +y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x \left (x +y\right ) y^{\prime } = \left (x -y\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}\left (x +2 y\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y^{2} y^{\prime } = x^{3}+y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = x y+x^{2} {\mathrm e}^{\frac {y}{x}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = x y+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y y^{\prime } = x^{2}+3 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (x^{2}-y^{2}\right ) y^{\prime } = 2 x y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y y^{\prime } = y^{2}+x \sqrt {4 x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = y+\sqrt {y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } y+x = \sqrt {y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (x +y\right ) y^{\prime }+y \left (3 x +y\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } = \sqrt {x +y+1}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \left (4 x +y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+2 x y = 5 y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = y+y^{3}
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+2 x y = 5 y^{4}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{\prime }+6 y = 3 x y^{{4}/{3}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x y^{\prime }+y^{3} {\mathrm e}^{-2 x} = 2 x y
\] |
[_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] |
✓ |
|
|
\[
{}\left ({\mathrm e}^{y}+x \right ) y^{\prime } = x \,{\mathrm e}^{-y}-1
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x +3 y+\left (3 x +2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}4 x -y+\left (6 y-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 x^{2}+2 y^{2}+\left (4 x y+6 y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\frac {2 x^{{5}/{2}}-3 y^{{5}/{3}}}{2 x^{{5}/{2}} y^{{2}/{3}}}+\frac {\left (3 y^{{5}/{3}}-2 x^{{5}/{2}}\right ) y^{\prime }}{3 x^{{3}/{2}} y^{{5}/{3}}} = 0
\] |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
|
|
\[
{}x^{3}+3 y-x y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{2}+3 y^{2}-x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y+y^{2}-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}3 y+x^{4} y^{\prime } = 2 x y
\] |
[_separable] |
✓ |
|
|
\[
{}2 x y^{2}+x^{2} y^{\prime } = y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}2 x^{2} y+x^{3} y^{\prime } = 1
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+2 x y = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{\prime }+2 y = 6 x^{2} \sqrt {y}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = 1+x^{2}+y^{2}+x^{2} y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = x y+3 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}6 x y^{3}+2 y^{4}+\left (9 x^{2} y^{2}+8 x y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x^{3} y^{\prime } = x^{2} y-y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+3 y = 3 x^{2} {\mathrm e}^{-3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = x^{2}-2 x y+y^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
|
|
\[
{}2 x^{2} y-x^{3} y^{\prime } = y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}3 x^{5} y^{2}+x^{3} y^{\prime } = 2 y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime }+3 y = \frac {3}{x^{{3}/{2}}}
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime } = 6 y+12 x^{4} y^{{2}/{3}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}9 x^{2} y^{2}+x^{{3}/{2}} y^{\prime } = y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}2 y+\left (x +1\right ) y^{\prime } = 3 x +3
\] |
[_linear] |
✓ |
|
|
\[
{}3 y+x^{3} y^{4}+3 x y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (2 x +1\right ) y^{\prime }+y = \left (2 x +1\right )^{{3}/{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = 3 \left (y+7\right ) x^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 3 \left (y+7\right ) x^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x y^{3}-x y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-3 x^{2}-2 y^{2}}{4 x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {3 y+x}{y-3 x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x y+2 x}{x^{2}+1}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 1+y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}3 y+y^{\prime } = {\mathrm e}^{-2 t}+t
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}-2 y+y^{\prime } = {\mathrm e}^{2 t} t^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y = 1+t \,{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}-2 y+y^{\prime } = 3 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}2 t y+y^{\prime } = 2 t \,{\mathrm e}^{-t^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}4 t y+\left (t^{2}+1\right ) y^{\prime } = \frac {1}{\left (t^{2}+1\right )^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y+2 y^{\prime } = 3 t
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}-y+t y^{\prime } = t^{2} {\mathrm e}^{-t}
\] |
[_linear] |
✓ |
|
|
\[
{}y+2 y^{\prime } = 3 t^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}2 y+y^{\prime } = t \,{\mathrm e}^{-2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}2 y+t y^{\prime } = t^{2}-t +1
\] |
[_linear] |
✓ |
|
|
\[
{}-2 y+y^{\prime } = {\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}-y+2 y^{\prime } = {\mathrm e}^{\frac {t}{3}}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}-2 y+3 y^{\prime } = {\mathrm e}^{-\frac {\pi t}{2}}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}\left (t +1\right ) y+t y^{\prime } = 2 t \,{\mathrm e}^{-t}
\] |
[_linear] |
✓ |
|
|
\[
{}\frac {2 y}{3}+y^{\prime } = 1-\frac {t}{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}-\frac {3 y}{2}+y^{\prime } = 2 \,{\mathrm e}^{t}+3 t
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}\sin \left (x \right ) y^{2}+y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime } = \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \left (-2 x +1\right ) y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-2 x +1}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}r^{\prime } = \frac {r^{2}}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x y^{2}}{\sqrt {x^{2}+1}}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x}{1+2 y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 y^{2}+x y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 \left (x +1\right ) \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {t \left (4-y\right ) y}{3}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {t y \left (4-y\right )}{t +1}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {a y+b}{d +c y}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}+x y+x^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{2}+3 y^{2}}{2 x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {4 y-3 x}{2 x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {4 x +3 y}{2 x +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {3 y+x}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2}+3 x y+y^{2}-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{2}-3 y^{2}}{2 x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {3 y^{2}-x^{2}}{2 x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y+\left (-4+t \right ) t y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 t y+\left (-t^{2}+4\right ) y^{\prime } = 3 t^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}2 t y+\left (-t^{2}+4\right ) y^{\prime } = 3 t^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {4 t}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 t y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{3}+y^{\prime } = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = t \left (3-y\right ) y
\] |
[_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] |
✓ |
|
|
\[
{}y^{\prime } = y \left (-2+y\right ) \left (-1+y\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = -1+{\mathrm e}^{y}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = -1+{\mathrm e}^{-y}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {2 \arctan \left (y\right )}{1+y^{2}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = -k \left (-1+y\right )^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{2} \left (y^{2}-1\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y \left (1-y^{2}\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = -b \sqrt {y}+a y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{2} \left (4-y^{2}\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \left (1-y\right )^{2} y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}3+2 x +\left (2 y-2\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 x +4 y+\left (2 x -2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 y+2 x y^{2}+\left (2 x +2 x^{2} y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-a x -b y}{b x +c y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-a x +b y}{b x -c y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\frac {x}{\left (y^{2}+x^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (y^{2}+x^{2}\right )^{{3}/{2}}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 x -y+\left (2 y-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = -1+{\mathrm e}^{2 x}+y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y+\left (-{\mathrm e}^{-2 y}+2 x y\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
|
|
\[
{}3 x y+y^{2}+\left (x y+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{3}-2 y}{x}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = 3-6 x +y-2 x y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 1+2 x +y^{2}+2 x y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}x +y+\left (x +2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (1+{\mathrm e}^{x}\right ) y^{\prime } = y-y \,{\mathrm e}^{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{2 x}+3 y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x +y}
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime } = {\mathrm e}^{\frac {y}{x}} x +y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}3 t +2 y = -t y^{\prime }
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x y+3 y^{2}-\left (2 x y+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-3 x^{2} y-y^{2}}{2 x^{3}+3 x y}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } = 2 y
\] |
[_quadrature] |
✓ |
|
|
\[
{}x y^{\prime }+y = x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = x
\] |
[_separable] |
✓ |
|
|
\[
{}2 y^{\prime }+x \left (y^{2}-1\right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x^{2} \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{2}-2 x^{2} y+2}{x^{3}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = x \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y \left (y+1\right )}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = a y^{\frac {a -1}{a}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {x}{2}-1+\frac {\sqrt {x^{2}+4 x +4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y^{\prime }+a y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }+3 x^{2} y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime }+y \ln \left (x \right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime }+3 y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+\frac {\left (x +1\right ) y}{x} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime }+\left (1+\frac {1}{\ln \left (x \right )}\right ) y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime }+\left (1+x \cot \left (x \right )\right ) y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-\frac {2 x y}{x^{2}+1} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+\frac {k y}{x} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+\tan \left (k x \right ) y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+3 y = 1
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = x \,{\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{x} = \frac {7}{x^{2}}+3
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime }+\left (2 x^{2}+1\right ) y = x^{3} {\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime }+2 y = \frac {2}{x^{2}}+1
\] |
[_linear] |
✓ |
|
|
\[
{}\left (-2+x \right ) \left (x -1\right ) y^{\prime }-\left (4 x -3\right ) y = \left (-2+x \right )^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+7 y = {\mathrm e}^{3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+4 x y = \frac {2}{x^{2}+1}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{x} = \frac {2}{x^{2}}+1
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime }+2 y = 8 x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime }-2 y = -x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = x
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }-2 x y = x \left (x^{2}-1\right )
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime }-2 y = -1
\] |
[_separable] |
✓ |
|
|
\[
{}\sec \left (y\right )^{2} y^{\prime }-3 \tan \left (y\right ) = -1
\] |
[_quadrature] |
✓ |
|
|
\[
{}\frac {x y^{\prime }}{y}+2 \ln \left (y\right ) = 4 x^{2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
|
|
\[
{}\frac {y^{\prime }}{\left (y+1\right )^{2}}-\frac {1}{x \left (y+1\right )} = -\frac {3}{x^{2}}
\] |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x y^{\prime }+y^{2}+y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y y^{\prime } = \left (y^{2}-1\right )^{{3}/{2}}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x^{2} \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \left (x -1\right ) \left (y-1\right ) \left (y-2\right )
\] |
[_separable] |
✓ |
|
|
\[
{}\left (y-1\right )^{2} y^{\prime } = 2 x +3
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+x \left (y^{2}+y\right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+\frac {\left (y+1\right ) \left (y-1\right ) \left (y-2\right )}{x +1} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+2 x \left (y+1\right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 x y \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } \left (x^{2}+2\right ) = 4 x \left (y^{2}+2 y+1\right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -2 x \left (y^{3}-3 y+2\right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x}{1+2 y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 y-y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } y+x = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+x^{2} \left (y+1\right ) \left (y-2\right )^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +1\right ) \left (-2+x \right ) y^{\prime }+y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1+y^{2}}{x^{2}+1}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = a y-b y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}x y^{\prime }-2 y = \frac {x^{6}}{y+x^{2}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } = 2 x y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x +3 y}{x -4 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \sqrt {x +y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\tan \left (y\right )}{x -1}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y^{{2}/{5}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 3 x \left (y-1\right )^{{1}/{3}}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-y = x y^{2}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y+x \,{\mathrm e}^{-\frac {y}{x}}}{x}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = y^{2}+x y-x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}y^{\prime }-2 y = 2 \sqrt {y}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +y}{x}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}+2 x y}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{3} y^{\prime } = y^{4}+x^{4}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\sec \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = y^{2}+x y+x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x y y^{\prime } = x^{2}+2 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y^{2}+x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}}}{2 x y}
\] |
[[_homogeneous, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x y+y^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{3}+y^{3}}{x y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y y^{\prime }+x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}-3 x y-5 x^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = 2 x^{2}+y^{2}+4 x y
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x y y^{\prime } = 3 x^{2}+4 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{3}+2 x y^{2}+x^{2} y+x^{3}}{x \left (x +y\right )^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +2 y}{2 x +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{y-2 x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x y^{2}+2 y^{3}}{x^{3}+x^{2} y+x y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{3}+x^{2} y+3 y^{3}}{x^{3}+3 x y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = y^{2}+x y-4 x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x y y^{\prime } = x^{2}-x y+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y^{2}-x y+2 x^{2}}{x y+2 x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}+x y+x^{2}}{x y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-6 x +y-3}{2 x -y-1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x +y+1}{x +2 y-4}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-x +3 y-14}{x +y-2}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 x y^{2} y^{\prime } = y^{3}+x
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y y^{\prime } = 3 x^{6}+6 y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{3} y^{\prime } = 2 y^{2}+2 x^{2} y-2 x^{4}
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = y^{2} {\mathrm e}^{-x}+4 y+2 \,{\mathrm e}^{x}
\] |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
|
|
\[
{}2 x \left (y+2 \sqrt {x}\right ) y^{\prime } = \left (y+\sqrt {x}\right )^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = \frac {3 x^{2} y^{2}+6 x y+2}{x^{2} \left (2 x y+3\right )}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime }+\frac {3 y}{x} = \frac {3 x^{4} y^{2}+10 x^{2} y+6}{x^{3} \left (2 x^{2} y+5\right )}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } = 1+x -\left (2 x +1\right ) y+x y^{2}
\] |
[_Riccati] |
✓ |
|
|
\[
{}6 x^{2} y^{2}+4 x^{3} y y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}14 y^{3} x^{2}+21 x^{2} y^{2} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}4 x +7 y+\left (4 y+3 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x +y+\left (2 x +2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\frac {x}{\left (y^{2}+x^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (y^{2}+x^{2}\right )^{{3}/{2}}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}{\mathrm e}^{x y} \left (x^{4} y+4 x^{3}\right )+3 y+\left (x^{5} {\mathrm e}^{x y}+3 x \right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
|
|
\[
{}\left (2 x -1\right ) \left (y-1\right )+\left (x +2\right ) \left (x -3\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}7 x +4 y+\left (4 x +3 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2}+y^{2}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = -\frac {{\mathrm e}^{-x^{2}} \left (3 x +2 y \,{\mathrm e}^{x^{2}}\right )}{2 x +3 y \,{\mathrm e}^{x^{2}}}
\] |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y+\left (2 x +\frac {1}{y}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}-y^{2}+x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y-x y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}3 x^{2} y+2 x^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 y^{3}+3 y^{2} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}27 x y^{2}+8 y^{3}+\left (18 x^{2} y+12 x y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x^{2} y+4 x y+2 y+\left (x^{2}+x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}-y+\left (x^{4}-x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y \sin \left (y\right )+x \left (\sin \left (y\right )-y \cos \left (y\right )\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 y+3 \left (x^{2}+y^{3} x^{2}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{4} y^{4}+x^{5} y^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{4} y^{3}+y+\left (x^{5} y^{2}-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}12 x y+6 y^{3}+\left (9 x^{2}+10 x y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}3 x^{2} y^{2}+2 y+2 x y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+y^{2}+k^{2} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }+y^{2}-3 y+2 = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }+y^{2}+5 y-6 = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }+y^{2}+8 y+7 = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }+y^{2}+14 y+50 = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}6 y^{\prime }+6 y^{2}-y-1 = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}36 y^{\prime }+36 y^{2}-12 y+1 = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }+y^{2}+4 x y+4 x^{2}+2 = 0
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
|
|
\[
{}\left (2 x +1\right ) \left (y^{\prime }+y^{2}\right )-2 y-2 x -3 = 0
\] |
[_rational, _Riccati] |
✓ |
|
|
\[
{}\left (3 x -1\right ) \left (y^{\prime }+y^{2}\right )-\left (2+3 x \right ) y-6 x +8 = 0
\] |
[_rational, _Riccati] |
✓ |
|
|
\[
{}x^{2} \left (y^{\prime }+y^{2}\right )-7 x y+7 = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
|
|
\[
{}\cos \left (t \right ) y+y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\sqrt {t}\, \sin \left (t \right ) y+y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}t^{2} y+y^{\prime } = t^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}\sqrt {t^{2}+1}\, y+y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}-2 t y+y^{\prime } = t
\] |
[_separable] |
✓ |
|
|
\[
{}4 t y+\left (t^{2}+1\right ) y^{\prime } = t
\] |
[_separable] |
✓ |
|
|
\[
{}\left (t^{2}+1\right ) y^{\prime } = 1+y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \left (t +1\right ) \left (y+1\right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 1-t +y^{2}-t y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{3+t +y}
\] |
[_separable] |
✓ |
|
|
\[
{}\sqrt {t^{2}+1}\, y^{\prime } = \frac {t y^{3}}{\sqrt {t^{2}+1}}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = k \left (a -y\right ) \left (b -y\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}t y^{\prime } = y+\sqrt {t^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}2 t y y^{\prime } = 3 y^{2}-t^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (t -\sqrt {t y}\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y+t}{t -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}{\mathrm e}^{\frac {t}{y}} \left (-t +y\right ) y^{\prime }+y \left (1+{\mathrm e}^{\frac {t}{y}}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {t +y+1}{t -y+3}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}1+t -2 y+\left (4 t -3 y-6\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}t +2 y+3+\left (2 t +4 y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\frac {y^{2}}{2}-2 \,{\mathrm e}^{t} y+\left (-{\mathrm e}^{t}+y\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 t y^{3}+3 t^{2} y^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}3 t y+y^{2}+\left (t^{2}+t y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{\left (-t +y\right )^{2}}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}\cos \left (t \right ) y+y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\sqrt {t}\, \sin \left (t \right ) y+y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}t^{2} y+y^{\prime } = t^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}\sqrt {t^{2}+1}\, y+y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}-2 t y+y^{\prime } = t
\] |
[_separable] |
✓ |
|
|
\[
{}\left (t^{2}+1\right ) y^{\prime } = 1+y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \left (t +1\right ) \left (y+1\right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 1-t +y^{2}-t y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{3+t +y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = k \left (a -y\right ) \left (b -y\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y}{t}+\frac {y^{2}}{t^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}t y^{\prime } = y+\sqrt {t^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}2 t y y^{\prime } = 3 y^{2}-t^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (t -\sqrt {t y}\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y+t}{t -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}{\mathrm e}^{\frac {t}{y}} \left (-t +y\right ) y^{\prime }+y \left (1+{\mathrm e}^{\frac {t}{y}}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {t +y+1}{t -y+3}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}1+t -2 y+\left (4 t -3 y-6\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}t +2 y+3+\left (2 t +4 y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\frac {y^{2}}{2}-2 \,{\mathrm e}^{t} y+\left (-{\mathrm e}^{t}+y\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 t y^{3}+3 t^{2} y^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}3 t y+y^{2}+\left (t^{2}+t y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } = 2 t \left (y+1\right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{\left (-t +y\right )^{2}}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = t y^{3}-y
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}x^{\prime } = x \left (-x+1\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime } = -x \left (-x+1\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime } = x^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{2}+x +\left (y-x^{2} y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}1+y^{2}+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime }+y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 x y
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime }-1+y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } \tan \left (x \right )-y = 1
\] |
[_separable] |
✓ |
|
|
\[
{}y+3+\cot \left (x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime }+y = y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}x y+\sqrt {x^{2}+1}\, y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y = x y+x^{2} y^{\prime }
\] |
[_separable] |
✓ |
|
|
\[
{}y^{2}+y^{\prime } y+x^{2} y y^{\prime }-1 = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime }+2 y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{y}
\] |
[_quadrature] |
✓ |
|
|
\[
{}{\mathrm e}^{y} \left (1+y^{\prime }\right ) = 1
\] |
[_quadrature] |
✓ |
|
|
\[
{}1+y^{2} = \frac {y^{\prime }}{x^{3} \left (x -1\right )}
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{2}+x +1\right ) y^{\prime } = y^{2}+2 y+5
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{2}-2 x -8\right ) y^{\prime } = y^{2}+y-2
\] |
[_separable] |
✓ |
|
|
\[
{}x +y = x y^{\prime }
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x +y\right ) y^{\prime }+x = y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}-y+x y^{\prime } = \sqrt {x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x -y}{4 y+x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}-y+x y^{\prime } = \sqrt {x^{2}-y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } y+x = 2 y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y^{\prime }-y+\sqrt {y^{2}-x^{2}} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{2}+x^{2} = x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (x y-x^{2}\right ) y^{\prime }-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x y^{\prime }+y = 2 \sqrt {x y}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x +y+\left (x -y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y \left (x^{2}-x y+y^{2}\right )+x y^{\prime } \left (y^{2}+x y+x^{2}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }-y-x \sin \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\cosh \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{2}+x^{2} = 2 x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (\frac {x}{y}+\frac {y}{x}\right ) y^{\prime }+1 = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{\mathrm e}^{\frac {y}{x}} x +y = x y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (3 x y-2 x^{2}\right ) y^{\prime } = 2 y^{2}-x y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{2} \left (y^{\prime } y-x \right )+x^{3} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\tanh \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x +y-\left (x -y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x +\left (x -2 y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}2 x -y+1+\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x -y+2+\left (y-1+x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x -y+\left (y-x +1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y-1+x}{x -y-1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x +y+\left (2 x +2 y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x -y+1+\left (x -y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x +2 y+\left (3 x +6 y+3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x +2 y+2 = \left (2 x +y-1\right ) y^{\prime }
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 x -y+1+\left (x -3 y-5\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}6 x -3 y+6+\left (2 x -y+5\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x +y+4 = \left (2 x +2 y-1\right ) y^{\prime }
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x +3 y-1+\left (2 x +3 y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 x -y+2+\left (x +2 y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 x +2 y+3-\left (x +2 y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x -2 y+3+\left (1-x +2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x +y+\left (4 x -2 y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x +y+\left (x -2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 x +y+\left (3 y+x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}a_{1} x +b_{1} y+c_{1} +\left (b_{1} x +b_{2} y+c_{2} \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x y-\left (y^{2}+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y \,{\mathrm e}^{x}-2 x +{\mathrm e}^{x} y^{\prime } = 0
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}\frac {2}{y}-\frac {y}{x^{2}}+\left (\frac {1}{x}-\frac {2 x}{y^{2}}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\frac {y \left (2+x^{3} y\right )}{x^{3}} = \frac {\left (1-2 x^{3} y\right ) y^{\prime }}{x^{2}}
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}\frac {2 y}{x^{3}}+\frac {2 x}{y^{2}} = \left (\frac {1}{x^{2}}+\frac {2 x^{2}}{y^{3}}\right ) y^{\prime }
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
|
|
\[
{}\frac {x^{2}+3 y^{2}}{x \left (3 x^{2}+4 y^{2}\right )}+\frac {\left (2 x^{2}+y^{2}\right ) y^{\prime }}{y \left (3 x^{2}+4 y^{2}\right )} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\frac {x^{2}-y^{2}}{x \left (2 x^{2}+y^{2}\right )}+\frac {\left (x^{2}+2 y^{2}\right ) y^{\prime }}{y \left (2 x^{2}+y^{2}\right )} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }+\ln \left (x \right )-y = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x y+\left (y+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x -2 x y\right ) y^{\prime }+2 y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y+y^{2}+x^{3} y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{3}-1+x^{2} y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (x^{3} y^{3}-1\right ) y^{\prime }+x^{2} y^{4} = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}y \left (y-x^{2}\right )+x^{3} y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y+x y^{2}+\left (x -x^{2} y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}2 x y+\left (y-x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y = x \left (x^{2} y-1\right ) y^{\prime }
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}{\mathrm e}^{x} y^{\prime } = 2 x y^{2}+y \,{\mathrm e}^{x}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}\left (2 x +3 x^{2} y\right ) y^{\prime }+y+2 x y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y \left (1-x^{4} y^{2}\right )+x y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y \left (x^{2}-1\right )+x \left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{2}-y+\left (2 x^{3} y+x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y \left (x +y^{2}\right )+x \left (x -y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}x y^{\prime }+2 y = x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = 2 x \,{\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = y+3 x^{2} {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}x^{\prime }+x = {\mathrm e}^{-y}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y+\left (2 x -3 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y^{\prime }-2 x^{4}-2 y = 0
\] |
[_linear] |
✓ |
|
|
\[
{}1 = \left ({\mathrm e}^{y}+x \right ) y^{\prime }
\] |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
|
|
\[
{}y^{2} x^{\prime }+\left (y^{2}+2 y \right ) x = 1
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime } = 5 y+x +1
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+y-2 x y-2 x^{2} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}2 y = \left (y^{4}+x \right ) y^{\prime }
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}y x^{\prime } = 2 y \,{\mathrm e}^{3 y}+x \left (3 y +2\right )
\] |
[_linear] |
✓ |
|
|
\[
{}y+2 \left (x -2 y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}x y y^{\prime } = x^{2}-y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{\prime } t +x \left (1-x^{2} t^{4}\right ) = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+y^{2} = x y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{\prime }+y = y^{2} x^{2} \cos \left (x \right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}x y^{\prime }+2 y = 3 x^{3} y^{{4}/{3}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = x \left (1-{\mathrm e}^{2 y-x^{2}}\right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
|
|
\[
{}2 y = \left (x^{2} y^{4}+x \right ) y^{\prime }
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}\left (1-x \right ) y^{\prime }-y-1 = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{2}+\left (x y+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}2 x +y-\left (x -2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x -2 y+1+\left (y-2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 \,{\mathrm e}^{x}-t^{2}+t \,{\mathrm e}^{x} x^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 y+6 = x y y^{\prime }
\] |
[_separable] |
✓ |
|
|
\[
{}x -3 y = \left (3 y-x +2\right ) y^{\prime }
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y-x y^{\prime } = 2 y^{\prime }+2 y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}\tan \left (y\right ) = \left (3 x +4\right ) y^{\prime }
\] |
[_separable] |
✓ |
|
|
\[
{}2 x y+y^{4}+\left (x y^{3}-2 x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}y+\left (-2 y+3 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}r^{\prime } = r \cot \left (\theta \right )
\] |
[_separable] |
✓ |
|
|
\[
{}\left (4 y+3 x \right ) y^{\prime }+2 x +y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y^{\prime }-y-\sqrt {y^{2}+x^{2}} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x +y+\left (2 x +3 y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
|
|
\[
{}2 x y^{\prime }-y+\frac {x^{2}}{y^{2}} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{\prime }+y \left (1+y^{2}\right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y \sqrt {y^{2}+x^{2}}+x y = x^{2} y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y \cos \left (\frac {x}{y}\right )-\left (y+x \cos \left (\frac {x}{y}\right )\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y \left (3 x^{2}+y\right )-x \left (x^{2}-y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x +\left (2 x +3 y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }-5 y-x \sqrt {y} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y-y^{2}-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{\prime }-2 y-2 x^{4} y^{3} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (-2 x^{2}-3 x y\right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x y^{\prime } = x^{4}+4 y
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime }+y = x^{3} y^{6}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{\prime } = x+x^{2} {\mathrm e}^{\theta }
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
|
|
\[
{}y^{2}+x^{2} = 2 x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}3 x y+\left (3 x^{2}+y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime }+2 y = 3 \,{\mathrm e}^{2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}4 x y^{2}+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x -2 y+3 = \left (x -2 y+1\right ) y^{\prime }
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{2}+\left (x^{3}-2 x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{3}+2 x^{2} y+\left (-3 x^{3}-2 x y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}2 \left (x^{2}+1\right ) y^{\prime } = \left (2 y^{2}-1\right ) x y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}4 y^{2} = {y^{\prime }}^{2} x^{2}
\] |
[_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] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}+\left (x +y-2 x y\right ) {y^{\prime }}^{2}-2 y^{\prime } x y \left (x +y\right ) = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y {y^{\prime }}^{2}+\left (y^{2}-x^{3}-x y^{2}\right ) y^{\prime }-x y \left (y^{2}+x^{2}\right ) = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y = x +3 \ln \left (y^{\prime }\right )
\] |
[_separable] |
✓ |
|
|
\[
{}x = y-{y^{\prime }}^{3}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}+x y y^{\prime } = 2 y^{2}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y = x y^{\prime }+\ln \left (y^{\prime }\right )
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y = x y^{\prime }+{\mathrm e}^{y^{\prime }}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y^{2}-2 x y y^{\prime }+{y^{\prime }}^{2} \left (x^{2}-1\right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x^{2} y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -x \,{\mathrm e}^{y}
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime } = \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-y^{2} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 2 y-4
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = -y^{3}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{t}}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{t}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {t}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}-y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = -1+y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 1-y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{3}-y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 1-y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \left (t^{2}+1\right ) y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 2 y+{\mathrm e}^{-3 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = 2 y+{\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = t -y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 t y}{t^{2}+1}+t +1
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 2 y
\] |
[_quadrature] |
✓ |
|
|
\[
{}t y^{\prime } = y+t^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y}{t +1}
\] |
[_separable] |
✓ |
|
|
\[
{}t y^{\prime } = -y+t^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+4 \tan \left (2 t \right ) y = \tan \left (2 t \right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-x y^{3} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\frac {y^{\prime }}{\tan \left (x \right )}-\frac {y}{x^{2}+1} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+x y^{2} = 4 y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}2 x y^{\prime }+3 x +y = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+4 x y = \left (-x^{2}+1\right )^{{3}/{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x +y^{3}\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}\left (y-x \right ) y^{\prime }+2 x +3 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1}{x +2 y+1}
\] |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {x +y}{3 x +3 y-4}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x \left (1-2 x^{2} y\right ) y^{\prime }+y = 3 x^{2} y^{2}
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime }+\frac {x y}{a^{2}+x^{2}} = x
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {4 y^{2}}{x^{2}}-y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{x} = 1
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y^{2}}{x^{2}} = {\frac {1}{4}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y^{2}}{x^{2}} = {\frac {1}{4}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}\left (5 x +y-7\right ) y^{\prime } = 3 x +3 y+3
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y^{\prime }+y-\frac {y^{2}}{x^{{3}/{2}}} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = 2 x y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}}{x^{2}+1}
\] |
[_separable] |
✓ |
|
|
\[
{}{\mathrm e}^{x +y} y^{\prime }-1 = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x \ln \left (x \right )}
\] |
[_separable] |
✓ |
|
|
\[
{}y-\left (-2+x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x \left (y-1\right )}{x^{2}+3}
\] |
[_separable] |
✓ |
|
|
\[
{}y-x y^{\prime } = 3-2 x^{2} y^{\prime }
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x \left (y^{2}-1\right )}{2 \left (-2+x \right ) \left (x -1\right )}
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime }-y+c = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+y^{2} = -1
\] |
[_separable] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+x y = a x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y^{3} \sin \left (x \right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-y = {\mathrm e}^{2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = 2 x^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {2 x y}{x^{2}+1} = 4 x
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {2 x y}{x^{2}+1} = \frac {4}{\left (x^{2}+1\right )^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{x} = 2 x^{2} \ln \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\alpha y = {\mathrm e}^{\beta x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}\left (3 x -y\right ) y^{\prime } = 3 y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\left (x +y\right )^{2}}{2 x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}\sin \left (\frac {y}{x}\right ) \left (-y+x y^{\prime }\right ) = x \cos \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = \sqrt {16 x^{2}-y^{2}}+y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}-y+x y^{\prime } = \sqrt {9 x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (x^{2}-y^{2}\right )-x \left (y^{2}+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }+y \ln \left (x \right ) = y \ln \left (y\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}+2 x y-2 x^{2}}{x^{2}-x y+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}2 x y y^{\prime }-2 y^{2}-x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}} = 0
\] |
[[_homogeneous, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = y^{2}+3 x y+x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}y^{\prime } y = \sqrt {y^{2}+x^{2}}-x
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}2 x \left (2 x +y\right ) y^{\prime } = y \left (4 x -y\right )
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x y^{\prime } = x \tan \left (\frac {y}{x}\right )+y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x \sqrt {y^{2}+x^{2}}+y^{2}}{x y}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = -y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{2 x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 x y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}}{x^{2}+1}
\] |
[_separable] |
✓ |
|
|
\[
{}{\mathrm e}^{x +y} y^{\prime }-1 = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x \ln \left (x \right )}
\] |
[_separable] |
✓ |
|
|
\[
{}y-\left (x -1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x \left (y-1\right )}{x^{2}+3}
\] |
[_separable] |
✓ |
|
|
\[
{}y-x y^{\prime } = 3-2 x^{2} y^{\prime }
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x \left (y^{2}-1\right )}{2 \left (-2+x \right ) \left (x -1\right )}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{2} y-32}{-x^{2}+16}+2
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime }-y+c = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+y^{2} = -1
\] |
[_separable] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+x y = a x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y^{3} \sin \left (x \right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 \sqrt {y-1}}{3}
\] |
[_quadrature] |
✓ |
|
|
\[
{}m v^{\prime } = m g -k v^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime }+\frac {2 x}{4-t} = 5
\] |
[_linear] |
✓ |
|
|
\[
{}y-{\mathrm e}^{x}+y^{\prime } = 0
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{-2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}-y+x y^{\prime } = x^{2} \ln \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}+x y+x^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}\left (3 x -y\right ) y^{\prime } = 3 y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\left (x +y\right )^{2}}{2 x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}\sin \left (\frac {y}{x}\right ) \left (-y+x y^{\prime }\right ) = x \cos \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = \sqrt {16 x^{2}-y^{2}}+y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}-y+x y^{\prime } = \sqrt {9 x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y \left (x^{2}-y^{2}\right )-x \left (x^{2}-y^{2}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime }+y \ln \left (x \right ) = y \ln \left (y\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}+2 x y-2 x^{2}}{x^{2}-x y+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}2 x y y^{\prime }-2 y^{2}-x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}} = 0
\] |
[[_homogeneous, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = y^{2}+3 x y+x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}y^{\prime } y = \sqrt {y^{2}+x^{2}}-x
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}2 x \left (2 x +y\right ) y^{\prime } = y \left (4 x -y\right )
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x y^{\prime } = x \tan \left (\frac {y}{x}\right )+y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x \sqrt {y^{2}+x^{2}}+y^{2}}{x y}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {4 y-2 x}{x +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x -y}{4 y+x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y-\sqrt {y^{2}+x^{2}}}{x}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}-y+x y^{\prime } = \sqrt {4 x^{2}-y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +a y}{a x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +\frac {y}{2}}{\frac {x}{2}-y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = 6 x^{4} y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x \left (y^{\prime }+y^{3} x^{2}\right )+y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{\left (\pi -1\right ) x} = \frac {3 x y^{\pi }}{1-\pi }
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \left (-y+9 x \right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = \left (4 x +y+2\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = \sin \left (3 x -3 y+1\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y \left (\ln \left (x y\right )-1\right )}{x}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
|
|
\[
{}y^{\prime } = 2 x \left (x +y\right )^{2}-1
\] |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +2 y-1}{2 x -y+3}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+\frac {2 y}{x}-y^{2} = -\frac {2}{x^{2}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
|
|
\[
{}y^{\prime }+\frac {7 y}{x}-3 y^{2} = \frac {3}{x^{2}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
|
|
\[
{}\frac {y^{\prime }}{y}-\frac {2 \ln \left (y\right )}{x} = \frac {1-2 \ln \left (x \right )}{x}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}4 x y^{2}+6 y+\left (5 x^{2} y+8 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}5 x +2 y+1+\left (2 x +y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 x -y+1-\left (6 x -2 y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x -2 y-3+\left (2 x +y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 x -y-6+\left (x +y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x +3 y+1+\left (4 x +6 y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = x \left (y-1\right )+\left (y-1\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
|
|
\[
{}3 y-2 x +\left (3 x -2\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}{\mathrm e}^{2 y}+\left (x +1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime }-x^{2} y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y-2 x}{x}
\] |
[_linear] |
✓ |
|
|
\[
{}x^{3}+y^{3}-x y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }+y = x^{2}+2
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x -2 y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}+x^{2}}{2 x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x y^{\prime } = x +y
\] |
[_linear] |
✓ |
|
|
\[
{}{\mathrm e}^{-y}+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x -y}{2 x +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {3 x -y+1}{3 y-x +5}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } y = x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-y = x^{3}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}x y^{\prime }+y = x
\] |
[_linear] |
✓ |
|
|
\[
{}-y+x y^{\prime } = x^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime }+n y = x^{n}
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime }-n y = x^{n}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{3}+x \right ) y^{\prime }+y = x
\] |
[_linear] |
✓ |
|
|
\[
{}3 y^{2} y^{\prime } = 2 x -1
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 6 x y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x -y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 3 \cos \left (y\right )^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}x y^{\prime } = y
\] |
[_separable] |
✓ |
|
|
\[
{}\left (1-x \right ) y^{\prime } = y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {4 x y}{x^{2}+1}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y}{x^{2}-1}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{\prime }-y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\cot \left (x \right ) y^{\prime } = y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{-2 y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-2 x y = 2 x
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime } = x y+y
\] |
[_separable] |
✓ |
|
|
\[
{}x \cos \left (y\right ) y^{\prime } = 1+\sin \left (y\right )
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime } = 2 y \left (y-1\right )
\] |
[_separable] |
✓ |
|
|
\[
{}2 x y^{\prime } = 1-y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}\left (1-x \right ) y^{\prime } = x y
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime } = \left (x^{2}+1\right ) y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x} \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
|
|
\[
{}x y y^{\prime } = \sqrt {y^{2}-9}
\] |
[_separable] |
✓ |
|
|
\[
{}\left (y-1+x \right ) y^{\prime } = x +1-y
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y y^{\prime } = 2 x^{2}-y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2}-y^{2}+x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime }-2 x y-2 y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x \sin \left (\frac {y}{x}\right ) y^{\prime } = y \sin \left (\frac {y}{x}\right )+x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = y+2 \,{\mathrm e}^{-\frac {y}{x}}
\] |
[[_homogeneous, ‘class D‘]] |
✓ |
|
|
\[
{}y^{\prime } = \left (x +y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = \sin \left (x +1-y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +y+4}{x -y-6}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +y+4}{x +y-6}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x +\frac {2}{y}\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y+y \cos \left (x y\right )+\left (x +x \cos \left (x y\right )\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}-\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}1+y+\left (1-x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (3 x^{2}-y^{2}\right ) y^{\prime }-2 x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x +3 x^{3} y^{4}\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}\left (x -1-y^{2}\right ) y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
|
|
\[
{}y-\left (x +x y^{3}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +y\right ) y^{\prime } = y-x
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y^{\prime }-3 y = x^{4}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y = 2 x \,{\mathrm e}^{-x}+x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}2 y-x^{3} = x y^{\prime }
\] |
[_linear] |
✓ |
|
|
\[
{}\left (1-x y\right ) y^{\prime } = y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}2 x +3 y+1+\left (2 y-3 x +5\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y^{\prime } = \sqrt {y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{2} = \left (x^{3}-x y\right ) y^{\prime }
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{3} x^{2}+y = \left (x^{3} y^{2}-x \right ) y^{\prime }
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}\left (x y-x^{2}\right ) y^{\prime } = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y+x^{2} = x y^{\prime }
\] |
[_linear] |
✓ |
|
|
\[
{}6 x +4 y+3+\left (3 x +2 y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\cos \left (x +y\right )-x \sin \left (x +y\right ) = x \sin \left (x +y\right ) y^{\prime }
\] |
[[_1st_order, _with_linear_symmetries], _exact] |
✓ |
|
|
\[
{}y^{\prime } \ln \left (x -y\right ) = 1+\ln \left (x -y\right )
\] |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = {\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{2}-3 x y-2 x^{2} = \left (x^{2}-x y\right ) y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+2 x y = 4 x^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}2 x y+x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\frac {x}{y^{2}+x^{2}}+\frac {y}{x^{2}}+\left (\frac {y}{y^{2}+x^{2}}-\frac {1}{x}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (x -1\right ) y^{\prime } = \cot \left (y\right )
\] |
[_separable] |
✓ |
|
|
\[
{}\sqrt {x^{2}+1}\, y^{\prime }+\sqrt {1+y^{2}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x \left (1+y^{2}\right )}{y \left (x^{2}+1\right )}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{2} y^{\prime } = 2+3 y^{6}
\] |
[_quadrature] |
✓ |
|
|
\[
{}x y^{3}+{\mathrm e}^{x^{2}} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+\frac {x}{y}+2 = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}-y+x y^{\prime } = x \cot \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x \cos \left (\frac {y}{x}\right )^{2}-y+x y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = y \left (1+\ln \left (y\right )-\ln \left (x \right )\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y+\left (y^{2}+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (1-{\mathrm e}^{-\frac {y}{x}}\right ) y^{\prime }+1-\frac {y}{x} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x^{2}-x y+y^{2}-x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}\left (3+2 x +4 y\right ) y^{\prime } = x +2 y+1
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x +y-1}{x -y-2}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y+2 = \left (2 x +y-4\right ) y^{\prime }
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \sin \left (x -y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \left (x +1\right )^{2}+\left (4 y+1\right )^{2}+8 x y+1
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
|
|
\[
{}x^{2}+\ln \left (y\right )+\frac {x y^{\prime }}{y} = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
|
|
\[
{}2 x y+\left (x^{2}+2 x y+y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y+x \left (y^{2}+\ln \left (x \right )\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
|
|
\[
{}y^{2}+\left (x y+y^{2}-1\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
|
|
\[
{}2 y \left (x +y+2\right )+\left (y^{2}-x^{2}-4 x -1\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
|
|
\[
{}x -\sqrt {y^{2}+x^{2}}+\left (y-\sqrt {y^{2}+x^{2}}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
|
|
\[
{}y^{2}-\left (x y+x^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}2 x^{2} y^{2}+y+\left (x^{3} y-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{2}+\left (x y+\tan \left (x y\right )\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
|
|
\[
{}2 x^{2} y^{4}-y+\left (4 x^{3} y^{3}-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}y \left (1+y^{2}\right )+x \left (y^{2}-x +1\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
|
|
\[
{}y^{2}+\left ({\mathrm e}^{x}-y\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2} y^{2}-2 y+\left (x^{3} y-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}2 x^{3} y+y^{3}-\left (x^{4}+2 x y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}1-\left (y-2 x y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (y^{3}+\frac {x}{y}\right ) y^{\prime } = 1
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}1+\left (x -y^{2}\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
|
|
\[
{}y^{2}+\left (x y+y^{2}-1\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
|
|
\[
{}y+\left (y^{2} {\mathrm e}^{y}-x \right ) y^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}1+y+\left (x -y \left (y+1\right )^{2}\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {4 x^{3} y^{2}}{x^{4} y+2}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}6 y^{2}-x \left (2 x^{3}+y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y = 2 x y^{\prime }+y^{2} {y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}+y^{2} = x y y^{\prime }
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x y^{\prime }-y = y^{\prime } \ln \left (y^{\prime } y\right )
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y = x y^{\prime }-x^{2} {y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y \left (y-2 x y^{\prime }\right )^{3} = {y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
|
|
\[
{}2 x y^{\prime }-y = \ln \left (y^{\prime }\right )
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
|
|
\[
{}x y^{2} \left (x y^{\prime }+y\right ) = 1
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y+2}{x +1}
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime } = y-{\mathrm e}^{\frac {y}{x}} x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}2 \sqrt {x y}-y-x y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{\frac {x y^{\prime }}{y}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}-y+x y^{\prime } = x \tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}2 y-x \left (\ln \left (x^{2} y\right )-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 \left (y+2\right )^{2}}{\left (y-1+x \right )^{2}}
\] |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
|
|
\[
{}x y+2 x^{3} y+x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime } = y+\sqrt {x^{2}-y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{3}+\left (3 x^{2}-2 x y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}\left (1+y^{\prime }\right ) \ln \left (\frac {x +y}{x +3}\right ) = \frac {x +y}{x +3}
\] |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
|
|
\[
{}2 x^{3} y y^{\prime }+3 x^{2} y^{2}+7 = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x^{2} \left (-y+x y^{\prime }\right ) = \left (x +y\right ) y
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{4}+x y+\left (x y^{3}-x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}x^{2}+3 \ln \left (y\right )-\frac {x y^{\prime }}{y} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
|
|
\[
{}y+\left (x y-x -y^{3}\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
|
|
\[
{}y+2 y^{3} y^{\prime } = \left (x +4 y \ln \left (y\right )\right ) y^{\prime }
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 y^{\prime }+x = 4 \sqrt {y}
\] |
[[_1st_order, _with_linear_symmetries], _Chini] |
✓ |
|
|
\[
{}y^{\prime }-6 x \,{\mathrm e}^{x -y}-1 = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x +\sin \left (\frac {y}{x}\right )^{2} \left (y-x y^{\prime }\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{3}-1+x^{2} y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = a +b x +c y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = a +b \,{\mathrm e}^{k x}+c y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = x \left (x^{2}-y\right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = x^{2} \left (a \,x^{3}+b y\right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = a \,x^{n} y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y \cot \left (x \right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \left (2 \csc \left (2 x \right )+\cot \left (x \right )\right ) y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y \sec \left (x \right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y \tan \left (x \right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \left (a +\cos \left (\ln \left (x \right )\right )+\sin \left (\ln \left (x \right )\right )\right ) y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \left (x +y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = \left (x -y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = 3-3 x +3 y+\left (x -y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = x \left (x^{3}+2\right )-\left (2 x^{2}-y\right ) y
\] |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = 1+x \left (-x^{3}+2\right )+\left (2 x^{2}-y\right ) y
\] |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = \left (3+x -4 y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = \left (1+4 x +9 y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = a +b y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = x y \left (y+3\right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 1-x -x^{3}+\left (2 x^{2}+1\right ) y-x y^{2}
\] |
[_Riccati] |
✓ |
|
|
\[
{}y^{\prime } = x +\left (-2 x +1\right ) y-\left (1-x \right ) y^{2}
\] |
[_Riccati] |
✓ |
|
|
\[
{}y^{\prime } = a x y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x^{n} \left (a +b y^{2}\right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+\tan \left (x \right ) \left (1-y^{2}\right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \left (a +b y+c y^{2}\right ) f \left (x \right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y \left (a +b y^{2}\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2}+\operatorname {a3} y^{3}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = x y^{3}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y \left (1-x y^{2}\right ) = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \left (a +b x y\right ) y^{2}
\] |
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
|
|
\[
{}y^{\prime }+y^{3} \sec \left (x \right ) \tan \left (x \right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = a \,x^{\frac {n}{1-n}}+b y^{n}
\] |
[[_homogeneous, ‘class G‘], _Chini] |
✓ |
|
|
\[
{}y^{\prime } = a +b y+\sqrt {\operatorname {A0} +\operatorname {B0} y}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = a x +b \sqrt {y}
\] |
[[_homogeneous, ‘class G‘], _Chini] |
✓ |
|
|
\[
{}y^{\prime }+x^{3} = x \sqrt {x^{4}+4 y}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime } = \sqrt {a +b y^{2}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = a +b \cos \left (y\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = a +b \sin \left (y\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \sqrt {a +b \cos \left (y\right )}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x +y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = a f \left (y\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = f \left (a +b x +c y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}2 y^{\prime }+a x = \sqrt {a^{2} x^{2}-4 b \,x^{2}-4 c y}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
|
|
\[
{}3 y^{\prime } = x +\sqrt {x^{2}-3 y}
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }+x +y = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime }+x^{2}-y = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime } = x^{3}-y
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime } = 1+x^{3}+y
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime } = x^{m}+y
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime } = x^{2} \sin \left (x \right )+y
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime } = a y
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime } = 1+x +a y
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime } = a x +b y
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime } = a \,x^{2}+b y
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime } = a +b \,x^{n}+c y
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime }+\left (b x +a \right ) y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime } = x^{3}+\left (-2 x^{2}+1\right ) y
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime } = a +b y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime }+\left (1-x y\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{\prime } = \left (1-x y\right ) y
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{\prime } = \left (x y+1\right ) y
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{\prime } = x^{3}+\left (2 x^{2}+1\right ) y+x y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x y^{\prime } = y \left (1+2 x y\right )
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{\prime }+\left (a +b \,x^{n} y\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{\prime } = 2 x -y+a \,x^{n} \left (x -y\right )^{2}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Riccati] |
✓ |
|
|
\[
{}x y^{\prime }+\left (1-a y \ln \left (x \right )\right ) y = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}x y^{\prime } = y \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime }+y \left (1-x y^{2}\right ) = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{\prime }+y = a \left (x^{2}+1\right ) y^{3}
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{\prime } = a y+b \left (x^{2}+1\right ) y^{3}
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{\prime } = 4 y-4 \sqrt {y}
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime }+2 y = \sqrt {1+y^{2}}
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime } = y+\sqrt {y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = y+\sqrt {x^{2}-y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = y+a \sqrt {y^{2}+b^{2} x^{2}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }+x -y+x \cos \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = y-x \cos \left (\frac {y}{x}\right )^{2}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = y-\cot \left (y\right )^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime }-y+x \sec \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = y+x \sec \left (\frac {y}{x}\right )^{2}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = y+x \sin \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }+\tan \left (y\right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime }+x +\tan \left (x +y\right ) = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime } = y-x \tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = \left (1+y^{2}\right ) \left (x^{2}+\arctan \left (y\right )\right )
\] |
[‘y=_G(x,y’)‘] |
✓ |
|
|
\[
{}x y^{\prime } = {\mathrm e}^{\frac {y}{x}} x +y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = x +y+{\mathrm e}^{\frac {y}{x}} x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = y \ln \left (y\right )
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime } = \left (1+\ln \left (x \right )-\ln \left (y\right )\right ) y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }+\left (1-\ln \left (x \right )-\ln \left (y\right )\right ) y = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
|
|
\[
{}x y^{\prime } = y-2 x \tanh \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = y f \left (x^{m} y^{n}\right )
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime } = x^{3} \left (3 x +4\right )+y
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime } = \left (x +1\right )^{4}+2 y
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime } = a y+b x y^{2}
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime }+y+\left (x +1\right )^{4} y^{3} = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime } = 1+y+\left (x +1\right ) \sqrt {y+1}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x +a \right ) y^{\prime } = b x +y
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x +a \right ) y^{\prime }+b \,x^{2}+y = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x +a \right ) y^{\prime } = 2 \left (x +a \right )^{5}+3 y
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x +a \right ) y^{\prime } = b +c y
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +a \right ) y^{\prime } = b x +c y
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x +a \right ) y^{\prime } = y \left (1-a y\right )
\] |
[_separable] |
✓ |
|
|
\[
{}\left (-x +a \right ) y^{\prime } = y+\left (c x +b \right ) y^{3}
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x y^{\prime } = 2 x^{3}-y
\] |
[_linear] |
✓ |
|
|
\[
{}2 x y^{\prime } = y \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
|
|
\[
{}2 x y^{\prime }+y \left (1+y^{2}\right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 x y^{\prime }+4 y+a +\sqrt {a^{2}-4 b -4 c y} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (-2 x +1\right ) y^{\prime } = 16+32 x -6 y
\] |
[_linear] |
✓ |
|
|
\[
{}\left (2 x +1\right ) y^{\prime } = 4 \,{\mathrm e}^{-y}-2
\] |
[_separable] |
✓ |
|
|
\[
{}2 \left (x +1\right ) y^{\prime }+2 y+\left (x +1\right )^{4} y^{3} = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
|
|
\[
{}3 x y^{\prime } = \left (2+x y^{3}\right ) y
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = -y+a
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = a +b x +c \,x^{2}+x y
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = a +b x +c \,x^{2}-x y
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+\left (-2 x +1\right ) y = x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = a +b x y
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = \left (b x +a \right ) y
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+x^{2}+x y+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = \left (1+2 x -y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = a +b y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = \left (x +a y\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = \left (a x +b y\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+a \,x^{2}+b x y+c y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+2+x y \left (4+x y\right ) = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = a +b \,x^{2} y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = a +b x y+c \,x^{2} y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = 2 y \left (x -y^{2}\right )
\] |
[[_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] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = 5-x y
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+a -x y = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }-x +x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = x \left (x^{2}+1\right )-x y
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = x \left (3 x^{2}-y\right )
\] |
[_linear] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+2 x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = 2 x \left (x^{2}+1\right )^{2}+2 x y
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = \left (2 b x +a \right ) y
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = 1+y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = 1-y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = 1-\left (2 x -y\right ) y
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x y \left (1-y\right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = x y \left (1+a y\right )
\] |
[_separable] |
✓ |
|
|
\[
{}\left (a^{2}+x^{2}\right ) y^{\prime } = b +x y
\] |
[_linear] |
✓ |
|
|
\[
{}\left (a^{2}+x^{2}\right ) y^{\prime } = \left (b +y\right ) \left (x +\sqrt {a^{2}+x^{2}}\right )
\] |
[_separable] |
✓ |
|
|
\[
{}\left (a^{2}+x^{2}\right ) y^{\prime }+\left (x -y\right ) y = 0
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (a^{2}+x^{2}\right ) y^{\prime } = a^{2}+3 x y-2 y^{2}
\] |
[_rational, _Riccati] |
✓ |
|
|
\[
{}\left (a^{2}+x^{2}\right ) y^{\prime }+x y+b x y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x \left (x +1\right ) y^{\prime } = \left (-2 x +1\right ) y
\] |
[_separable] |
✓ |
|
|
\[
{}x \left (1-x \right ) y^{\prime }+\left (2 x +1\right ) y = a
\] |
[_linear] |
✓ |
|
|
\[
{}x \left (1-x \right ) y^{\prime } = a +2 \left (2-x \right ) y
\] |
[_linear] |
✓ |
|
|
\[
{}x \left (x +1\right ) y^{\prime } = \left (x +1\right ) \left (x^{2}-1\right )+\left (x^{2}+x -1\right ) y
\] |
[_linear] |
✓ |
|
|
\[
{}x \left (x +a \right ) y^{\prime } = \left (b +c y\right ) y
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +a \right )^{2} y^{\prime } = 2 \left (x +a \right ) \left (b +y\right )
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x -a \right )^{2} y^{\prime }+k \left (x +y-a \right )^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
|
|
\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime }+k y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime } = \left (x -a \right ) \left (x -b \right )+\left (2 x -a -b \right ) y
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime } = c y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime }+k \left (y-a \right ) \left (y-b \right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime }+k \left (x +y-a \right ) \left (x +y-b \right )+y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime } = y
\] |
[_separable] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime }+1+2 x y-x^{2} y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x \left (-2 x +1\right ) y^{\prime } = 4 x -\left (1+4 x \right ) y+y^{2}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
|
|
\[
{}2 \left (x^{2}+x +1\right ) y^{\prime } = 1+8 x^{2}-\left (2 x +1\right ) y
\] |
[_linear] |
✓ |
|
|
\[
{}a \,x^{2} y^{\prime } = x^{2}+a x y+b^{2} y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}\left (b \,x^{2}+a \right ) y^{\prime } = A +B y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}x \left (a x +1\right ) y^{\prime }+a -y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{3} y^{\prime } = a +b \,x^{2} y
\] |
[_linear] |
✓ |
|
|
\[
{}x^{3} y^{\prime } = 3-x^{2}+x^{2} y
\] |
[_linear] |
✓ |
|
|
\[
{}x^{3} y^{\prime } = x^{4}+y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x^{3} y^{\prime } = y \left (y+x^{2}\right )
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{3} y^{\prime } = x^{2} \left (y-1\right )+y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x^{3} y^{\prime } = \left (x +1\right ) y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{3} y^{\prime }+20+x^{2} y \left (1-x^{2} y\right ) = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x^{3} y^{\prime } = \left (2 x^{2}+y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x \left (x^{2}+1\right ) y^{\prime } = a \,x^{3}+y
\] |
[_linear] |
✓ |
|
|
\[
{}x \left (x^{2}+1\right ) y^{\prime } = \left (-x^{2}+1\right ) y
\] |
[_separable] |
✓ |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime } = \left (x^{2}-x +1\right ) y
\] |
[_separable] |
✓ |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime } = a \,x^{3}+\left (-2 x^{2}+1\right ) y
\] |
[_linear] |
✓ |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime } = x^{3} \left (-x^{2}+1\right )+\left (-2 x^{2}+1\right ) y
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} \left (1-x \right ) y^{\prime } = \left (2-x \right ) x y-y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x^{3} y^{\prime } = \left (x^{2}-y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x^{3} y^{\prime } = \left (3 x^{2}+y^{2} a \right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{4} y^{\prime } = \left (x^{3}+y\right ) y
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{4} y^{\prime }+a^{2}+x^{4} y^{2} = 0
\] |
[_rational, [_Riccati, _special]] |
✓ |
|
|
\[
{}x^{4} y^{\prime }+x^{3} y+\csc \left (x y\right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
|
|
\[
{}\left (-x^{4}+1\right ) y^{\prime } = 2 x \left (1-y^{2}\right )
\] |
[_separable] |
✓ |
|
|
\[
{}x \left (-2 x^{3}+1\right ) y^{\prime } = 2 \left (-x^{3}+1\right ) y
\] |
[_separable] |
✓ |
|
|
\[
{}\left (c \,x^{2}+b x +a \right )^{2} \left (y^{\prime }+y^{2}\right )+A = 0
\] |
[_rational, _Riccati] |
✓ |
|
|
\[
{}x^{5} y^{\prime } = 1-3 x^{4} y
\] |
[_linear] |
✓ |
|
|
\[
{}x^{n} y^{\prime } = a +b \,x^{n -1} y
\] |
[_linear] |
✓ |
|
|
\[
{}x^{n} y^{\prime } = a^{2} x^{-2+2 n}+b^{2} y^{2}
\] |
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
|
|
\[
{}y^{\prime } \sqrt {-x^{2}+1} = 1+y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } \sqrt {b^{2}+x^{2}} = \sqrt {y^{2}+a^{2}}
\] |
[_separable] |
✓ |
|
|
\[
{}\left (1-4 \cos \left (x \right )^{2}\right ) y^{\prime } = \tan \left (x \right ) \left (1+4 \cos \left (x \right )^{2}\right ) y
\] |
[_separable] |
✓ |
|
|
\[
{}\left (-\sin \left (x \right )+1\right ) y^{\prime }+y \cos \left (x \right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (\cos \left (x \right )-\sin \left (x \right )\right ) y^{\prime }+y \left (\cos \left (x \right )+\sin \left (x \right )\right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x \ln \left (x \right ) = a x \left (\ln \left (x \right )+1\right )-y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } y+x = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } y+a x +b y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } y = \operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } y = \sqrt {y^{2}+a^{2}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } y = \sqrt {y^{2}-a^{2}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}\left (y+1\right ) y^{\prime } = x +y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x +y\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x -y\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x +y\right ) y^{\prime }+x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x +y\right ) y^{\prime } = x -y
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}1-y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x -y\right ) y^{\prime } = \left ({\mathrm e}^{-\frac {x}{y}}+1\right ) y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (x +y+1\right ) y^{\prime }+1+4 x +3 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x +y+2\right ) y^{\prime } = 1-x -y
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (3-x -y\right ) y^{\prime } = 1+x -3 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (3-x +y\right ) y^{\prime } = 11-4 x +3 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (2 x +y\right ) y^{\prime }+x -2 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (2+2 x -y\right ) y^{\prime }+3+6 x -3 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (2 x -y+3\right ) y^{\prime }+2 = 0
\] |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}\left (4+2 x -y\right ) y^{\prime }+5+x -2 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (5-2 x -y\right ) y^{\prime }+4-x -2 y = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (1-3 x +y\right ) y^{\prime } = 2 x -2 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (2-3 x +y\right ) y^{\prime }+5-2 x -3 y = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (4 x -y\right ) y^{\prime }+2 x -5 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (6-4 x -y\right ) y^{\prime } = 2 x -y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (1+5 x -y\right ) y^{\prime }+5+x -5 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (a +b x +y\right ) y^{\prime }+a -b x -y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x^{2}-y\right ) y^{\prime } = 4 x y
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x -2 y\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x +2 y\right ) y^{\prime }+2 x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x -2 y\right ) y^{\prime }+2 x +y = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x -2 y+1\right ) y^{\prime } = 1+2 x -y
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x +2 y+1\right ) y^{\prime }+1-x -2 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x +2 y+1\right ) y^{\prime }+7+x -4 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (3+2 x -2 y\right ) y^{\prime } = 1+6 x -2 y
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (1-4 x -2 y\right ) y^{\prime }+2 x +y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (6 x -2 y\right ) y^{\prime } = 2+3 x -y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (19+9 x +2 y\right ) y^{\prime }+18-2 x -6 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x \,{\mathrm e}^{-x}-2 y\right ) y^{\prime } = 2 x \,{\mathrm e}^{-2 x}-\left ({\mathrm e}^{-x}+x \,{\mathrm e}^{-x}-2 y\right ) y
\] |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}\left (x -3 y\right ) y^{\prime }+4+3 x -y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (4-x -3 y\right ) y^{\prime }+3-x -3 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (2 x +3 y+2\right ) y^{\prime } = 1-2 x -3 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (5-2 x -3 y\right ) y^{\prime }+1-2 x -3 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (1+9 x -3 y\right ) y^{\prime }+2+3 x -y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (4 y+x \right ) y^{\prime }+4 x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (3+2 x +4 y\right ) y^{\prime } = x +2 y+1
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (5+2 x -4 y\right ) y^{\prime } = 3+x -2 y
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (5+3 x -4 y\right ) y^{\prime } = 2+7 x -3 y
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}4 \left (1-x -y\right ) y^{\prime }+2-x = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}\left (11-11 x -4 y\right ) y^{\prime } = 62-8 x -25 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (6+3 x +5 y\right ) y^{\prime } = 2+x +7 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (7 x +5 y\right ) y^{\prime }+10 x +8 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (5-x +6 y\right ) y^{\prime } = 3-x +4 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 \left (x +2 y\right ) y^{\prime } = 1-x -2 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (1+x +9 y\right ) y^{\prime }+1+x +5 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (8+5 x -12 y\right ) y^{\prime } = 3+2 x -5 y
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (140+7 x -16 y\right ) y^{\prime }+25+8 x +y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (3+9 x +21 y\right ) y^{\prime } = 45+7 x -5 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (a x +b y\right ) y^{\prime }+x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}\left (a x +b y\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (a x +b y\right ) y^{\prime }+b x +a y = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (a x +b y\right ) y^{\prime } = b x +a y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y y^{\prime }+1+y^{2} = 0
\] |
[_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] |
✓ |
|
|
\[
{}x y y^{\prime } = x^{2}-x y+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x y y^{\prime }+2 x^{2}-2 x y-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x y y^{\prime } = a +b y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}x y y^{\prime } = a \,x^{n}+b y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y y^{\prime }+x^{2} \operatorname {arccot}\left (\frac {y}{x}\right )-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y y^{\prime }+x^{2} {\mathrm e}^{-\frac {2 y}{x}}-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (x y+1\right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x \left (y+2\right ) y^{\prime }+a x = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}x \left (4+y\right ) y^{\prime } = 2 x +2 y+y^{2}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x \left (x +y\right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x \left (x -y\right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x \left (x +y\right ) y^{\prime } = y^{2}+x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x \left (x -y\right ) y^{\prime }+2 x^{2}+3 x y-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x \left (x +y\right ) y^{\prime }-\left (x +y\right ) y+x \sqrt {x^{2}-y^{2}} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x \left (2 x +y\right ) y^{\prime } = x^{2}+x y-y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x \left (4 x -y\right ) y^{\prime }+4 x^{2}-6 x y-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x \left (x^{3}+y\right ) y^{\prime } = \left (x^{3}-y\right ) y
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x \left (2 x^{3}+y\right ) y^{\prime } = \left (2 x^{3}-y\right ) y
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x \left (2 x^{3}+y\right ) y^{\prime } = 6 y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}\left (x +a \right ) \left (x +b \right ) y^{\prime } = x y
\] |
[_separable] |
✓ |
|
|
\[
{}2 x y y^{\prime }+a +y^{2} = 0
\] |
[_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] |
✓ |
|
|
\[
{}2 x y y^{\prime } = y^{2}+x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x y y^{\prime } = 4 x^{2} \left (2 x +1\right )+y^{2}
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}x \left (x -2 y\right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x \left (x +2 y\right ) y^{\prime }+\left (2 x -y\right ) y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x \left (x -2 y\right ) y^{\prime }+\left (2 x -y\right ) y = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}2 x \left (2 x^{2}+y\right ) y^{\prime }+\left (12 x^{2}+y\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x \left (2 x +3 y\right ) y^{\prime } = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x \left (2 x +3 y\right ) y^{\prime }+3 \left (x +y\right )^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}a x y y^{\prime } = y^{2}+x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}a x y y^{\prime }+x^{2}-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x \left (a +b y\right ) y^{\prime } = c y
\] |
[_separable] |
✓ |
|
|
\[
{}x \left (x -a y\right ) y^{\prime } = y \left (y-a x \right )
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x \left (x^{n}+a y\right ) y^{\prime }+\left (b +c y\right ) y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
|
|
\[
{}x \left (1-x y\right ) y^{\prime }+\left (x y+1\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x \left (2-x y\right ) y^{\prime }+2 y-x y^{2} \left (x y+1\right ) = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
|
|
\[
{}x \left (3-x y\right ) y^{\prime } = y \left (x y-1\right )
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y y^{\prime }+x \left (1-y^{2}\right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x \left (1-2 x y\right ) y^{\prime }+\left (1+2 x y\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x \left (1+2 x y\right ) y^{\prime }+\left (2+3 x y\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x \left (1+2 x y\right ) y^{\prime }+\left (1+2 x y-x^{2} y^{2}\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
|
|
\[
{}x^{2} \left (x -2 y\right ) y^{\prime } = 2 x^{3}-4 x y^{2}+y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}2 \left (x +1\right ) x y y^{\prime } = 1+y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}3 x^{2} y y^{\prime }+1+2 x y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} \left (4 x -3 y\right ) y^{\prime } = \left (6 x^{2}-3 x y+2 y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}\left (1-x^{3} y\right ) y^{\prime } = x^{2} y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}2 x^{3} y y^{\prime }+a +3 x^{2} y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}x \left (3+2 x^{2} y\right ) y^{\prime }+\left (4+3 x^{2} y\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}8 x^{3} y y^{\prime }+3 x^{4}-6 x^{2} y^{2}-y^{4} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y \left (b \,x^{2}+a \right ) y^{\prime } = A +B y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}3 x^{4} y y^{\prime } = 1-2 x^{3} y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (y^{2}+x^{2}\right ) y^{\prime }+x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (y^{2}+x^{2}\right ) y^{\prime } = x y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x^{2}-y^{2}\right ) y^{\prime } = 2 x y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x^{2}-y^{2}\right ) y^{\prime }+x \left (x +2 y\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (y^{2}+x^{2}\right ) y^{\prime }+2 x \left (2 x +y\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (1-x^{2}+y^{2}\right ) y^{\prime } = 1+x^{2}-y^{2}
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
|
|
\[
{}\left (3 x^{2}-y^{2}\right ) y^{\prime } = 2 x y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x^{4}+y^{2}\right ) y^{\prime } = 4 x^{3} y
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}\left (1+y+x y+y^{2}\right ) y^{\prime }+1+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
|
|
\[
{}\left (x +y\right )^{2} y^{\prime } = a^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}\left (x -y\right )^{2} y^{\prime } = a^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}\left (x^{2}+2 x y-y^{2}\right ) y^{\prime }+x^{2}-2 x y+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x +y\right )^{2} y^{\prime } = x^{2}-2 x y+5 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (a +b +x +y\right )^{2} y^{\prime } = 2 \left (a +y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
|
|
\[
{}\left (2 x^{2}+4 x y-y^{2}\right ) y^{\prime } = x^{2}-4 x y-2 y^{2}
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (3 x +y\right )^{2} y^{\prime } = 4 \left (3 x +2 y\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (1-3 x -y\right )^{2} y^{\prime } = \left (1-2 y\right ) \left (3-6 x -4 y\right )
\] |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
|
|
\[
{}\left (2 x^{2}+3 y^{2}\right ) y^{\prime }+x \left (3 x +y\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (3 x^{2}+2 x y+4 y^{2}\right ) y^{\prime }+2 x^{2}+6 x y+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (1-3 x +2 y\right )^{2} y^{\prime } = \left (4+2 x -3 y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
|
|
\[
{}\left (x^{2}+y^{2} a \right ) y^{\prime } = x y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x^{2}+x y+y^{2} a \right ) y^{\prime } = a \,x^{2}+x y+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (a \,x^{2}+2 x y-y^{2} a \right ) y^{\prime }+x^{2}-2 a x y-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (a \,x^{2}+2 b x y+c y^{2}\right ) y^{\prime }+k \,x^{2}+2 a x y+b y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (3 x -y^{2}\right ) y^{\prime }+\left (5 x -2 y^{2}\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}x \left (1-x^{2}+y^{2}\right ) y^{\prime }+\left (1+x^{2}-y^{2}\right ) y = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
|
|
\[
{}x \left (a -x^{2}-y^{2}\right ) y^{\prime }+\left (a +x^{2}+y^{2}\right ) y = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
|
|
\[
{}x \left (2 x^{2}+y^{2}\right ) y^{\prime } = \left (2 x^{2}+3 y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x \left (a -x^{2}-y^{2}\right )+y\right ) y^{\prime }+x -\left (a -x^{2}-y^{2}\right ) y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
|
|
\[
{}x \left (a +y\right )^{2} y^{\prime } = b y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}x \left (x^{2}-x y+y^{2}\right ) y^{\prime }+\left (y^{2}+x y+x^{2}\right ) y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (x^{2}-x y-y^{2}\right ) y^{\prime } = \left (x^{2}+x y-y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (x^{2}+a x y+y^{2}\right ) y^{\prime } = \left (x^{2}+b x y+y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (-2 y^{2}+x^{2}\right ) y^{\prime } = \left (2 x^{2}-y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (x^{2}+2 y^{2}\right ) y^{\prime } = \left (2 x^{2}+3 y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}2 x \left (5 x^{2}+y^{2}\right ) y^{\prime } = x^{2} y-y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (x^{2}+a x y+2 y^{2}\right ) y^{\prime } = \left (a x +2 y\right ) y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}3 x y^{2} y^{\prime } = 2 x -y^{3}
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}x \left (x -3 y^{2}\right ) y^{\prime }+\left (2 x -y^{2}\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
|
|
\[
{}6 x y^{2} y^{\prime }+x +2 y^{3} = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}x \left (x +6 y^{2}\right ) y^{\prime }+x y-3 y^{3} = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}x \left (x^{2}-6 y^{2}\right ) y^{\prime } = 4 \left (x^{2}+3 y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (3 x -7 y^{2}\right ) y^{\prime }+\left (5 x -3 y^{2}\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}\left (1-x^{2} y^{2}\right ) y^{\prime } = x y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}\left (1-x^{2} y^{2}\right ) y^{\prime } = \left (x y+1\right ) y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x \left (1+x y^{2}\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}x \left (1+x y^{2}\right ) y^{\prime } = \left (2-3 x y^{2}\right ) y
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}x^{3} \left (1+y^{2}\right ) y^{\prime }+3 x^{2} y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x \left (1-x y\right )^{2} y^{\prime }+\left (1+x^{2} y^{2}\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}\left (1-x^{4} y^{2}\right ) y^{\prime } = x^{3} y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}\left (x^{3}-y^{3}\right ) y^{\prime }+x^{2} y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x^{3}+y^{3}\right ) y^{\prime }+x^{2} \left (a x +3 y\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (3 x^{2}+y^{2}\right ) y y^{\prime }+x \left (x^{2}+3 y^{2}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}2 y^{3} y^{\prime } = x^{3}-x y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (3 x^{2}+2 y^{2}\right ) y y^{\prime }+x^{3} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (5 x^{2}+2 y^{2}\right ) y y^{\prime }+x \left (x^{2}+5 y^{2}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (3 x^{3}+6 x^{2} y-3 x y^{2}+20 y^{3}\right ) y^{\prime }+4 x^{3}+9 x^{2} y+6 x y^{2}-y^{3} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x^{3}+a y^{3}\right ) y^{\prime } = x^{2} y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (x -y^{3}\right ) y^{\prime } = \left (3 x +y^{3}\right ) y
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}x \left (2 x^{3}+y^{3}\right ) y^{\prime } = \left (2 x^{3}-x^{2} y+y^{3}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (2 x^{3}-y^{3}\right ) y^{\prime } = \left (x^{3}-2 y^{3}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (x^{3}+3 x^{2} y+y^{3}\right ) y^{\prime } = \left (3 x^{2}+y^{2}\right ) y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (x^{3}-2 y^{3}\right ) y^{\prime } = \left (2 x^{3}-y^{3}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (x^{4}-2 y^{3}\right ) y^{\prime }+\left (2 x^{4}+y^{3}\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}x \left (2-x y^{2}-2 x y^{3}\right ) y^{\prime }+1+2 y = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
|
|
\[
{}x \left (1-x y\right ) \left (1-x^{2} y^{2}\right ) y^{\prime }+\left (x y+1\right ) \left (1+x^{2} y^{2}\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}\left (x^{2}-y^{4}\right ) y^{\prime } = x y
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}\left (x^{3}-y^{4}\right ) y^{\prime } = 3 x^{2} y
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}\left (a^{2} x^{2}+\left (y^{2}+x^{2}\right )^{2}\right ) y^{\prime } = a^{2} x y
\] |
[_rational] |
✓ |
|
|
\[
{}2 \left (x -y^{4}\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}\left (a \,x^{3}+\left (a x +b y\right )^{3}\right ) y y^{\prime }+x \left (\left (a x +b y\right )^{3}+b y^{3}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}2 x \left (x^{3}+y^{4}\right ) y^{\prime } = \left (x^{3}+2 y^{4}\right ) y
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}x \left (1-x^{2} y^{4}\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}\left (x^{2}-y^{5}\right ) y^{\prime } = 2 x y
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}x \left (x^{3}+y^{5}\right ) y^{\prime } = \left (x^{3}-y^{5}\right ) y
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}\left (1+a \left (x +y\right )\right )^{n} y^{\prime }+a \left (x +y\right )^{n} = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}x \left (a +x y^{n}\right ) y^{\prime }+b y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}y^{\prime } \sqrt {y} = \sqrt {x}
\] |
[_separable] |
✓ |
|
|
\[
{}\left (1+\sqrt {x +y}\right ) y^{\prime }+1 = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } \sqrt {x y}+x -y = \sqrt {x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x -2 \sqrt {x y}\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (x -\sqrt {y^{2}+x^{2}}\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (x +\sqrt {y^{2}+x^{2}}\right ) y^{\prime }+y \sqrt {y^{2}+x^{2}} = 0
\] |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
|
|
\[
{}x y \left (x +\sqrt {x^{2}-y^{2}}\right ) y^{\prime } = x y^{2}-\left (x^{2}-y^{2}\right )^{{3}/{2}}
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
|
|
\[
{}\left (x \sqrt {x^{2}+y^{2}+1}-y \left (y^{2}+x^{2}\right )\right ) y^{\prime } = x \left (y^{2}+x^{2}\right )+y \sqrt {x^{2}+y^{2}+1}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (1+\left (x +y\right ) \tan \left (y\right )\right ) y^{\prime }+1 = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x \left (x -y \tan \left (\frac {y}{x}\right )\right ) y^{\prime }+\left (x +y \tan \left (\frac {y}{x}\right )\right ) y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (1-2 x -\ln \left (y\right )\right ) y^{\prime }+2 y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} = a^{2} y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} = x^{2} y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}+y^{\prime } y = \left (x +y\right ) x
\] |
[_quadrature] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-y^{\prime } y+{\mathrm e}^{x} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+x y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-2 \left (x -y\right ) y^{\prime }-4 x y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}+\left (a x +b y\right ) y^{\prime }+a b x y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-x y y^{\prime }+y^{2} \ln \left (a y\right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-\left (1+2 x y\right ) y^{\prime }+2 x y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-\left (x -y\right ) y y^{\prime }-x y^{3} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-x y \left (y^{2}+x^{2}\right ) y^{\prime }+x^{4} y^{4} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}4 {y^{\prime }}^{2}+2 x \,{\mathrm e}^{-2 y} y^{\prime }-{\mathrm e}^{-2 y} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x {y^{\prime }}^{2}-\left (2 x +3 y\right ) y^{\prime }+6 y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}x {y^{\prime }}^{2}-\left (x y+1\right ) y^{\prime }+y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}x {y^{\prime }}^{2}+\left (1-x \right ) y y^{\prime }-y^{2} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}x {y^{\prime }}^{2}+\left (1-x^{2} y\right ) y^{\prime }-x y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2} = y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2} = \left (x -y\right )^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-x y^{\prime }+y \left (1-y\right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x +y \left (y+1\right ) = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+2 x \left (2 x +y\right ) y^{\prime }-4 a +y^{2} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+3 x y y^{\prime }+2 y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+4 x y y^{\prime }-5 y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-5 x y y^{\prime }+6 y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+\left (a +b \,x^{2} y^{3}\right ) y^{\prime }+a b y^{3} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }-y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y {y^{\prime }}^{2}-\left (x y+1\right ) y^{\prime }+x = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-x y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}\left (x^{2}-a y\right ) {y^{\prime }}^{2}-2 x y y^{\prime } = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1 = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (y^{2}+x^{2}\right ) y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x^{2}-y^{2}\right ) y^{\prime }-x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}-\left (x^{2}-y^{2}\right ) y^{\prime }-x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}-\left (a -b \,x^{2}+y^{2}\right ) y^{\prime }-b x y = 0
\] |
[_rational] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (3 x^{2}-2 y^{2}\right ) y^{\prime }-6 x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{2} {y^{\prime }}^{2} = a^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-\left (x +1\right ) y y^{\prime }+x = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}\left (x +y\right )^{2} {y^{\prime }}^{2} = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x +y\right )^{2} {y^{\prime }}^{2}-\left (x^{2}-x y-2 y^{2}\right ) y^{\prime }-\left (x -y\right ) y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}4 y^{2} {y^{\prime }}^{2}+2 \left (3 x +1\right ) x y y^{\prime }+3 x^{3} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{2}-4 y^{2}\right ) {y^{\prime }}^{2}+6 x y y^{\prime }-4 x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}4 x^{2} y^{2} {y^{\prime }}^{2} = \left (y^{2}+x^{2}\right )^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}+x -y = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}-a x y y^{\prime }+2 y^{2} a = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}-x y^{4} y^{\prime }-y^{5} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}+\left (\cos \left (x \right ) \cot \left (x \right )-y\right ) {y^{\prime }}^{2}-\left (1+y \cos \left (x \right ) \cot \left (x \right )\right ) y^{\prime }+y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}+\left (2 x -y^{2}\right ) {y^{\prime }}^{2}-2 x y^{2} y^{\prime } = 0
\] |
[_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] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}-\left (y^{2}+x y+x^{2}\right ) {y^{\prime }}^{2}+x y \left (y^{2}+x y+x^{2}\right ) y^{\prime }-x^{3} y^{3} = 0
\] |
[_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] |
✓ |
|
|
\[
{}3 {y^{\prime }}^{3}-x^{4} y^{\prime }+2 x^{3} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x {y^{\prime }}^{3}-\left (x +x^{2}+y\right ) {y^{\prime }}^{2}+\left (x^{2}+y+x y\right ) y^{\prime }-x y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}x {y^{\prime }}^{3}-2 y {y^{\prime }}^{2}+4 x^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{3} {y^{\prime }}^{3}+6 x^{2} y {y^{\prime }}^{2}-\left (1-6 x y\right ) y y^{\prime }+2 y^{3} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
|
|
\[
{}x^{4} {y^{\prime }}^{3}-x^{3} y {y^{\prime }}^{2}-x^{2} y^{2} y^{\prime }+x y^{3} = 1
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{6} {y^{\prime }}^{3}-x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y {y^{\prime }}^{3}-3 x y^{\prime }+3 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
|
|
\[
{}\left (x +2 y\right ) {y^{\prime }}^{3}+3 \left (x +y\right ) {y^{\prime }}^{2}+\left (2 x +y\right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{2} {y^{\prime }}^{3}-x y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{2} {y^{\prime }}^{3}+2 x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 y^{2} {y^{\prime }}^{3}-2 x y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}16 y^{2} {y^{\prime }}^{3}+2 x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{4} {y^{\prime }}^{3}-6 x y^{\prime }+2 y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 \left (y+1\right )^{{3}/{2}}+3 x y^{\prime }-3 y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } \sin \left (y^{\prime }\right )+\cos \left (y^{\prime }\right ) = y
\] |
[_quadrature] |
✓ |
|
|
\[
{}{\mathrm e}^{y^{\prime }-y}-{y^{\prime }}^{2}+1 = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}\ln \left (y^{\prime }\right )+x y^{\prime }+a = y
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}\ln \left (y^{\prime }\right )+x y^{\prime }+a +b y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
|
|
\[
{}\ln \left (y^{\prime }\right )+4 x y^{\prime }-2 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
|
|
\[
{}\ln \left (y^{\prime }\right )+a \left (-y+x y^{\prime }\right ) = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y \ln \left (y^{\prime }\right )+y^{\prime }-y \ln \left (y\right )-x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } \ln \left (y^{\prime }\right )-\left (x +1\right ) y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x y}{x^{2}-y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +y-3}{x -y-1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x +y-1}{4 x +2 y+5}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-\frac {2 y}{x +1} = \left (x +1\right )^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}\frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}y+x y^{2}-x y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y \left (x^{2}+1\right ) y^{\prime }-1-y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (y-x \right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (2 \sqrt {x y}-x \right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }-y-\sqrt {y^{2}+x^{2}} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}8 y+10 x +\left (5 y+7 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x -y+1+\left (2 y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y = a \,x^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+y = \arctan \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) z^{\prime }-x z = a x z^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime }+y = y^{2} \ln \left (x \right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}-y+x y^{\prime } = \sqrt {y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}8 y+10 x +\left (5 y+7 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2}+2 x y-y^{2}+\left (y^{2}+2 x y-x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{2}+\left (x y+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}\left (x^{2} y^{2}+x y\right ) y+\left (x^{2} y^{2}-1\right ) x y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}\left (x^{3} y^{3}+x^{2} y^{2}+x y+1\right ) y+\left (x^{3} y^{3}-x^{2} y^{2}-x y+1\right ) x y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}y = x y^{\prime }+x \sqrt {1+{y^{\prime }}^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x y+\left (y^{2}+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x +\sqrt {y^{2}-x y}\right ) y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x +y-\left (x -y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y^{\prime }-y-x \sin \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}2 x^{2} y+y^{3}+\left (x y^{2}-2 x^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{2}+\left (x \sqrt {y^{2}-x^{2}}-x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
|
|
\[
{}\frac {y \cos \left (\frac {y}{x}\right )}{x}-\left (\frac {x \sin \left (\frac {y}{x}\right )}{y}+\cos \left (\frac {y}{x}\right )\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y+x \ln \left (\frac {y}{x}\right ) y^{\prime }-2 x y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}2 y \,{\mathrm e}^{\frac {x}{y}}+\left (y-2 x \,{\mathrm e}^{\frac {x}{y}}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}{\mathrm e}^{\frac {y}{x}} x -y \sin \left (\frac {y}{x}\right )+x \sin \left (\frac {y}{x}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{2}+x^{2} = 2 x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}{\mathrm e}^{\frac {y}{x}} x +y = x y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{x}+\csc \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y-y^{2}-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x +2 y-4-\left (2 x -4 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 x +2 y+1-\left (3 x +2 y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x +y-1+\left (2 x +2 y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x +y-1-\left (x -y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x +y+\left (2 x +2 y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}7 y-3+\left (2 x +1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x +2 y+\left (3 x +6 y+3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x +2 y+\left (y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 x -2 y+4-\left (2 x +7 y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 x +2 y+3-\left (x +2 y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y+7+\left (2 x +y+3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x +y+2-\left (x -y-4\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y \left (2 y^{3} x^{2}+3\right )+x \left (y^{3} x^{2}-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}x^{2}-y^{2}-y-\left (x^{2}-y^{2}-x \right ) y^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
|
|
\[
{}x y^{\prime }+y = x^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+a y = b
\] |
[_quadrature] |
✓ |
|
|
\[
{}x y^{\prime }+y = y^{2} \ln \left (x \right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}x^{\prime }+2 x y = {\mathrm e}^{-y^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-\frac {2 x y}{x^{2}+1} = 1
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+2 y = 3 \,{\mathrm e}^{-2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+2 y = \frac {3 \,{\mathrm e}^{-2 x}}{4}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}-y+x y^{\prime } = x^{2} \sin \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime }+x y^{2}-y = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{\prime }-y \left (2 y \ln \left (x \right )-1\right ) = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}x^{2} \left (x -1\right ) y^{\prime }-y^{2}-x \left (-2+x \right ) y = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }-y = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1}{x^{2}}-\frac {y}{x}-y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = 1+\frac {y}{x}-\frac {y^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime }-y-1 = \left (x +1\right ) \sqrt {y+1}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}{\mathrm e}^{y} \left (y^{\prime }+1\right ) = {\mathrm e}^{x}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}\left (x -y\right )^{2} y^{\prime } = 4
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}-y+x y^{\prime } = \sqrt {y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (3 x +2 y+1\right ) y^{\prime }+4 x +3 y+2 = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x^{2}-y^{2}\right ) y^{\prime } = 2 x y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y+\left (1+y^{2} {\mathrm e}^{2 x}\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y+y^{2}+x^{3} y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \left (x^{2}+2 y-1\right )^{{2}/{3}}-x
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime }+y = x^{2} \left (1+{\mathrm e}^{x}\right ) y^{2}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}2 y-x y \ln \left (x \right )-2 y^{\prime } x \ln \left (x \right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+a y = k \,{\mathrm e}^{b x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \left (x +y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
|
|
\[
{}x y^{\prime }-y^{2}+1 = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime } = x +y+{\mathrm e}^{\frac {y}{x}} x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }-y \left (\ln \left (x y\right )-1\right ) = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
|
|
\[
{}x^{3} y^{\prime }-y^{2}-x^{2} y = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{\prime }+a y+b \,x^{n} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime }-y-x \sin \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (x y-x^{2}\right ) y^{\prime }+y^{2}-3 x y-2 x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+y^{2}+x y+x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+x y-3 x y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }-2 x y \ln \left (y\right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (2 x y+4 x^{3}\right ) y^{\prime }+y^{2}+12 x^{2} y = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}\left (x^{2}-y\right ) y^{\prime }-4 x y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y y^{\prime }+x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x y y^{\prime }+3 x^{2}-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (2 x y^{3}-x^{4}\right ) y^{\prime }+2 x^{3} y-y^{4} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x y-1\right )^{2} x y^{\prime }+\left (1+x^{2} y^{2}\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}\left (y^{2}+x^{2}\right ) y^{\prime }+2 x \left (2 x +y\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}3 x y^{2} y^{\prime }+y^{3}-2 x = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 y^{3} y^{\prime }+x y^{2}-x^{3} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}-a y^{3}-\frac {b}{x^{{3}/{2}}}+y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Abel] |
✓ |
|
|
\[
{}a x y^{3}+b y^{2}+y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
|
|
\[
{}y^{\prime }+y \tan \left (x \right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{a x}+a y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = a x y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}x y \left (x^{2}+1\right ) y^{\prime } = 1+y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+b^{2} y^{2} = a^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1+y^{2}}{x^{2}+1}
\] |
[_separable] |
✓ |
|
|
\[
{}a x y^{\prime }+2 y = x y y^{\prime }
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y^{2} = \frac {a^{2}}{x^{4}}
\] |
[_rational, _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = y
\] |
[_quadrature] |
✓ |
|
|
\[
{}x y^{\prime } = y
\] |
[_separable] |
✓ |
|
|
\[
{}x y y^{\prime }+1+y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+2 x y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (y+1\right ) y^{\prime } = y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }-x y = x
\] |
[_separable] |
✓ |
|
|
\[
{}2 y^{\prime } = 3 \left (y-2\right )^{{1}/{3}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}\left (x +x y\right ) y^{\prime }+y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{x} = 2 x^{{3}/{2}} \sqrt {y}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}3 x y^{2} y^{\prime }+3 y^{3} = 1
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x -y\right ) y^{\prime }+x +y+1 = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+y^{2}-x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } y = \sqrt {y^{2}+x^{2}}-x
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y+\left (y^{2}-x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{2}-x y+\left (x y+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } = \cos \left (x +y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x}-\tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (x -1\right ) y^{\prime }+y-\frac {1}{x^{2}}+\frac {2}{x^{3}} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = x y^{2}-\frac {2 y}{x}-\frac {1}{x^{3}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-x} y^{2}+y-{\mathrm e}^{x}
\] |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
|
|
\[
{}x^{2} y^{\prime }-x y = \frac {1}{x}
\] |
[_linear] |
✓ |
|
|
\[
{}3 x^{3} y^{2} y^{\prime }-y^{3} x^{2} = 1
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }-2 y-y^{2} {\mathrm e}^{3 x} = 0
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
|
|
\[
{}y+2 x -x y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\left (2 x +y\right ) y^{\prime }-x +2 y = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\sin \left (x \right )^{2} y^{\prime }+\sin \left (x \right )^{2}+\left (x +y\right ) \sin \left (2 x \right ) = 0
\] |
[_linear] |
✓ |
|
|
\[
{}3 x^{2} y+x^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}-y+x y^{\prime } = x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime } = x y+y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 3 x^{2} y
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime } = y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-\sin \left (x +y\right ) = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = 4 y^{2}-3 y+1
\] |
[_quadrature] |
✓ |
|
|
\[
{}x y^{\prime } = \frac {1}{y^{3}}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime } = 3 x t^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}x v^{\prime } = \frac {1-4 v^{2}}{3 v}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\sec \left (y\right )^{2}}{x^{2}+1}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 3 x^{2} \left (1+y^{2}\right )^{{3}/{2}}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime }-x^{3} = x
\] |
[_quadrature] |
✓ |
|
|
\[
{}\frac {y^{\prime }}{y}+y \,{\mathrm e}^{\cos \left (x \right )} \sin \left (x \right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \left (1+y^{2}\right ) \tan \left (x \right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x^{3} \left (1-y\right )
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2}+2 y^{\prime } y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 8 x^{3} {\mathrm e}^{-2 y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x^{2} \left (y+1\right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \sqrt {\sin \left (x \right )+1}\, \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 y-2 t y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \left (x -3\right ) \left (y+1\right )^{{2}/{3}}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x y^{3}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x y^{3}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x y^{3}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x y^{3}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}-3 y+2
\] |
[_quadrature] |
✓ |
|
|
\[
{}\left (t^{2}+1\right ) y^{\prime } = t y-y
\] |
[_separable] |
✓ |
|
|
\[
{}3 r = r^{\prime }-\theta ^{3}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-y-{\mathrm e}^{3 x} = 0
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x}+2 x +1
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime }+2 y = \frac {1}{x^{3}}
\] |
[_linear] |
✓ |
|
|
\[
{}t +y+1-y^{\prime } = 0
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = x^{2} {\mathrm e}^{-4 x}-4 y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y x^{\prime }+2 x = 5 y^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x y-x = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{x} = x \,{\mathrm e}^{x}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+4 y-{\mathrm e}^{-x} = 0
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+\frac {3 y}{x}+2 = 3 x
\] |
[_linear] |
✓ |
|
|
\[
{}\left ({\mathrm e}^{4 y}+2 x \right ) y^{\prime }-1 = 0
\] |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
|
|
\[
{}y^{\prime }+\frac {3 y}{x} = x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}u^{\prime } = \alpha \left (1-u\right )-\beta u
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{2} y+x^{4} \cos \left (x \right )-x^{3} y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x^{{10}/{3}}-2 y+x y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\sqrt {-2 y-y^{2}}+\left (-x^{2}+2 x +3\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-4 y = 32 x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+\frac {3 y}{x} = x^{2}-4 x +3
\] |
[_linear] |
✓ |
|
|
\[
{}2 x y^{3}-\left (-x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}t^{3} y^{2}+\frac {t^{4} y^{\prime }}{y^{6}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-y = {\mathrm e}^{2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+2 x y-x +1 = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y = \left (x +1\right )^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{1-x}+2 x -x^{2} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{1-x}+x -x^{2} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = x y+1
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+x y = x y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}3 x y^{\prime }+y+x^{2} y^{4} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }-\frac {2 y}{x}-x^{2} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {2 y}{x}-x^{3} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime } = 1+y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+2 y = {\mathrm e}^{3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}-y+x y^{\prime } = x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}x \cos \left (y\right ) y^{\prime }-\sin \left (y\right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{3}+x y^{2}\right ) y^{\prime } = 2 y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+2 x y = x
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime }-2 y = x^{3} \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{x} = y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{\prime }+3 y = x^{2} y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x \left (-3+y\right ) y^{\prime } = 4 y
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime } = x^{2} y
\] |
[_separable] |
✓ |
|
|
\[
{}x^{3}+\left (y+1\right )^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (2 y-x \right ) y^{\prime } = 2 x +y
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y+y^{2}+\left (x^{2}-x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x^{3}+y^{3} = 3 x y^{2} y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y-3 x +\left (4 y+3 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x^{3}+3 x y^{2}\right ) y^{\prime } = y^{3}+3 x^{2} y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (3 x +3 y-4\right ) y^{\prime } = -x -y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x -y-1+\left (4 y+x -1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x y+1\right ) y+x \left (1+x y+x^{2} y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}x^{2}-2 x y+5 y^{2} = \left (x^{2}+2 x y+y^{2}\right ) y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y+\left (x^{2}-4 x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x y+y^{2}}{x^{2}+2 x y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = x \left (y+1\right )
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime }+2 y = 3 x -1
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = y^{2}-x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-2 y+3 x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{2}+x^{2} y^{\prime } = x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}2 x y y^{\prime } = x^{2}-y^{2}
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x -2 y+1}{2 x -4 y}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (-x^{3}+1\right ) y^{\prime }+x^{2} y = x^{2} \left (-x^{3}+1\right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+x +x y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x \left (1+y^{2}\right )-\left (x^{2}+1\right ) y y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{x} = x y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }-5 y = 3 \,{\mathrm e}^{x}-2 x +1
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-y = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+\frac {4 y}{x} = x^{4}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{x} = x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime } = 2 y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } y+x = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 x^{3} y^{\prime } = y \left (3 x^{2}+y^{2}\right )
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}4 y+x y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}1+2 y+\left (-x^{2}+4\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{2}-x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}1+y-\left (x +1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{2}+y+\left (x^{2} y-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x \sin \left (\frac {y}{x}\right )-y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y \sqrt {y^{2}+x^{2}}-x \left (x +\sqrt {y^{2}+x^{2}}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
|
|
\[
{}x +y+1+\left (2 x +2 y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}1+2 y-\left (4-x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x +2 y+\left (2 x +3 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x y^{\prime }-2 y = \sqrt {4 y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{2}-x^{2}+x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (1+2 x y\right ) y+x \left (1-x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}1+\left (-x^{2}+1\right ) \cot \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{3}+y^{3}+3 x y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}3 x +2 y+1-\left (3 x +2 y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y^{\prime }+2 y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y y^{\prime }+x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = -2 \left (2 x +3 y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
|
|
\[
{}y \left (x -2 y\right )-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y y^{\prime }+x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2}+y^{2}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}x +y+1-\left (x -y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}1+y^{2} = \left (x^{2}+x \right ) y^{\prime }
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y = 2 x +2
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-y = x y
\] |
[_separable] |
✓ |
|
|
\[
{}-3 y-\left (-2+x \right ) {\mathrm e}^{x}+x y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y = y^{2} {\mathrm e}^{x}
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
|
|
\[
{}x y^{\prime }+y-x^{3} y^{6} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2+y^{2}-\left (x y+2 y+y^{3}\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
|
|
\[
{}2 y^{5} x -y+2 x y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{\prime } = 2 y+x^{3} {\mathrm e}^{x}
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+x y y^{\prime }-6 y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x {y^{\prime }}^{2}+\left (y-1-x^{2}\right ) y^{\prime }-x \left (y-1\right ) = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y = 2 x y^{\prime }+y^{2} {y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}-4 x^{4} y^{\prime }+8 x^{3} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime } = 1-x +2 y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y \sin \left (x \right )
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime } = \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
|
|
\[
{}x y y^{\prime } = \sqrt {1+y^{2}}
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+2 x y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime }+y = y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}2 x^{2} y y^{\prime }+y^{2} = 2
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-x y^{2} = 2 x y
\] |
[_separable] |
✓ |
|
|
\[
{}\left (1+z^{\prime }\right ) {\mathrm e}^{-z} = 1
\] |
[_quadrature] |
✓ |
|
|
\[
{}\frac {y}{x -1}+\frac {x y^{\prime }}{y+1} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\frac {1}{\sqrt {x}}+\frac {y^{\prime }}{\sqrt {y}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\frac {1}{\sqrt {-x^{2}+1}}+\frac {y^{\prime }}{\sqrt {1-y^{2}}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \left (y-1\right ) \left (x +1\right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x -y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{\sqrt {x}}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}z^{\prime } = 10^{x +z}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \cos \left (x -y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime }-y = 2 x -3
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y = 2 x +1
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \cos \left (x -y-1\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime }+\sin \left (x +y\right )^{2} = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = 2 \sqrt {2 x +y+1}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \left (x +y+1\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
|
|
\[
{}x -y+\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y-2 x y+x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{2}+x^{2} y^{\prime } = x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}\left (y^{2}+x^{2}\right ) y^{\prime } = 2 x y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}-y+x y^{\prime } = x \tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = y-{\mathrm e}^{\frac {y}{x}} x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}-y+x y^{\prime } = \left (x +y\right ) \ln \left (\frac {x +y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = y \cos \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y+\sqrt {x y}-x y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }-\sqrt {x^{2}-y^{2}}-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x +y-\left (x -y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}-y+x y^{\prime } = y^{\prime } y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{2}+\left (x^{2}-x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{2}+x y+x^{2} = x^{2} y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}\frac {1}{x^{2}-x y+y^{2}} = \frac {y^{\prime }}{2 y^{2}-x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x y}{3 x^{2}-y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x}{y}+\frac {y}{x}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{\prime } = y+\sqrt {y^{2}-x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (2 \sqrt {x y}-x \right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = y \ln \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } \left (y^{\prime }+y\right ) = \left (x +y\right ) x
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-3 x y y^{\prime }+2 y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}-y+x y^{\prime } = \sqrt {y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime }+\frac {x +2 y}{x} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +y-2}{y-x -4}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x -4 y+6+\left (x +y-2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y-x +5}{2 x -y-4}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {4 x +3 y+15}{2 x +y+7}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +3 y-5}{x -y-1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 \left (y+2\right )^{2}}{\left (x +y+1\right )^{2}}
\] |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
|
|
\[
{}2 x +y+1-\left (4 x +2 y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x -y-1+\left (y-x +2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (4 y+x \right ) y^{\prime } = 2 x +3 y-5
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y+2 = \left (2 x +y-4\right ) y^{\prime }
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (y^{\prime }+1\right ) \ln \left (\frac {x +y}{x +3}\right ) = \frac {x +y}{x +3}
\] |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x -2 y+5}{y-2 x -4}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {3 x -y+1}{2 x +y+4}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x y^{\prime }+\left (x^{2} y^{4}+1\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x +3+\left (2 y-2\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 x +4 y+\left (2 x -2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = x^{2} \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime }-2 \sqrt {x y} = y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y-1+x}{x -y+3}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{2}-x y+x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x +y-\left (x -y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{2 x}+\frac {x^{2}}{2 y}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {2}{t}+\frac {y}{t}+\frac {y^{2}}{t}
\] |
[_separable] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-a^{2} y^{2} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y+\sqrt {y^{2}+x^{2}}-x y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (1+x^{2} y^{2}\right ) y+\left (x^{2} y^{2}-1\right ) x y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}\phi ^{\prime }-\frac {\phi ^{2}}{2}-\phi \cot \left (\theta \right ) = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y \,{\mathrm e}^{x y}+x \,{\mathrm e}^{x y} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2}+y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2}-y^{2}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x +y^{\prime } y+y-x y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+\cos \left (x \right ) y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+5 y = 2
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = k y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }-2 y = 1
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-2 y = x^{2}+x
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}3 y^{\prime }+y = 2 \,{\mathrm e}^{-x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+3 y = {\mathrm e}^{i x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+i y = x
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}L y^{\prime }+R y = E
\] |
[_quadrature] |
✓ |
|
|
\[
{}L y^{\prime }+R y = E \,{\mathrm e}^{i \omega x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = x
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime }+y = 3 x^{3}-1
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y \,{\mathrm e}^{x} = 3 \,{\mathrm e}^{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = x \,{\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}2 x y+x^{2} y^{\prime } = 1
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = y+1
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 1+y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 1+y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = x^{2} y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } y = x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x^{2} y^{2}-4 x^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 2 \sqrt {y}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 2 \sqrt {y}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}}{x y+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}+x y+x^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y+x \,{\mathrm e}^{-\frac {2 y}{x}}}{x}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x -y+2}{y-1+x}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x +3 y+1}{-2 y-1+x}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +y+1}{2 x +2 y-1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\left (y-1+x \right )^{2}}{2 \left (x +2\right )^{2}}
\] |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x y^{\prime } = 2 y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } y = {\mathrm e}^{2 x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = k y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x y}{y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}2 x y y^{\prime } = y^{2}+x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}}{x y-x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}\left (y \cos \left (y\right )-\sin \left (y\right )+x \right ) y^{\prime } = y
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}1+y^{2}+y^{2} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x y^{2}}{1-x^{2} y}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x^{5} y^{\prime }+y^{5} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 4 x y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y \tan \left (x \right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+1+y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y \ln \left (y\right )-x y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-y \tan \left (x \right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y y^{\prime } = y-1
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{2}-x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } y = x +1
\] |
[_separable] |
✓ |
|
|
\[
{}y^{2} y^{\prime } = x +2
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x^{2} y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime }+y = x^{4} y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{\prime }+y = x y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y-x y^{\prime } = y^{\prime } y^{2} {\mathrm e}^{y}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime }+2 = x^{3} \left (y-1\right ) y^{\prime }
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
|
|
\[
{}x y^{\prime } = 2 x^{2} y+y \ln \left (x \right )
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +\frac {2}{y}\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y+y \cos \left (x y\right )+\left (x +x \cos \left (x y\right )\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}1+y+\left (1-x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 x \left (1+\sqrt {x^{2}-y}\right ) = \sqrt {x^{2}-y}\, y^{\prime }
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
|
|
\[
{}\frac {y-x y^{\prime }}{\left (x +y\right )^{2}}+y^{\prime } = 1
\] |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
|
|
\[
{}x^{2}-2 y^{2}+x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime }-3 x y-2 y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x \sin \left (\frac {y}{x}\right ) y^{\prime } = y \sin \left (\frac {y}{x}\right )+x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = y+2 x \,{\mathrm e}^{-\frac {y}{x}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x -y-\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y^{\prime } = 2 x -6 y
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime } = \sqrt {y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = 2 x y+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{3}+y^{3}-x y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +y+4}{x -y-6}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +y+4}{x +y-6}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x -2 y+\left (y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y-1+x}{x +4 y+2}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x +3 y-1-4 \left (x +1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1-x y^{2}}{2 x^{2} y}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2+3 x y^{2}}{4 x^{2} y}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y-x y^{2}}{x +x^{2} y}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } = \sin \left (\frac {y}{x}\right )-\cos \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}{\mathrm e}^{\frac {x}{y}}-\frac {y y^{\prime }}{x} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{2}-x y}{y^{2} \cos \left (\frac {x}{y}\right )}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y \tan \left (\frac {y}{x}\right )}{x}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y}{x}+\frac {x^{3}}{y}+x \tan \left (\frac {y}{x^{2}}\right )
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
|
|
\[
{}x y^{\prime }+y = x
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}+x^{2}}{x^{2}-y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +2 y}{2 x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x y+x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}-y+x y^{\prime } = 2 x
\] |
[_linear] |
✓ |
|
|
\[
{}y^{2} y^{\prime } = x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{2}+2 y^{2}}{-2 y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}2 x \cos \left (y\right )-x^{2} \sin \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\frac {1}{y}-\frac {x y^{\prime }}{y^{2}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 x y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y = 1
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }-y = 2
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }+y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }-y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }-y = x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}x y^{\prime } = y
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{x} = x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{x} = x
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-2 y = x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x {y^{\prime }}^{2}-\left (2 x +3 y\right ) y^{\prime }+6 y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-5 x y y^{\prime }+6 y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+x y^{\prime }-y^{2}-y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x {y^{\prime }}^{2}+\left (1-x^{2} y\right ) y^{\prime }-x y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-\left (x^{2} y+3\right ) y^{\prime }+3 x^{2} y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}x {y^{\prime }}^{2}-\left (x y+1\right ) y^{\prime }+y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-x^{2} y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +y\right )^{2} {y^{\prime }}^{2} = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-x y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-x y \left (x +y\right ) y^{\prime }+x^{3} y^{3} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (4 x -y\right ) {y^{\prime }}^{2}+6 \left (x -y\right ) y^{\prime }+2 x -5 y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}\left (x -y\right )^{2} {y^{\prime }}^{2} = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (-1+x y^{2}\right ) y^{\prime }-y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}\left (y^{2}+x^{2}\right )^{2} {y^{\prime }}^{2} = 4 x^{2} y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x +y\right )^{2} {y^{\prime }}^{2}+\left (2 y^{2}+x y-x^{2}\right ) y^{\prime }+\left (y-x \right ) y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y \left (y^{2}+x^{2}\right ) \left (-1+{y^{\prime }}^{2}\right ) = y^{\prime } \left (x^{4}+x^{2} y^{2}+y^{4}\right )
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x {y^{\prime }}^{3}-\left (x +x^{2}+y\right ) {y^{\prime }}^{2}+\left (x^{2}+y+x y\right ) y^{\prime }-x y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1 = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{4} {y^{\prime }}^{3}-6 x y^{\prime }+2 y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}+x^{4} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{6} {y^{\prime }}^{3}-3 x y^{\prime }-3 y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y = x^{6} {y^{\prime }}^{3}-x y^{\prime }
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}6 x {y^{\prime }}^{2}-\left (3 x +2 y\right ) y^{\prime }+y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-y \left (x +1\right ) y^{\prime }+x = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}4 y^{2} {y^{\prime }}^{3}-2 x y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2} = \left (x -y\right )^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}x {y^{\prime }}^{2}+y \left (1-x \right ) y^{\prime }-y^{2} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}x {y^{\prime }}^{3}-2 y {y^{\prime }}^{2}+4 x^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x \ln \left (x \right )}
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+y^{2} = -1
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = 5 x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x -y}{4 y+x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = 6 x^{4} y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = y+1
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-x y-1}{4 x^{3} y-2 x^{2}}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } = \sqrt {y}+x
\] |
[[_1st_order, _with_linear_symmetries], _Chini] |
✓ |
|
|
\[
{}y^{2}+x^{2} y^{\prime } = x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {5 x^{2}-x y+y^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}2 t +3 x+\left (x+2\right ) x^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1}{1-y}
\] |
[_quadrature] |
✓ |
|
|
\[
{}p^{\prime } = a p-b p^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{2}+\frac {2}{x}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } y-y = x
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}f^{\prime } = \frac {1}{f}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }+\sin \left (x -y\right ) = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}x^{\prime } = 4 A k \left (\frac {x}{A}\right )^{{3}/{4}}-3 k x
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y \left (1+\frac {a^{2} x}{\sqrt {a^{2} \left (x^{2}+1\right )}}\right )}{\sqrt {a^{2} \left (x^{2}+1\right )}}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 \sqrt {y}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \sqrt {1-y^{2}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}w^{\prime } = -\frac {1}{2}-\frac {\sqrt {1-12 w}}{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-\frac {y}{x}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = y \left (1-y^{2}\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{2 y \ln \left (y\right )+y-x}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+{\mathrm e}^{-y} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = a x y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = a x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = a x +b y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = b y
\] |
[_quadrature] |
✓ |
|
|
\[
{}c y^{\prime } = a x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}c y^{\prime } = a x +b y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}c y^{\prime } = y
\] |
[_quadrature] |
✓ |
|
|
\[
{}c y^{\prime } = b y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \cos \left (x \right )+\frac {y}{x}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \sqrt {1+6 x +y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \left (1+6 x +y\right )^{{1}/{3}}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \left (1+6 x +y\right )^{{1}/{4}}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \left (a +b x +y\right )^{4}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \left (\pi +x +7 y\right )^{{7}/{2}}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \left (a +b x +c y\right )^{6}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x +y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 10+{\mathrm e}^{x +y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \left (x +y\right )^{4}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }+a y-c \,{\mathrm e}^{b x} = 0
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+2 x y-x \,{\mathrm e}^{-x^{2}} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-\left (\sin \left (\ln \left (x \right )\right )+\cos \left (\ln \left (x \right )\right )+a \right ) y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y^{2}-1 = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }+y^{2}-2 x^{2} y+x^{4}-2 x -1 = 0
\] |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
|
|
\[
{}y^{\prime }-y^{2}-3 y+4 = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }-\left (x +y\right )^{2} = 0
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
|
|
\[
{}y^{\prime }+y^{2} a -b = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }-\left (A y-a \right ) \left (B y-b \right ) = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }-x y^{2}-3 x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-a \,x^{n} \left (1+y^{2}\right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+f \left (x \right ) \left (y^{2}+2 a y+b \right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-a y^{3}-\frac {b}{x^{{3}/{2}}} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Abel] |
✓ |
|
|
\[
{}y^{\prime }-\operatorname {a3} y^{3}-\operatorname {a2} y^{2}-\operatorname {a1} y-\operatorname {a0} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }+a x y^{3}+b y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
|
|
\[
{}y^{\prime }-a y^{n}-b \,x^{\frac {n}{1-n}} = 0
\] |
[[_homogeneous, ‘class G‘], _Chini] |
✓ |
|
|
\[
{}y^{\prime }-a \sqrt {y}-b x = 0
\] |
[[_homogeneous, ‘class G‘], _Chini] |
✓ |
|
|
\[
{}y^{\prime }-a \sqrt {1+y^{2}}-b = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }-\frac {\sqrt {y^{2}-1}}{\sqrt {x^{2}-1}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-a \cos \left (y\right )+b = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }-\cos \left (b x +a y\right ) = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime }-f \left (a x +b y\right ) = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y-x f \left (x^{2}+y^{2} a \right )}{x +a y f \left (x^{2}+y^{2} a \right )} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime }-y-\frac {x}{\ln \left (x \right )} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime }-y-x^{2} \sin \left (x \right ) = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime }-y-\frac {x \cos \left (\ln \left (\ln \left (x \right )\right )\right )}{\ln \left (x \right )} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime }+a y+b \,x^{n} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime }-y^{2}+1 = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime }+x y^{2}-y = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{\prime }+x y^{2}-y-a \,x^{3} = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x y^{\prime }+x y^{2}-\left (2 x^{2}+1\right ) y-x^{3} = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x y^{\prime }-y^{2} \ln \left (x \right )+y = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}x y^{\prime }-y \left (2 y \ln \left (x \right )-1\right ) = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}x y^{\prime }-y-\sqrt {y^{2}+x^{2}} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }+a \sqrt {y^{2}+x^{2}}-y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }-{\mathrm e}^{\frac {y}{x}} x -y-x = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }-y \ln \left (y\right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime }-y \left (\ln \left (x y\right )-1\right ) = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
|
|
\[
{}x y^{\prime }-y-x \sin \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }+x \cos \left (\frac {y}{x}\right )-y+x = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }+x \tan \left (\frac {y}{x}\right )-y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }-y f \left (x y\right ) = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
|
|
\[
{}x y^{\prime }-y f \left (x^{a} y^{b}\right ) = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
|
|
\[
{}2 x y^{\prime }-y-2 x^{3} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\left (2 x +1\right ) y^{\prime }-4 \,{\mathrm e}^{-y}+2 = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{\prime }-\left (x -1\right ) y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+y^{2}+x y+x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x^{2} y^{\prime }-y^{2}-x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime }-y^{2}-x y-x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x^{2} \left (y^{\prime }+y^{2}\right )+4 x y+2 = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x^{2} \left (y^{\prime }+y^{2}\right )+a x y+b = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x^{2} \left (y^{\prime }+y^{2} a \right )-b = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x y-x \left (x^{2}+1\right ) = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }-x y+a = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+y^{2}-2 x y+1 = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }-\left (y-x \right ) y = 0
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+a x y^{2}+x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }-2 x y \ln \left (y\right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime }+k \left (x +y-a \right ) \left (x +y-b \right )+y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
|
|
\[
{}x \left (2 x -1\right ) y^{\prime }+y^{2}-\left (1+4 x \right ) y+4 x = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
|
|
\[
{}3 x^{2} y^{\prime }-7 y^{2}-3 x y-x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x^{3} y^{\prime }-y^{2}-x^{4} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x^{3} y^{\prime }-y^{2}-x^{2} y = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{3} y^{\prime }-x^{4} y^{2}+x^{2} y+20 = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x \left (x^{2}+1\right ) y^{\prime }+x^{2} y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x \left (x^{2}-1\right ) y^{\prime }-\left (2 x^{2}-1\right ) y+a \,x^{3} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} \left (x -1\right ) y^{\prime }-y^{2}-x \left (-2+x \right ) y = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{4} \left (y^{\prime }+y^{2}\right )+a = 0
\] |
[_rational, [_Riccati, _special]] |
✓ |
|
|
\[
{}\left (2 x^{4}-x \right ) y^{\prime }-2 \left (x^{3}-1\right ) y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (a \,x^{2}+b x +c \right )^{2} \left (y^{\prime }+y^{2}\right )+A = 0
\] |
[_rational, _Riccati] |
✓ |
|
|
\[
{}x^{n} y^{\prime }+y^{2}-\left (n -1\right ) x^{n -1} y+x^{-2+2 n} = 0
\] |
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
|
|
\[
{}x^{n} y^{\prime }-y^{2} a -b \,x^{-2+2 n} = 0
\] |
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
|
|
\[
{}x^{2 n +1} y^{\prime }-a y^{3}-b \,x^{3 n} = 0
\] |
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
|
|
\[
{}x^{m \left (n -1\right )+n} y^{\prime }-a y^{n}-b \,x^{n \left (m +1\right )} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
|
|
\[
{}\sqrt {x^{2}-1}\, y^{\prime }-\sqrt {y^{2}-1} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x \ln \left (x \right )+y-a x \left (\ln \left (x \right )+1\right ) = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } y+a y+x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } y-\sqrt {y^{2} a +b} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } y-x \,{\mathrm e}^{\frac {x}{y}} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (y+1\right ) y^{\prime }-y-x = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (y-1+x \right ) y^{\prime }-y+2 x +3 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (y+2 x -2\right ) y^{\prime }-y+x +1 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (y-2 x +1\right ) y^{\prime }+y+x = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (y-x^{2}\right ) y^{\prime }+4 x y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x +2 y+1\right ) y^{\prime }-x -2 y+1 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (2 y+x +7\right ) y^{\prime }-y+2 x +4 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (2 y-x \right ) y^{\prime }-y-2 x = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (2 y-6 x \right ) y^{\prime }-y+3 x +2 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (4 y+2 x +3\right ) y^{\prime }-2 y-x -1 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (4 y-2 x -3\right ) y^{\prime }+2 y-x -1 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (4 y-3 x -5\right ) y^{\prime }-3 y+7 x +2 = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (4 y+11 x -11\right ) y^{\prime }-25 y-8 x +62 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (12 y-5 x -8\right ) y^{\prime }-5 y+2 x +3 = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (a y+b x +c \right ) y^{\prime }+\alpha y+\beta x +\gamma = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y y^{\prime }+y^{2}+x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x \left (4+y\right ) y^{\prime }-y^{2}-2 y-2 x = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}\left (\left (x +y\right ) x +a \right ) y^{\prime }-\left (x +y\right ) y-b = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}\left (x y-x^{2}\right ) y^{\prime }+y^{2}-3 x y-2 x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}2 x y y^{\prime }-y^{2}+a x = 0
\] |
[[_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] |
✓ |
|
|
\[
{}\left (2 x y+4 x^{3}\right ) y^{\prime }+y^{2}+112 x^{2} y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x \left (2 x +3 y\right ) y^{\prime }+3 \left (x +y\right )^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}\left (2+3 x \right ) \left (y-2 x -1\right ) y^{\prime }-y^{2}+x y-7 x^{2}-9 x -3 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}\left (a x y+b \,x^{n}\right ) y^{\prime }+\alpha y^{3}+\beta y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
|
|
\[
{}x \left (-2+x y\right ) y^{\prime }+y^{3} x^{2}+x y^{2}-2 y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
|
|
\[
{}x \left (x y-3\right ) y^{\prime }+x y^{2}-y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}\left (2 x^{2} y+x \right ) y^{\prime }-y^{3} x^{2}+2 x y^{2}+y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
|
|
\[
{}\left (2 x^{2} y-x \right ) y^{\prime }-2 x y^{2}-y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}\left (2 x^{2} y-x^{3}\right ) y^{\prime }+y^{3}-4 x y^{2}+2 x^{3} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}2 x \left (x^{3} y+1\right ) y^{\prime }+\left (3 x^{3} y-1\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}\left (y^{2}+x^{2}\right ) y^{\prime }+2 x \left (2 x +y\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (y^{2}+x^{2}\right ) y^{\prime }-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (y^{2}-x^{2}\right ) y^{\prime }+2 x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (y^{2}+x^{4}\right ) y^{\prime }-4 x^{3} y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}\left (x +y\right )^{2} y^{\prime }-a^{2} = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}\left (y^{2}+2 x y-x^{2}\right ) y^{\prime }-y^{2}+2 x y+x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (y+3 x -1\right )^{2} y^{\prime }-\left (2 y-1\right ) \left (4 y+6 x -3\right ) = 0
\] |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
|
|
\[
{}\left (4 y^{2}+x^{2}\right ) y^{\prime }-x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (4 y^{2}+2 x y+3 x^{2}\right ) y^{\prime }+y^{2}+6 x y+2 x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (2 y-3 x +1\right )^{2} y^{\prime }-\left (3 y-2 x -4\right )^{2} = 0
\] |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
|
|
\[
{}\left (2 y-4 x +1\right )^{2} y^{\prime }-\left (y-2 x \right )^{2} = 0
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (y^{2} a +2 b x y+c \,x^{2}\right ) y^{\prime }+b y^{2}+2 c x y+d \,x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (b \left (\beta y+\alpha x \right )^{2}-\beta \left (a x +b y\right )\right ) y^{\prime }+a \left (\beta y+\alpha x \right )^{2}-\alpha \left (a x +b y\right ) = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
|
|
\[
{}\left (a y+b x +c \right )^{2} y^{\prime }+\left (\alpha y+\beta x +\gamma \right )^{2} = 0
\] |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
|
|
\[
{}x \left (y^{2}-3 x \right ) y^{\prime }+2 y^{3}-5 x y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}x \left (y^{2}+x^{2}-a \right ) y^{\prime }-y \left (y^{2}+x^{2}+a \right ) = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
|
|
\[
{}x \left (y^{2}+x y-x^{2}\right ) y^{\prime }-y^{3}+x y^{2}+x^{2} y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (y^{2}+x^{2} y+x^{2}\right ) y^{\prime }-2 y^{3}-2 x^{2} y^{2}+x^{4} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
|
|
\[
{}2 x \left (y^{2}+5 x^{2}\right ) y^{\prime }+y^{3}-x^{2} y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}3 x y^{2} y^{\prime }+y^{3}-2 x = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (3 x y^{2}-x^{2}\right ) y^{\prime }+y^{3}-2 x y = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
|
|
\[
{}6 x y^{2} y^{\prime }+2 y^{3}+x = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (6 x y^{2}+x^{2}\right ) y^{\prime }-y \left (3 y^{2}-x \right ) = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}\left (x^{2} y^{2}+x \right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}\left (x y-1\right )^{2} x y^{\prime }+\left (1+x^{2} y^{2}\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}\left (10 x^{3} y^{2}+x^{2} y+2 x \right ) y^{\prime }+5 y^{3} x^{2}+x y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}\left (y^{3}-x^{3}\right ) y^{\prime }-x^{2} y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}2 y^{3} y^{\prime }+x y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (2 y^{3}+5 x^{2} y\right ) y^{\prime }+5 x y^{2}+x^{3} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (20 y^{3}-3 x y^{2}+6 x^{2} y+3 x^{3}\right ) y^{\prime }-y^{3}+6 x y^{2}+9 x^{2} y+4 x^{3} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (2 x y^{3}-x^{4}\right ) y^{\prime }-y^{4}+2 x^{3} y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (2 y^{3} x^{2}+x^{2} y^{2}-2 x \right ) y^{\prime }-2 y-1 = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
|
|
\[
{}y \left (y^{3}-2 x^{3}\right ) y^{\prime }+\left (2 y^{3}-x^{3}\right ) x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y \left (\left (b x +a y\right )^{3}+b \,x^{3}\right ) y^{\prime }+x \left (\left (b x +a y\right )^{3}+a y^{3}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}a \,x^{2} y^{n} y^{\prime }-2 x y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}y^{m} x^{n} \left (a x y^{\prime }+b y\right )+\alpha x y^{\prime }+\beta y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}\left (f \left (x +y\right )+1\right ) y^{\prime }+f \left (x +y\right ) = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
|
|
\[
{}\left (\sqrt {x y}-1\right ) x y^{\prime }-\left (\sqrt {x y}+1\right ) y = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
|
|
\[
{}\left (2 x^{{5}/{2}} y^{{3}/{2}}+x^{2} y-x \right ) y^{\prime }-x^{{3}/{2}} y^{{5}/{2}}+x y^{2}-y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}\left (1+\sqrt {x +y}\right ) y^{\prime }+1 = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}\left (x +\sqrt {y^{2}+x^{2}}\right ) y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (y \sqrt {y^{2}+x^{2}}+\left (y^{2}-x^{2}\right ) \sin \left (\alpha \right )-2 x y \cos \left (\alpha \right )\right ) y^{\prime }+x \sqrt {y^{2}+x^{2}}+2 x y \sin \left (\alpha \right )+\left (y^{2}-x^{2}\right ) \cos \left (\alpha \right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (x \sqrt {x^{2}+y^{2}+1}-y \left (y^{2}+x^{2}\right )\right ) y^{\prime }-y \sqrt {x^{2}+y^{2}+1}-x \left (y^{2}+x^{2}\right ) = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x \left (3 \,{\mathrm e}^{x y}+2 \,{\mathrm e}^{-x y}\right ) \left (x y^{\prime }+y\right )+1 = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
|
|
\[
{}\left (\ln \left (y\right )+2 x -1\right ) y^{\prime }-2 y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime } \cot \left (\frac {y}{x}\right )+2 x \sin \left (\frac {y}{x}\right )-y \cot \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘]] |
✓ |
|
|
\[
{}x \cos \left (y\right ) y^{\prime }+\sin \left (y\right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } \cos \left (a y\right )-b \left (1-c \cos \left (a y\right )\right ) \sqrt {\cos \left (a y\right )^{2}-1+c \cos \left (a y\right )} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}\left (x^{2} y \sin \left (x y\right )-4 x \right ) y^{\prime }+x y^{2} \sin \left (x y\right )-y = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
|
|
\[
{}\left (-y+x y^{\prime }\right ) \cos \left (\frac {y}{x}\right )^{2}+x = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (y \sin \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right )\right ) x y^{\prime }-\left (x \cos \left (\frac {y}{x}\right )+y \sin \left (\frac {y}{x}\right )\right ) y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (y f \left (y^{2}+x^{2}\right )-x \right ) y^{\prime }+y+x f \left (y^{2}+x^{2}\right ) = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}+\left (y^{\prime }-y\right ) {\mathrm e}^{x} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}+\left (b x +a y\right ) y^{\prime }+a b x y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-x y y^{\prime }+y^{2} \ln \left (a y\right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}+y \left (y-x \right ) y^{\prime }-x y^{3} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x y^{\prime }+y+2 x \right )^{2}-4 x y-4 x^{2}-4 a = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+y \left (y+1\right )-x = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+3 x y y^{\prime }+2 y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+4 x y y^{\prime }-5 y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+\left (x^{2} y-2 x y+x^{3}\right ) y^{\prime }+\left (y^{2}-x^{2} y\right ) \left (1-x \right ) = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+\left (a \,x^{2} y^{3}+b \right ) y^{\prime }+a b y^{3} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}\left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y {y^{\prime }}^{2}-\left (y-x \right ) y^{\prime }-x = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (y^{2}+x^{2}\right ) y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}a x y {y^{\prime }}^{2}-\left (y^{2} a +b \,x^{2}+c \right ) y^{\prime }+b x y = 0
\] |
[_rational] |
✓ |
|
|
\[
{}x y^{2} {y^{\prime }}^{2}-2 y^{3} y^{\prime }+2 x y^{2}-x^{3} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}-\left (y^{2}+x y+x^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+x^{2} y^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}-x y^{4} y^{\prime }-y^{5} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{3} {y^{\prime }}^{3}-3 x^{2} y {y^{\prime }}^{2}+\left (3 x y^{2}+x^{6}\right ) y^{\prime }-y^{3}-2 x^{5} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 \left (x y^{\prime }+y\right )^{3}-y^{\prime } y = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
|
|
\[
{}{y^{\prime }}^{3} \sin \left (x \right )-\left (y \sin \left (x \right )-\cos \left (x \right )^{2}\right ) {y^{\prime }}^{2}-\left (y \cos \left (x \right )^{2}+\sin \left (x \right )\right ) y^{\prime }+y \sin \left (x \right ) = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{2} {y^{\prime }}^{3}+2 x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}16 y^{2} {y^{\prime }}^{3}+2 x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{7} y^{2} {y^{\prime }}^{3}-\left (3 x^{6} y^{3}-1\right ) {y^{\prime }}^{2}+3 x^{5} y^{4} y^{\prime }-x^{4} y^{5} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
|
|
\[
{}a {y^{\prime }}^{m}+b {y^{\prime }}^{n}-y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}x \left (\sqrt {1+{y^{\prime }}^{2}}+y^{\prime }\right )-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}a y \sqrt {1+{y^{\prime }}^{2}}-2 x y y^{\prime }+y^{2}-x^{2} = 0
\] |
[_rational] |
✓ |
|
|
\[
{}\ln \left (y^{\prime }\right )+x y^{\prime }+a y+b = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
|
|
\[
{}\ln \left (y^{\prime }\right )+a \left (-y+x y^{\prime }\right ) = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y \ln \left (y^{\prime }\right )+y^{\prime }-y \ln \left (y\right )-x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} \sin \left (y^{\prime }\right )-y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = F \left (\frac {y}{x +a}\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = 2 x +F \left (y-x^{2}\right )
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {a x}{2}+F \left (y+\frac {a \,x^{2}}{4}+\frac {b x}{2}\right )
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime } = F \left (y \,{\mathrm e}^{-b x}\right ) {\mathrm e}^{b x}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 a}{y+2 F \left (y^{2}-4 a x \right ) a}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {F \left (-\frac {-1+y \ln \left (x \right )}{y}\right ) y^{2}}{x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-2 x^{2}+x +F \left (y+x^{2}-x \right )}{x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 a}{x^{2} \left (-y+2 F \left (\frac {x y^{2}-4 a}{x}\right ) a \right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y+F \left (\frac {y}{x}\right )}{x -1}
\] |
[[_homogeneous, ‘class D‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {F \left (-\frac {2 y \ln \left (x \right )-1}{y}\right ) y^{2}}{x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y^{2} \left (2 x -F \left (-\frac {-2+x y}{2 y}\right )\right )}{4 x}
\] |
[NONE] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{\sqrt {y}+F \left (\frac {x -y}{\sqrt {y}}\right )}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\left (y \,{\mathrm e}^{-\frac {x^{2}}{4}} x +2 F \left (y \,{\mathrm e}^{-\frac {x^{2}}{4}}\right )\right ) {\mathrm e}^{\frac {x^{2}}{4}}}{2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {-x^{2}+2 x^{3} y-F \left (\left (x y-1\right ) x \right )}{x^{4}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}+2 x y+x^{2}+{\mathrm e}^{2 F \left (-\left (x -y\right ) \left (x +y\right )\right )}}{y^{2}+2 x y+x^{2}-{\mathrm e}^{2 F \left (-\left (x -y\right ) \left (x +y\right )\right )}}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1}{y+\sqrt {x}}
\] |
[[_homogeneous, ‘class G‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1}{y+2+\sqrt {3 x +1}}
\] |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{y+x^{{3}/{2}}}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{{5}/{3}}}{y+x^{{4}/{3}}}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\left (-1+y \ln \left (x \right )\right )^{2}}{x}
\] |
[_Riccati] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x \left (-2+3 \sqrt {x^{2}+3 y}\right )}{3}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\left (2 y \ln \left (x \right )-1\right )^{2}}{x}
\] |
[_Riccati] |
✓ |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{b x}}{y \,{\mathrm e}^{-b x}+1}
\] |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{2} \left (1+2 \sqrt {x^{3}-6 y}\right )}{2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{x}}{y \,{\mathrm e}^{-x}+1}
\] |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{\frac {2 x}{3}}}{y \,{\mathrm e}^{-\frac {2 x}{3}}+1}
\] |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x \left (x +2 \sqrt {x^{3}-6 y}\right )}{2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime } = \left (-\ln \left (y\right )+x^{2}\right ) y
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x \left (-2+3 x \sqrt {x^{2}+3 y}\right )}{3}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime } = \left (-\ln \left (y\right )+x \right ) y
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{3}+x^{2}+2 \sqrt {x^{3}-6 y}}{2 x +2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {x}{4}+\frac {1}{4}+x \sqrt {x^{2}-2 x +1+8 y}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {x}{2}-\frac {a}{2}+x \sqrt {x^{2}+2 a x +a^{2}+4 y}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\left (\ln \left (y\right )+x^{2}\right ) y}{x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+1+x \sqrt {x^{2}-4 x +4 y}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {2 x^{2}+2 x -3 \sqrt {x^{2}+3 y}}{3 \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{3} {\mathrm e}^{-\frac {4 x}{3}}}{y \,{\mathrm e}^{-\frac {2 x}{3}}+1}
\] |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\left (\ln \left (y\right )+x^{3}\right ) y}{x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {x}{4}+\frac {1}{4}+x^{2} \sqrt {x^{2}-2 x +1+8 y}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {x^{2}-1-4 \sqrt {x^{2}-2 x +1+8 y}}{4 \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {a x}{2}-\frac {b}{2}+x \sqrt {a^{2} x^{2}+2 a b x +b^{2}+4 a y-4 c}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {x}{2}-\frac {a}{2}+x^{2} \sqrt {x^{2}+2 a x +a^{2}+4 y}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {a x}{2}-\frac {b}{2}+x^{2} \sqrt {a^{2} x^{2}+2 a b x +b^{2}+4 a y-4 c}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x}{2}+\frac {1}{2}+x^{2} \sqrt {x^{2}+2 x +1-4 y}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+1+x^{2} \sqrt {x^{2}-4 x +4 y}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime } = \left (-\ln \left (y\right )+1+x^{2}+x^{3}\right ) y
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{3} {\mathrm e}^{-2 b x}}{y \,{\mathrm e}^{-b x}+1}
\] |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{3} {\mathrm e}^{-2 x}}{y \,{\mathrm e}^{-x}+1}
\] |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {x^{2}-x -2-2 \sqrt {x^{2}-4 x +4 y}}{2 \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{2}+2 x +1+2 \sqrt {x^{2}+2 x +1-4 y}}{2 x +2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 a}{x \left (-x y+2 a x y^{2}-8 a^{2}\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y \left (-1+\ln \left (x \left (x +1\right )\right ) y x^{4}-\ln \left (x \left (x +1\right )\right ) x^{3}\right )}{x}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \left (1+y^{2} {\mathrm e}^{-2 b x}+y^{3} {\mathrm e}^{-3 b x}\right ) {\mathrm e}^{b x}
\] |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
|
|
\[
{}y^{\prime } = \left (1+y^{2} {\mathrm e}^{-\frac {4 x}{3}}+y^{3} {\mathrm e}^{-2 x}\right ) {\mathrm e}^{\frac {2 x}{3}}
\] |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
|
|
\[
{}y^{\prime } = \left (1+y^{2} {\mathrm e}^{-2 x}+y^{3} {\mathrm e}^{-3 x}\right ) {\mathrm e}^{x}
\] |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y \left (1-x +y x^{2} \ln \left (x \right )+x^{3} y-x \ln \left (x \right )-x^{2}\right )}{\left (x -1\right ) x}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\left (\ln \left (y\right )+x +x^{3}+x^{4}\right ) y}{x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-\ln \left (x \right )+{\mathrm e}^{\frac {1}{x}}+4 x^{2} y+2 x +2 x y^{2}+2 x^{3}}{\ln \left (x \right )-{\mathrm e}^{\frac {1}{x}}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-b y a +b^{2}+a b +b^{2} x -b a \sqrt {x}-a^{2}}{a \left (-a y+b +a +b x -a \sqrt {x}\right )}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y \left (-\ln \left (\frac {1}{x}\right )+{\mathrm e}^{x}+y x^{2} \ln \left (x \right )+x^{3} y-x \ln \left (x \right )-x^{2}\right )}{\left (-\ln \left (\frac {1}{x}\right )+{\mathrm e}^{x}\right ) x}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {x^{2}+x +a x +a -2 \sqrt {x^{2}+2 a x +a^{2}+4 y}}{2 \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y \left (-{\mathrm e}^{x}+\ln \left (2 x \right ) x^{2} y-\ln \left (2 x \right ) x \right ) {\mathrm e}^{-x}}{x}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\left (18 x^{{3}/{2}}+36 y^{2}-12 x^{3} y+x^{6}\right ) \sqrt {x}}{36}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y^{3}}{\left (-1+2 y \ln \left (x \right )-y\right ) x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 a}{y+2 a y^{4}-16 a^{2} x y^{2}+32 a^{3} x^{2}}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y^{3}}{\left (-1+y \ln \left (x \right )-y\right ) x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-\ln \left (x \right )+2 \ln \left (2 x \right ) x y+\ln \left (2 x \right )+\ln \left (2 x \right ) y^{2}+\ln \left (2 x \right ) x^{2}}{\ln \left (x \right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {b y a -b c +b^{2} x +b a \sqrt {x}-a^{2}}{a \left (a y-c +b x +a \sqrt {x}\right )}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1+2 y}{x \left (-2+x y^{2}+2 x y^{3}\right )}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\left (2 y \ln \left (x \right )-1\right )^{3}}{\left (-1+2 y \ln \left (x \right )-y\right ) x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x^{2}+2 x +x^{4}-2 x^{2} y-1+y^{2}}{x +1}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 a}{-x^{2} y+2 a y^{4} x^{2}-16 a^{2} x y^{2}+32 a^{3}}
\] |
[‘y=_G(x,y’)‘] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1+2 y}{x \left (-2+x y+2 x y^{2}\right )}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\left (-1+y \ln \left (x \right )\right )^{3}}{\left (-1+y \ln \left (x \right )-y\right ) x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y \left (\tan \left (x \right )+\ln \left (2 x \right ) x -\ln \left (2 x \right ) x^{2} y\right )}{x \tan \left (x \right )}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\left (\ln \left (y\right ) x +\ln \left (y\right )+x^{4}\right ) y}{x \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{{3}/{2}}}{y^{{3}/{2}}+x^{2}-2 x y+y^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-4 x y+x^{3}+2 x^{2}-4 x -8}{-8 y+2 x^{2}+4 x -8}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-4 x y-x^{3}+4 x^{2}-4 x +8}{8 y+2 x^{2}-8 x +8}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\left (\ln \left (y\right ) x +\ln \left (y\right )+x \right ) y}{x \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y \left (-\ln \left (x \right )-x \ln \left (\frac {\left (x -1\right ) \left (x +1\right )}{x}\right )+\ln \left (\frac {\left (x -1\right ) \left (x +1\right )}{x}\right ) x^{2} y\right )}{x \ln \left (x \right )}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-8 x y-x^{3}+2 x^{2}-8 x +32}{32 y+4 x^{2}-8 x +32}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y \left (y+1\right )}{x \left (-y-1+x y\right )}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-4 a x y-a^{2} x^{3}-2 a \,x^{2} b -4 a x +8}{8 y+2 a \,x^{2}+4 b x +8}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x y+x +y^{2}}{\left (x -1\right ) \left (x +y\right )}
\] |
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-4 x y-x^{3}-2 a \,x^{2}-4 x +8}{8 y+2 x^{2}+4 a x +8}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x -y+\sqrt {y}}{x -y+\sqrt {y}+1}
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y \left (-\ln \left (\frac {1}{x}\right )-\ln \left (\frac {x^{2}+1}{x}\right ) x +\ln \left (\frac {x^{2}+1}{x}\right ) x^{2} y\right )}{x \ln \left (\frac {1}{x}\right )}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y \left (y+1\right )}{x \left (-y-1+x y^{4}\right )}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{3} y+x^{3}+x y^{2}+y^{3}}{\left (x -1\right ) x^{3}}
\] |
[[_homogeneous, ‘class D‘], _rational, _Abel] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y \left (-\tanh \left (\frac {1}{x}\right )-\ln \left (\frac {x^{2}+1}{x}\right ) x +\ln \left (\frac {x^{2}+1}{x}\right ) x^{2} y\right )}{x \tanh \left (\frac {1}{x}\right )}
\] |
[_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] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-\sinh \left (x \right )+x^{2} \ln \left (x \right )+2 y \ln \left (x \right ) x +\ln \left (x \right )+y^{2} \ln \left (x \right )}{\sinh \left (x \right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {\ln \left (x \right )-\sinh \left (x \right ) x^{2}-2 \sinh \left (x \right ) x y-\sinh \left (x \right )-\sinh \left (x \right ) y^{2}}{\ln \left (x \right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y \left (\ln \left (x -1\right )+\coth \left (x +1\right ) x -\coth \left (x +1\right ) x^{2} y\right )}{x \ln \left (x -1\right )}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {\ln \left (x -1\right )-\coth \left (x +1\right ) x^{2}-2 \coth \left (x +1\right ) x y-\coth \left (x +1\right )-\coth \left (x +1\right ) y^{2}}{\ln \left (x -1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y \left (-\cosh \left (\frac {1}{x +1}\right ) x +\cosh \left (\frac {1}{x +1}\right )-x +x^{2} y-x^{2}+x^{3} y\right )}{x \left (x -1\right ) \cosh \left (\frac {1}{x +1}\right )}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y \left (x y+1\right )}{x \left (x y+1-y\right )}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{3}+3 a \,x^{2}+3 a^{2} x +a^{3}+x y^{2}+y^{2} a +y^{3}}{\left (x +a \right )^{3}}
\] |
[[_homogeneous, ‘class C‘], _rational, _Abel] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y \left (-1-\cosh \left (\frac {x +1}{x -1}\right ) x +\cosh \left (\frac {x +1}{x -1}\right ) x^{2} y-\cosh \left (\frac {x +1}{x -1}\right ) x^{2}+\cosh \left (\frac {x +1}{x -1}\right ) x^{3} y\right )}{x}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y \left (-1-x \,{\mathrm e}^{\frac {x +1}{x -1}}+x^{2} {\mathrm e}^{\frac {x +1}{x -1}} y-{\mathrm e}^{\frac {x +1}{x -1}} x^{2}+x^{3} {\mathrm e}^{\frac {x +1}{x -1}} y\right )}{x}
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-b^{3}+6 b^{2} x -12 b \,x^{2}+8 x^{3}-4 b y^{2}+8 x y^{2}+8 y^{3}}{\left (2 x -b \right )^{3}}
\] |
[[_homogeneous, ‘class C‘], _rational, _Abel] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\left (y \,{\mathrm e}^{-\frac {x^{2}}{4}} x +2+2 y^{2} {\mathrm e}^{-\frac {x^{2}}{2}}+2 y^{3} {\mathrm e}^{-\frac {3 x^{2}}{4}}\right ) {\mathrm e}^{\frac {x^{2}}{4}}}{2}
\] |
[_Abel] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\left (1+2 y\right ) \left (y+1\right )}{x \left (-2 y-2+x +2 x y\right )}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-125+300 x -240 x^{2}+64 x^{3}-80 y^{2}+64 x y^{2}+64 y^{3}}{\left (4 x -5\right )^{3}}
\] |
[[_homogeneous, ‘class C‘], _rational, _Abel] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x \left (-1+x y+x y^{3}+x y^{4}\right )}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y \left (x^{3}+x^{2} y+y^{2}\right )}{x^{2} \left (x -1\right ) \left (x +y\right )}
\] |
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\left (1+2 y\right ) \left (y+1\right )}{x \left (-2 y-2+x y^{3}+2 x y^{4}\right )}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\left ({\mathrm e}^{-\frac {y}{x}} y+x \,{\mathrm e}^{-\frac {y}{x}}+x^{2}\right ) {\mathrm e}^{\frac {y}{x}}}{x}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\left ({\mathrm e}^{-\frac {y}{x}} y+x \,{\mathrm e}^{-\frac {y}{x}}+x^{3}\right ) {\mathrm e}^{\frac {y}{x}}}{x}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {b^{3}+y^{2} b^{3}+2 y b^{2} a x +x^{2} b \,a^{2}+y^{3} b^{3}+3 y^{2} b^{2} a x +3 y b \,a^{2} x^{2}+a^{3} x^{3}}{b^{3}}
\] |
[[_homogeneous, ‘class C‘], _Abel] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\alpha ^{3}+y^{2} \alpha ^{3}+2 y \alpha ^{2} \beta x +\alpha \,\beta ^{2} x^{2}+y^{3} \alpha ^{3}+3 y^{2} \alpha ^{2} \beta x +3 y \alpha \,\beta ^{2} x^{2}+\beta ^{3} x^{3}}{\alpha ^{3}}
\] |
[[_homogeneous, ‘class C‘], _Abel] |
✓ |
|
|
\[
{}y^{\prime } = \frac {a^{3}+y^{2} a^{3}+2 y a^{2} b x +a \,b^{2} x^{2}+y^{3} a^{3}+3 y^{2} a^{2} b x +3 y a \,b^{2} x^{2}+b^{3} x^{3}}{a^{3}}
\] |
[[_homogeneous, ‘class C‘], _Abel] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y \left ({\mathrm e}^{-\frac {x^{2}}{2}} x y+{\mathrm e}^{-\frac {x^{2}}{4}} x +2 y^{2} {\mathrm e}^{-\frac {3 x^{2}}{4}}\right ) {\mathrm e}^{\frac {x^{2}}{4}}}{2 y \,{\mathrm e}^{-\frac {x^{2}}{4}}+2}
\] |
[[_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {2 x}{3}+1+y^{2}+\frac {2 x^{2} y}{3}+\frac {x^{4}}{9}+y^{3}+x^{2} y^{2}+\frac {y x^{4}}{3}+\frac {x^{6}}{27}
\] |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
|
|
\[
{}y^{\prime } = 2 x +1+y^{2}-2 x^{2} y+x^{4}+y^{3}-3 x^{2} y^{2}+3 y x^{4}-x^{6}
\] |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1+2 y}{x \left (-2+x +x y^{2}+3 x y^{3}+2 x y+2 x y^{4}\right )}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y^{2} \left (x^{2} y-2 x -2 x y+y\right )}{2 \left (-2+x y-2 y\right ) x}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-2 x y+2 x^{3}-2 x -y^{3}+3 x^{2} y^{2}-3 y x^{4}+x^{6}}{-y+x^{2}-1}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {2 a}{-y-2 a -2 a y^{4}+16 a^{2} x y^{2}-32 a^{3} x^{2}-2 a y^{6}+24 y^{4} a^{2} x -96 y^{2} a^{3} x^{2}+128 a^{4} x^{3}}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-18 x y-6 x^{3}-18 x +27 y^{3}+27 x^{2} y^{2}+9 y x^{4}+x^{6}}{27 y+9 x^{2}+27}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x^{2}-4 x^{3} y+1+x^{4} y^{2}+x^{6} y^{3}-3 y^{2} x^{5}+3 y x^{4}-x^{3}}{x^{4}}
\] |
[_rational, _Abel] |
✓ |
|
|
\[
{}y^{\prime } = \frac {6 x^{2} y-2 x +1-5 x^{3} y^{2}-2 x y+y^{3} x^{4}}{x^{2} \left (x^{2} y-x +1\right )}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}+2 x y+x^{2}+{\mathrm e}^{-\frac {2}{-y^{2}+x^{2}-1}}}{y^{2}+2 x y+x^{2}-{\mathrm e}^{-\frac {2}{-y^{2}+x^{2}-1}}}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 a \left (-y^{2}+4 a x -1\right )}{-y^{3}+4 a x y-y-2 a y^{6}+24 y^{4} a^{2} x -96 y^{2} a^{3} x^{2}+128 a^{4} x^{3}}
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 a x}{-x^{3} y+2 a \,x^{3}+2 a y^{4} x^{3}-16 y^{2} a^{2} x^{2}+32 a^{3} x +2 a y^{6} x^{3}-24 y^{4} a^{2} x^{2}+96 y^{2} x \,a^{3}-128 a^{4}}
\] |
[_rational] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {-y^{3}-y+2 y^{2} \ln \left (x \right )-\ln \left (x \right )^{2} y^{3}-1+3 y \ln \left (x \right )-3 \ln \left (x \right )^{2} y^{2}+\ln \left (x \right )^{3} y^{3}}{y x}
\] |
[[_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 a \left (x y^{2}-4 a +x \right )}{-x^{3} y^{3}+4 a \,x^{2} y-x^{3} y+2 a y^{6} x^{3}-24 y^{4} a^{2} x^{2}+96 y^{2} x \,a^{3}-128 a^{4}}
\] |
[_rational] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {-y^{3}-y+4 y^{2} \ln \left (x \right )-4 \ln \left (x \right )^{2} y^{3}-1+6 y \ln \left (x \right )-12 \ln \left (x \right )^{2} y^{2}+8 \ln \left (x \right )^{3} y^{3}}{y x}
\] |
[[_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{{3}/{2}} \left (x -y+\sqrt {y}\right )}{y^{{3}/{2}} x -y^{{5}/{2}}+y^{2}+x^{3}-3 x^{2} y+3 x y^{2}-y^{3}}
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}}{y^{2}+y^{{3}/{2}}+\sqrt {y}\, x^{2}-2 y^{{3}/{2}} x +y^{{5}/{2}}+x^{3}-3 x^{2} y+3 x y^{2}-y^{3}}
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}+2 x y+x^{2}+{\mathrm e}^{-2 \left (x -y\right ) \left (x +y\right )}}{y^{2}+2 x y+x^{2}-{\mathrm e}^{-2 \left (x -y\right ) \left (x +y\right )}}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}+2 x y+x^{2}+{\mathrm e}^{2 \left (x -y\right )^{2} \left (x +y\right )^{2}}}{y^{2}+2 x y+x^{2}-{\mathrm e}^{2 \left (x -y\right )^{2} \left (x +y\right )^{2}}}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-8 y^{3} x^{2}+16 x y^{2}+16 x y^{3}-8+12 x y-6 x^{2} y^{2}+x^{3} y^{3}}{16 \left (-2+x y-2 y\right ) x}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {16 x y^{3}-8 y^{3}-8 y+8 x y^{2}-2 y^{3} x^{2}-8+12 x y-6 x^{2} y^{2}+x^{3} y^{3}}{32 y x}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-3 x^{2} y-2 x^{3}-2 x -x y^{2}-y+x^{3} y^{3}+3 x^{4} y^{2}+3 x^{5} y+x^{6}}{x \left (x y+x^{2}+1\right )}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x}{2}+1+y^{2}+\frac {x^{2} y}{4}-x y-\frac {x^{4}}{8}+\frac {x^{3}}{8}+\frac {x^{2}}{4}+y^{3}-\frac {3 x^{2} y^{2}}{4}-\frac {3 x y^{2}}{2}+\frac {3 y x^{4}}{16}+\frac {3 x^{3} y}{4}-\frac {x^{6}}{64}-\frac {3 x^{5}}{32}
\] |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+1+y^{2}+\frac {7 x^{2} y}{2}-2 x y+\frac {13 x^{4}}{16}-\frac {3 x^{3}}{2}+x^{2}+y^{3}+\frac {3 x^{2} y^{2}}{4}-3 x y^{2}+\frac {3 y x^{4}}{16}-\frac {3 x^{3} y}{2}+\frac {x^{6}}{64}-\frac {3 x^{5}}{16}
\] |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {x}{4}+1+y^{2}+\frac {7 x^{2} y}{16}-\frac {x y}{2}+\frac {5 x^{4}}{128}-\frac {5 x^{3}}{64}+\frac {x^{2}}{16}+y^{3}+\frac {3 x^{2} y^{2}}{8}-\frac {3 x y^{2}}{4}+\frac {3 y x^{4}}{64}-\frac {3 x^{3} y}{16}+\frac {x^{6}}{512}-\frac {3 x^{5}}{256}
\] |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-x^{2}+x +1+y^{2}+5 x^{2} y-2 x y+4 x^{4}-3 x^{3}+y^{3}+3 x^{2} y^{2}-3 x y^{2}+3 y x^{4}-6 x^{3} y+x^{6}-3 x^{5}}{x}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-32 x y+16 x^{3}+16 x^{2}-32 x -64 y^{3}+48 x^{2} y^{2}+96 x y^{2}-12 y x^{4}-48 x^{3} y-48 x^{2} y+x^{6}+6 x^{5}+12 x^{4}}{-64 y+16 x^{2}+32 x -64}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-32 x y-72 x^{3}+32 x^{2}-32 x +64 y^{3}+48 x^{2} y^{2}-192 x y^{2}+12 y x^{4}-96 x^{3} y+192 x^{2} y+x^{6}-12 x^{5}+48 x^{4}}{64 y+16 x^{2}-64 x +64}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y^{2}+2 x y+x^{2}+{\mathrm e}^{\frac {2 \left (x -y\right )^{3} \left (x +y\right )^{3}}{-y^{2}+x^{2}-1}}}{-y^{2}-2 x y-x^{2}+{\mathrm e}^{\frac {2 \left (x -y\right )^{3} \left (x +y\right )^{3}}{-y^{2}+x^{2}-1}}}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-128 x y-24 x^{3}+32 x^{2}-128 x +512 y^{3}+192 x^{2} y^{2}-384 x y^{2}+24 y x^{4}-96 x^{3} y+96 x^{2} y+x^{6}-6 x^{5}+12 x^{4}}{512 y+64 x^{2}-128 x +512}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-32 a x y-8 a^{2} x^{3}-16 a \,x^{2} b -32 a x +64 y^{3}+48 x^{2} a y^{2}+96 y^{2} b x +12 y a^{2} x^{4}+48 y a \,x^{3} b +48 y b^{2} x^{2}+a^{3} x^{6}+6 a^{2} x^{5} b +12 a \,x^{4} b^{2}+8 b^{3} x^{3}}{64 y+16 a \,x^{2}+32 b x +64}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-32 x y-8 x^{3}-16 a \,x^{2}-32 x +64 y^{3}+48 x^{2} y^{2}+96 a x y^{2}+12 y x^{4}+48 y a \,x^{3}+48 a^{2} x^{2} y+x^{6}+6 x^{5} a +12 a^{2} x^{4}+8 a^{3} x^{3}}{64 y+16 x^{2}+32 a x +64}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{2} y+x^{4}+2 x^{3}-3 x^{2}+x y+x +y^{3}+3 x^{2} y^{2}-3 x y^{2}+3 y x^{4}-6 x^{3} y+x^{6}-3 x^{5}}{x \left (y+x^{2}-x +1\right )}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {a x}{2}+1+y^{2}+\frac {a \,x^{2} y}{2}+b x y+\frac {a^{2} x^{4}}{16}+\frac {a \,x^{3} b}{4}+\frac {b^{2} x^{2}}{4}+y^{3}+\frac {3 x^{2} a y^{2}}{4}+\frac {3 y^{2} b x}{2}+\frac {3 y a^{2} x^{4}}{16}+\frac {3 y a \,x^{3} b}{4}+\frac {3 y b^{2} x^{2}}{4}+\frac {a^{3} x^{6}}{64}+\frac {3 a^{2} x^{5} b}{32}+\frac {3 a \,x^{4} b^{2}}{16}+\frac {b^{3} x^{3}}{8}
\] |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+1+y^{2}+\frac {x^{2} y}{2}+a x y+\frac {x^{4}}{16}+\frac {a \,x^{3}}{4}+\frac {a^{2} x^{2}}{4}+y^{3}+\frac {3 x^{2} y^{2}}{4}+\frac {3 a x y^{2}}{2}+\frac {3 y x^{4}}{16}+\frac {3 y a \,x^{3}}{4}+\frac {3 a^{2} x^{2} y}{4}+\frac {x^{6}}{64}+\frac {3 x^{5} a}{32}+\frac {3 a^{2} x^{4}}{16}+\frac {a^{3} x^{3}}{8}
\] |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}+2 x y+x^{2}+{\mathrm e}^{2+2 y^{4}-4 x^{2} y^{2}+2 x^{4}+2 y^{6}-6 x^{2} y^{4}+6 x^{4} y^{2}-2 x^{6}}}{y^{2}+2 x y+x^{2}-{\mathrm e}^{2+2 y^{4}-4 x^{2} y^{2}+2 x^{4}+2 y^{6}-6 x^{2} y^{4}+6 x^{4} y^{2}-2 x^{6}}}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right ) x +y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )+y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x +y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )-\sin \left (\frac {y}{x}\right ) y x -y \sin \left (\frac {y}{x}\right )+2 \sin \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x}{2 \cos \left (\frac {y}{x}\right ) \sin \left (\frac {y}{2 x}\right ) x \cos \left (\frac {y}{2 x}\right ) \left (x +1\right )}
\] |
[[_homogeneous, ‘class D‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\left (x y+1\right )^{3}}{x^{5}}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
|
|
\[
{}y^{\prime } = y \left (y^{2}+y \,{\mathrm e}^{b x}+{\mathrm e}^{2 b x}\right ) {\mathrm e}^{-2 b x}
\] |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
|
|
\[
{}y^{\prime } = y^{3}-3 x^{2} y^{2}+3 y x^{4}-x^{6}+2 x
\] |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
|
|
\[
{}y^{\prime } = y^{3}+x^{2} y^{2}+\frac {y x^{4}}{3}+\frac {x^{6}}{27}-\frac {2 x}{3}
\] |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{3}-3 x y^{2}+3 x^{2} y-x^{3}+x}{x}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Abel] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y \,{\mathrm e}^{-\frac {x^{2}}{2}} \left (2 y^{2}+2 y \,{\mathrm e}^{\frac {x^{2}}{4}}+2 \,{\mathrm e}^{\frac {x^{2}}{2}}+x \,{\mathrm e}^{\frac {x^{2}}{2}}\right )}{2}
\] |
[_Abel] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{3}-3 x y^{2}+3 x^{2} y-x^{3}+x^{2}}{\left (x -1\right ) \left (x +1\right )}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\left (x y+1\right ) \left (x^{2} y^{2}+x^{2} y+2 x y+1+x +x^{2}\right )}{x^{5}}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\left (y-x +\ln \left (x +1\right )\right )^{2}+x}{x +1}
\] |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = f \left (y\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = f \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = a \,x^{n} y^{2}+b \,x^{-n -2}
\] |
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = x^{2} a y^{2}+b
\] |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
|
|
\[
{}x^{4} y^{\prime } = -x^{4} y^{2}-a^{2}
\] |
[_rational, [_Riccati, _special]] |
✓ |
|
|
\[
{}\left (a \,x^{2}+b x +c \right )^{2} \left (y^{\prime }+y^{2}\right )+A = 0
\] |
[_rational, _Riccati] |
✓ |
|
|
\[
{}x y^{\prime } = a \,x^{n} y^{2}+b y+c \,x^{-n}
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
|
|
\[
{}\left (a x +c \right ) y^{\prime } = \alpha \left (b x +a y\right )^{2}+\beta \left (b x +a y\right )-b x +\gamma
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Riccati] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = x^{2} a y^{2}+b x y+c
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
|
|
\[
{}\left (a \,x^{2}+b \right ) y^{\prime }+y^{2}-2 x y+\left (-a +1\right ) x^{2}-b = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
|
|
\[
{}\left (a \,x^{2}+b x +c \right ) y^{\prime } = y^{2}+\left (2 \lambda x +b \right ) y+\lambda \left (\lambda -a \right ) x^{2}+\mu
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
|
|
\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime }+k \left (x +y-a \right ) \left (x +y-b \right )+y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = a \,{\mathrm e}^{\lambda x} y^{2}+b y+c \,{\mathrm e}^{-\lambda x}
\] |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = a \,{\mathrm e}^{\lambda x} y^{2}+b \,{\mathrm e}^{-\lambda x}
\] |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
|
|
\[
{}x y^{\prime } = \left (a y+b \ln \left (x \right )\right )^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
|
|
\[
{}y^{\prime } y-y = A
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } y-y = A x +B
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } y = \frac {y}{\sqrt {a x +b}}+1
\] |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } y = \left (3 a x +b \right ) y-a^{2} x^{3}-a \,x^{2} b +c x
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (A y+B x +a \right ) y^{\prime }+B y+k x +b = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (y+a x +b \right ) y^{\prime } = \alpha y+\beta x +\gamma
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\frac {y^{2}-2 x^{2}}{x y^{2}-x^{3}}+\frac {\left (2 y^{2}-x^{2}\right ) y^{\prime }}{y^{3}-x^{2} y} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\frac {1}{\sqrt {y^{2}+x^{2}}}+\left (\frac {1}{y}-\frac {x}{y \sqrt {y^{2}+x^{2}}}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}y+x +x y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}6 x -2 y+1+\left (2 y-2 x -3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{2}-x^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}{\mathrm e}^{\frac {y}{x}} x +y-x y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}2 x^{2} y+3 y^{3}-\left (x^{3}+2 x y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{2}-x y+x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x^{2} y+y^{3}-x^{3} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{3}+x^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x +y \cos \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}4 x +3 y+1+\left (x +y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}4 x -y+2+\left (x +y+3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x +y-\left (4 x +2 y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y+2 x y^{2}-y^{3} x^{2}+2 x^{2} y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
|
|
\[
{}2 y+3 x y^{2}+\left (2 x^{2} y+x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y+x y^{2}+\left (x -x^{2} y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime }-\frac {2 y}{x +1} = \left (x +1\right )^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+\left (-2 x +1\right ) y = x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y+1}{x +1} = \sqrt {y+1}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{4} y \left (3 y+2 x y^{\prime }\right )+x^{2} \left (4 y+3 x y^{\prime }\right ) = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{2} \left (3 y-6 x y^{\prime }\right )-x \left (y-2 x y^{\prime }\right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 x^{3} y-y^{2}-\left (2 x^{4}+x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{2}-x y+x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x +y-\left (x -y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2}+y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x -y^{2}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}3 x^{2}+6 x y+3 y^{2}+\left (2 x^{2}+3 x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x^{3} y-y^{4}+\left (x y^{3}-x^{4}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{2}-x^{2}+2 m y x +\left (m y^{2}-m \,x^{2}-2 x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }-y+2 x^{2} y-x^{3} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x +y\right ) y^{\prime }-1 = 0
\] |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}x +y^{\prime } y+y-x y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\sqrt {1-y^{2}}+\sqrt {-x^{2}+1}\, y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-x^{2} y = x^{5}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (y-x \right )^{2} y^{\prime } = 1
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}\left (y-x \right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}-y+x y^{\prime } = \sqrt {y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}-y+x y^{\prime } = \sqrt {x^{2}-y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \sin \left (\frac {y}{x}\right )-y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x -2 y+5+\left (2 x -y+4\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }-x y = a x y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{2} \left (x y^{\prime }+3 y\right )-2 y+x y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+y = \arctan \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}5 x y-3 y^{3}+\left (3 x^{2}-7 x y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}x y^{2}+y-x y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}3 x^{2} y+\left (x^{3}+x^{3} y^{2}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 x +3 y-1+\left (2 x +3 y-5\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{3}-2 x^{2} y+\left (2 x y^{2}-x^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (y^{2}+x^{2}\right ) \left (x +y^{\prime } y\right )+\sqrt {x^{2}+y^{2}+1}\, \left (y-x y^{\prime }\right ) = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}1+{\mathrm e}^{\frac {y}{x}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }-y^{2} \ln \left (x \right )+y = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}\left (2 \sqrt {x y}-x \right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+x y = 0
\] |
[_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] |
✓ |
|
|
\[
{}2 x y^{\prime }-y+\ln \left (y^{\prime }\right ) = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = y^{2}+x^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
|
|
\[
{}x +y^{\prime } y \left (2 {y^{\prime }}^{2}+3\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y = 2 x y^{\prime }+y^{2} {y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (-y+x y^{\prime }\right ) \left (x +y^{\prime } y\right ) = a^{2} y^{\prime }
\] |
[_rational] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-2 \left (x y+2 y^{\prime }\right ) y^{\prime }+y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime } = \frac {2 x}{t}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime } = -\frac {t}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime } = -x^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime } = {\mathrm e}^{-x}
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime }+2 x = t^{2}+4 t +7
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}2 x^{\prime } t = x
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime } = x \left (1-\frac {x}{4}\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime } = \sqrt {x}
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime } = {\mathrm e}^{-2 x}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 1+y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}u^{\prime } = \frac {1}{5-2 u}
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime } = a x+b
\] |
[_quadrature] |
✓ |
|
|
\[
{}Q^{\prime } = \frac {Q}{4+Q^{2}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime } = {\mathrm e}^{x^{2}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = r \left (a -y\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime } = \frac {2 x}{t +1}
\] |
[_separable] |
✓ |
|
|
\[
{}\left (2 u+1\right ) u^{\prime }-t -1 = 0
\] |
[_separable] |
✓ |
|
|
\[
{}R^{\prime } = \left (t +1\right ) \left (1+R^{2}\right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y+\frac {1}{y} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}\left (t +1\right ) x^{\prime }+x^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1}{2 y+1}
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime } = \left (4 t -x\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
|
|
\[
{}x^{\prime } = 2 t x^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime } = t^{2} {\mathrm e}^{-x}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime } = x \left (x+4\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime } = {\mathrm e}^{t +x}
\] |
[_separable] |
✓ |
|
|
\[
{}T^{\prime } = 2 a t \left (T^{2}-a^{2}\right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 t y^{2}}{t^{2}+1}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime } = 6 t \left (x-1\right )^{{2}/{3}}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime } = \frac {4 t^{2}+3 x^{2}}{2 x t}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{\prime } {\mathrm e}^{2 t}+2 x \,{\mathrm e}^{2 t} = {\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}+2 t y}{t^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = -y^{2} {\mathrm e}^{-t^{2}}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime } = -\frac {2 x}{t}+t
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}x^{\prime }+2 x t = {\mathrm e}^{-t^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}x^{\prime } t = -x+t^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}\theta ^{\prime } = -a \theta +{\mathrm e}^{t b}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}\left (t^{2}+1\right ) x^{\prime } = -3 x t +6 t
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime }+\frac {5 x}{t} = t +1
\] |
[_linear] |
✓ |
|
|
\[
{}x^{\prime } = \left (a +\frac {b}{t}\right ) x
\] |
[_separable] |
✓ |
|
|
\[
{}N^{\prime } = N-9 \,{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}\cos \left (\theta \right ) v^{\prime }+v = 3
\] |
[_separable] |
✓ |
|
|
\[
{}R^{\prime } = \frac {R}{t}+t \,{\mathrm e}^{-t}
\] |
[_linear] |
✓ |
|
|
\[
{}x^{\prime } = 2 x t
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime } = \left (t +x\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
|
|
\[
{}x^{\prime } = a x+b
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime }+p \left (t \right ) x = 0
\] |
[_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] |
✓ |
|
|
\[
{}x^{3}+3 t x^{2} x^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x+3 t x^{2} x^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2}-t^{2} x^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}t \cot \left (x\right ) x^{\prime } = -2
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y = x +1
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}2 x y y^{\prime }+x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{\prime }+y = x^{3} y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+3 y = 3 x^{2} {\mathrm e}^{-3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+4 x y = 8 x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y = 2 x \,{\mathrm e}^{-x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y = 2 x \,{\mathrm e}^{-x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}}{-2+x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}3 x +2 y+\left (2 x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\frac {\left (2 s-1\right ) s^{\prime }}{t}+\frac {s-s^{2}}{t^{2}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\frac {3-y}{x^{2}}+\frac {\left (y^{2}-2 x \right ) y^{\prime }}{x y^{2}} = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
|
|
\[
{}\frac {1+8 x y^{{2}/{3}}}{x^{{2}/{3}} y^{{1}/{3}}}+\frac {\left (2 x^{{4}/{3}} y^{{2}/{3}}-x^{{1}/{3}}\right ) y^{\prime }}{y^{{4}/{3}}} = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
|
|
\[
{}4 x +3 y^{2}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{2}+2 x y-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y+x \left (y^{2}+x^{2}\right )^{2}+\left (y \left (y^{2}+x^{2}\right )^{2}-x \right ) y^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
|
|
\[
{}4 x y+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y+2 x +y+2+\left (x^{2}+2 x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 r \left (s^{2}+1\right )+\left (r^{4}+1\right ) s^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\tan \left (\theta \right )+2 r \theta ^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x +y-x y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}2 x y+3 y^{2}-\left (x^{2}+2 x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}v^{3}+\left (u^{3}-u v^{2}\right ) v^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \tan \left (\frac {y}{x}\right )+y-x y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (2 s^{2}+2 s t +t^{2}\right ) s^{\prime }+s^{2}+2 s t -t^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}x^{3}+y^{2} \sqrt {y^{2}+x^{2}}-x y \sqrt {y^{2}+x^{2}}\, y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y+2+y \left (4+x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2}+3 y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x -5 y+\left (4 x -y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 x^{2}+9 x y+5 y^{2}-\left (6 x^{2}+4 x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x +2 y+\left (2 x -y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 x -y-\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2}+2 y^{2}+\left (4 x y-y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}2 x^{2}+2 x y+y^{2}+\left (x^{2}+2 x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime }+\frac {3 y}{x} = 6 x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}x^{4} y^{\prime }+2 x^{3} y = 1
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+3 y = 3 x^{2} {\mathrm e}^{-3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+4 x y = 8 x
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime }+\frac {x}{t^{2}} = \frac {1}{t^{2}}
\] |
[_separable] |
✓ |
|
|
\[
{}\left (u^{2}+1\right ) v^{\prime }+4 v u = 3 u
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{x} = -\frac {y^{2}}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime }+y = -2 x^{6} y^{4}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{\prime }-2 y = 2 x^{4}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+3 x^{2} y = x^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}2 x \left (y+1\right )-\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{2 x} = \frac {x}{y^{3}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}a y^{\prime }+b y = k \,{\mathrm e}^{-\lambda x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \left (1-x \right ) y^{2}+\left (2 x -1\right ) y-x
\] |
[_Riccati] |
✓ |
|
|
\[
{}y^{\prime } = -8 x y^{2}+4 x \left (1+4 x \right ) y-8 x^{3}-4 x^{2}+1
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
|
|
\[
{}6 x^{2} y-\left (x^{3}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (3 x^{2} y^{2}-x \right ) y^{\prime }+2 x y^{3}-y = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
|
|
\[
{}y-1+x \left (x +1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2}-2 y+x y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}3 x -5 y+\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}{\mathrm e}^{2 x} y^{2}+\left ({\mathrm e}^{2 x} y-2 y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}8 x^{3} y-12 x^{3}+\left (x^{4}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 x^{2}+x y+y^{2}+2 x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = \frac {4 x^{3} y^{2}-3 x^{2} y}{x^{3}-2 y x^{4}}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime }+x y = {\mathrm e}^{-x}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x -7 y}{3 y-8 x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+x y = x y^{3}
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime }+6 x^{2} y = 6 x^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x^{2}+y^{2}}{2 x y-x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x^{2}+y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 y^{2}+8+\left (-x^{2}+1\right ) y y^{\prime } = 0
\] |
[_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] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x +7 y}{2 x -2 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x y}{x^{2}+1}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+x y = \frac {y^{3}}{x}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}4 x y^{2}+6 y+\left (5 x^{2} y+8 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}8 y^{3} x^{2}-2 y^{4}+\left (5 x^{3} y^{2}-8 x y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}5 x +2 y+1+\left (2 x +y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 x -y+1-\left (6 x -2 y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x -2 y-3+\left (2 x +y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}10 x -4 y+12-\left (x +5 y+3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 x -y-6+\left (x +y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x +3 y+1+\left (4 x +6 y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}4 x +3 y+1+\left (x +y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x^{\prime } {\mathrm e}^{3 t}+3 x \,{\mathrm e}^{3 t} = {\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}x^{\prime } = -x+1
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime } = x \left (2-x\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime } = \left (1+x\right ) \left (2-x\right ) \sin \left (x\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime } = -x \left (-x+1\right ) \left (2-x\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime } = x^{2}-x^{4}
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime } = t^{3} \left (-x+1\right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \left (1+y^{2}\right ) \tan \left (x \right )
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime } = t^{2} x
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime } = -x^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{2} {\mathrm e}^{-t^{2}}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime }+p x = q
\] |
[_quadrature] |
✓ |
|
|
\[
{}x y^{\prime } = k y
\] |
[_separable] |
✓ |
|
|
\[
{}i^{\prime } = p \left (t \right ) i
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime } = \lambda x
\] |
[_quadrature] |
✓ |
|
|
\[
{}m v^{\prime } = -m g +k v^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime } = k x-x^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime } = -x \left (k^{2}+x^{2}\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{x} = x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}x^{\prime }+x t = 4 t
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime }+5 x = t
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}x y+y^{2}+x^{2}-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x^{\prime } = \frac {x^{2}+t \sqrt {t^{2}+x^{2}}}{x t}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x^{\prime } = k x-x^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}12 x +6 y-9+\left (5 x +2 y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y^{\prime } = y+\sqrt {y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }+y = x^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}y-x y^{\prime } = x^{2} y y^{\prime }
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x^{\prime }+3 x = {\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x -y}
\] |
[_separable] |
✓ |
|
|
\[
{}x \left (\ln \left (x \right )-\ln \left (y\right )\right ) y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}-\left (y^{2}+x^{2}\right ) y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} = 9 y^{4}
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime } = {\mathrm e}^{\frac {x}{t}}+\frac {x}{t}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y = x y^{\prime }+\frac {1}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x +y^{3}}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y-x -4}{2 x -y+5}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{x +1}+y^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 x +2 y-1+\left (x +y-2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \left (x -5 y\right )^{{1}/{3}}+2
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}\left (x -y\right ) y-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {3 x -4 y-2}{3 x -4 y-3}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-\frac {3 y}{x}+x^{3} y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}3 y^{2}-x +2 y \left (y^{2}-3 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}\left (x -y\right ) y-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +y-3}{y-x +1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y^{\prime }-y^{2} \ln \left (x \right )+y = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}\left (4 y+2 x +3\right ) y^{\prime }-2 y-x -1 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (y^{2}-x^{2}\right ) y^{\prime }+2 x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}3 x y^{2} y^{\prime }+y^{3}-2 x = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = 1+y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \cos \left (x +y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }+y = x y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } y = 1
\] |
[_quadrature] |
✓ |
|
|
\[
{}5 y^{\prime }-x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y \left (1-{y^{\prime }}^{2}\right ) = \left (x^{2}-y^{2}-a^{2}\right ) y^{\prime }
\] |
[_rational] |
✓ |
|
|
\[
{}y-x y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}1+y-\left (1-x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y-a +x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}z-\left (-a^{2}+t^{2}\right ) z^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1+y^{2}}{x^{2}+1}
\] |
[_separable] |
✓ |
|
|
\[
{}1+s^{2}-\sqrt {t}\, s^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}r^{\prime }+r \tan \left (t \right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }-\sqrt {1-y^{2}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\sqrt {-x^{2}+1}\, y^{\prime }-\sqrt {1-y^{2}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y-x +\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y+x +x y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x +y+\left (y-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}-y+x y^{\prime } = \sqrt {y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}8 y+10 x +\left (5 y+7 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 \sqrt {s t}-s+t s^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}t -s+t s^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{2} y^{\prime } = x^{3}+y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x \cos \left (\frac {y}{x}\right ) \left (x y^{\prime }+y\right ) = y \sin \left (\frac {y}{x}\right ) \left (-y+x y^{\prime }\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x +2 y+1-\left (4 y+2 x +3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x +2 y+1-\left (2 x -3\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\frac {y-x y^{\prime }}{\sqrt {y^{2}+x^{2}}} = m
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\frac {x +y^{\prime } y}{\sqrt {y^{2}+x^{2}}} = m
\] |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
|
|
\[
{}y+\frac {x}{y^{\prime }} = \sqrt {y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } y = -x +\sqrt {y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime }-\frac {2 y}{x +1} = \left (x +1\right )^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-\frac {a y}{x} = \frac {x +1}{x}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {n y}{x} = a \,x^{-n}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{-x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+\frac {\left (-2 x +1\right ) y}{x^{2}}-1 = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }-x y+a x y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime } = \left (y \ln \left (x \right )-2\right ) y
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}\left (y^{3}-x \right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
|
|
\[
{}\frac {x}{\left (x +y\right )^{2}}+\frac {\left (2 x +y\right ) y^{\prime }}{\left (x +y\right )^{2}} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}\frac {1}{x^{2}}+\frac {3 y^{2}}{x^{4}} = \frac {2 y y^{\prime }}{x^{3}}
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}\frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x +y^{\prime } y = \frac {y}{y^{2}+x^{2}}-\frac {x y^{\prime }}{y^{2}+x^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
|
|
\[
{}y = y^{\prime } y+y^{\prime }-{y^{\prime }}^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y = x y^{\prime }+y^{\prime }
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y}{x}-\sqrt {3}
\] |
[_linear] |
✓ |
|
|
\[
{}\frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }-x y-\alpha = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x \cos \left (\frac {y}{x}\right ) y^{\prime } = y \cos \left (\frac {y}{x}\right )-x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }-y^{2} \ln \left (x \right )+y = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}2 x +2 y-1+\left (x +y-2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}-y+x y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+\frac {1}{2 y} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{x} = 1
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+2 x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-y^{2} = 1
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }+3 y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}2 x y^{\prime }-y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-2 x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y = x^{2}+2 x -1
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = x \sqrt {y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x \ln \left (x \right )-\left (\ln \left (x \right )+1\right ) y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 1-y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y+1
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}-4
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 4-y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = x y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -x y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = x y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 1+y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}-3 y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x -y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \ln \left (x +y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x -y}{3 y+x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x y}{y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1}{x y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \ln \left (y-1\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \sqrt {\left (y+2\right ) \left (y-1\right )}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{y-x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x}{y^{2}}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \left (x y\right )^{{1}/{3}}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
|
|
\[
{}y^{\prime } = \sqrt {\frac {y-4}{x}}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y}{x}+y^{{1}/{4}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = 4 y-5
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }+3 y = 1
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = a y+b
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \cos \left (x \right )+\frac {y}{x}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y^{\prime } = 3 y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 1-y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -2 y+y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = x y+x
\] |
[_separable] |
✓ |
|
|
\[
{}x \,{\mathrm e}^{y}+y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y-x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 y^{\prime } y = 1
\] |
[_quadrature] |
✓ |
|
|
\[
{}2 x y y^{\prime }+y^{2} = -1
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1-x y}{x^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y \left (2 x +y\right )}{x \left (x +2 y\right )}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}}{1-x y}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } = 4 y+1
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x -1}+x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\sin \left (x^{2}\right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y}{x}+{\mathrm e}^{x}
\] |
[_linear] |
✓ |
|
|
\[
{}x -y^{\prime } y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y-x y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2}-y+x y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x y \left (1-y\right )-2 y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (2 x -1\right ) y+x \left (x +1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_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] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x}
\] |
[_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] |
✓ |
|
|
\[
{}y^{\prime } = \sqrt {\left (y+2\right ) \left (y-1\right )}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \sqrt {\left (y+2\right ) \left (y-1\right )}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{y-x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{y-x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x y}{y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x y}{y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y^{\prime }-i y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y+1}{t +1}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = t^{2} y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = t^{4} y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 y+1
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 2-y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-y}
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime } = 1+x^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 2 t y^{2}+3 y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {t}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = t y^{{1}/{3}}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1}{2 y+1}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y+1}{t}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y \left (1-y\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}v^{\prime } = t^{2} v-2-2 v+t^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1}{t y+t +y+1}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}-4
\] |
[_quadrature] |
✓ |
|
|
\[
{}w^{\prime } = \frac {w}{t}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \sec \left (y\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime } = -x t
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = t y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = t^{2} y^{3}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 2 y+1
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = t y^{2}+2 y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1-y^{2}}{y}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \left (1+y^{2}\right ) t
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1}{2 y+3}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 2 t y^{2}+3 t^{2} y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}+5}{y}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 1-2 y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 4 y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 2 y \left (1-y\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y+t +1
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = 3 y \left (1-y\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 2 y-t
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \left (t +1\right ) y
\] |
[_separable] |
✓ |
|
|
\[
{}S^{\prime } = S^{3}-2 S^{2}+S
\] |
[_quadrature] |
✓ |
|
|
\[
{}S^{\prime } = S^{3}-2 S^{2}+S
\] |
[_quadrature] |
✓ |
|
|
\[
{}S^{\prime } = S^{3}-2 S^{2}+S
\] |
[_quadrature] |
✓ |
|
|
\[
{}S^{\prime } = S^{3}-2 S^{2}+S
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}+y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}-y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{3}+y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = t y+t y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = t^{2}+t^{2} y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = t +t y
\] |
[_separable] |
✓ |
|
|
\[
{}\theta ^{\prime } = \frac {9}{10}-\frac {11 \cos \left (\theta \right )}{10}
\] |
[_quadrature] |
✓ |
|
|
\[
{}\theta ^{\prime } = \frac {11}{10}-\frac {9 \cos \left (\theta \right )}{10}
\] |
[_quadrature] |
✓ |
|
|
\[
{}v^{\prime } = -\frac {v}{R C}
\] |
[_quadrature] |
✓ |
|
|
\[
{}v^{\prime } = \frac {K -v}{R C}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 2 y+1
\] |
[_quadrature] |
✓ |
|
|
\[
{}w^{\prime } = \left (3-w\right ) \left (w+1\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}w^{\prime } = \left (3-w\right ) \left (w+1\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{\frac {2}{y}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{\frac {2}{y}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}-y^{3}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \sqrt {y}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 2-y
\] |
[_quadrature] |
✓ |
|
|
\[
{}\theta ^{\prime } = \frac {9}{10}-\frac {11 \cos \left (\theta \right )}{10}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y \left (-1+y\right ) \left (y-3\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y \left (-1+y\right ) \left (y-3\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y \left (-1+y\right ) \left (y-3\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = -y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{3}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1}{\left (y+1\right ) \left (t -2\right )}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1}{\left (2+y\right )^{2}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {t}{y-2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 3 y \left (y-2\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 3 y \left (y-2\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 3 y \left (y-2\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}-4 y-12
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}-4 y-12
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}-4 y-12
\] |
[_quadrature] |
✓ |
|
|
\[
{}w^{\prime } = w \cos \left (w\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}w^{\prime } = w \cos \left (w\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}w^{\prime } = w \cos \left (w\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}w^{\prime } = w \cos \left (w\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}w^{\prime } = w \cos \left (w\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}w^{\prime } = \left (1-w\right ) \sin \left (w\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1}{y-2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}v^{\prime } = -v^{2}-2 v-2
\] |
[_quadrature] |
✓ |
|
|
\[
{}w^{\prime } = 3 w^{3}-12 w^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 1+\cos \left (y\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \tan \left (y\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}w^{\prime } = \left (w^{2}-2\right ) \arctan \left (w\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}-4 y+2
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}-4 y+2
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}-4 y+2
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}-4 y+2
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}-4 y+2
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}-4 y+2
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y \cos \left (\frac {\pi y}{2}\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y-y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y \sin \left (\frac {\pi y}{2}\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{3}-y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \cos \left (\frac {\pi y}{2}\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}-y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y \sin \left (\frac {\pi y}{2}\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}-y^{3}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = -4 y+9 \,{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = -4 y+3 \,{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = 3 y-4 \,{\mathrm e}^{3 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{2}+4 \,{\mathrm e}^{\frac {t}{2}}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+2 y = {\mathrm e}^{\frac {t}{3}}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-2 y = 3 \,{\mathrm e}^{-2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-2 y = 7 \,{\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+2 y = 3 t^{2}+2 t -1
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+2 y = t^{2}+2 t +1+{\mathrm e}^{4 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-3 y = 2 t -{\mathrm e}^{4 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y}{t}+2
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {3 y}{t}+t^{5}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y}{t +1}+t^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = -2 t y+4 \,{\mathrm e}^{-t^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-\frac {2 t y}{t^{2}+1} = 3
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-\frac {2 y}{t} = t^{3} {\mathrm e}^{t}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y}{t +1}+2
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{t +1}+4 t^{2}+4 t
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y}{t}+2
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = -2 t y+4 \,{\mathrm e}^{-t^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-\frac {2 y}{t} = 2 t^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-\frac {3 y}{t} = 2 t^{3} {\mathrm e}^{2 t}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = -2 t y+4 \,{\mathrm e}^{-t^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+2 y = 3 \,{\mathrm e}^{-2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = 3 y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = -\sin \left (y\right )^{5}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \sin \left (y\right )^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y+{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = 3-2 y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = t y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 3 y+{\mathrm e}^{7 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {t y}{t^{2}+1}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = t +\frac {2 y}{t +1}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = 3+y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 2 y-y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = -3 y+{\mathrm e}^{-2 t}+t^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}x^{\prime } = -x t
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 3 y+2 \,{\mathrm e}^{3 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = t^{2} y^{3}+y^{3}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+5 y = 3 \,{\mathrm e}^{-5 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = 2 t y+3 t \,{\mathrm e}^{t^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = 2 t y^{2}+3 t^{2} y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}-2 y+1
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = t^{2} y+1+y+t^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y+1}{t}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 3-y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 3-\sin \left (y\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }+4 y = {\mathrm e}^{2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } y = 2 x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+3 x y = 6 x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-y^{3} = 8
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+x y^{2} = x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{3}-25 y+y^{\prime } = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}\left (-2+x \right ) y^{\prime } = y+3
\] |
[_separable] |
✓ |
|
|
\[
{}\left (y-2\right ) y^{\prime } = x -3
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+2 y-y^{2} = -2
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 2 \sqrt {y}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 3 y^{2}-y^{2} \sin \left (x \right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+4 y = 8
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }+x y = 4 x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+4 y = x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = x y-3 x -2 y+6
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \sin \left (x +y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}+9
\] |
[_quadrature] |
✓ |
|
|
\[
{}x y y^{\prime } = y^{2}+9
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1+y^{2}}{x^{2}+1}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{2 x -3 y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 x -1+2 x y-y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x y-4 x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-4 y = 2
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \sin \left (y\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 200 y-2 y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = x y-4 x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x y-3 x -2 y+6
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 3 y^{2}-y^{2} \sin \left (x \right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \tan \left (y\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = 1+y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}\left (y^{2}-1\right ) y^{\prime } = 4 x y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-y}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-y}+1
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 3 x y^{3}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-3 x^{2} y^{2} = -3 x^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-3 x^{2} y^{2} = 3 x^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 200 y-2 y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }-2 y = -10
\] |
[_quadrature] |
✓ |
|
|
\[
{}x y^{\prime } = y^{2}-y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}-1}{x y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 4 y+8
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y \sin \left (x \right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+4 y = y^{3}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }+2 y = 6
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }+2 y = 20 \,{\mathrm e}^{3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = 4 y+16 x
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-2 x y = x
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime }+3 y-10 x^{2} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime } = \sqrt {x}+3 y
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime }+\left (5 x +2\right ) y = \frac {20}{x}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-3 y = 6
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }+5 y = {\mathrm e}^{-3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}x y^{\prime }+3 y = 20 x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime } = y+x^{2} \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = x \left (3+3 x^{2}-y\right )
\] |
[_linear] |
✓ |
|
|
\[
{}-y+x y^{\prime } = x^{2} {\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1}{\left (3 x +3 y+2\right )^{2}}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\left (-2 y+3 x \right )^{2}+1}{-2 y+3 x}+\frac {3}{2}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\cos \left (-4 y+8 x -3\right ) y^{\prime } = 2+2 \cos \left (-4 y+8 x -3\right )
\] |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = 1+\left (y-x \right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
|
|
\[
{}x^{2} y^{\prime }-x y = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\frac {x}{y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\cos \left (\frac {y}{x}\right ) \left (y^{\prime }-\frac {y}{x}\right ) = 1+\sin \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x -y}{x +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+3 y = 3 y^{3}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }-\frac {3 y}{x} = \frac {y^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _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] |
✓ |
|
|
\[
{}3 y^{\prime } = -2+\sqrt {2 x +3 y+4}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}3 y^{\prime }+\frac {2 y}{x} = 4 \sqrt {y}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = 4+\frac {1}{\sin \left (4 x -y\right )}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}\left (y-x \right ) y^{\prime } = 1
\] |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}\left (x +y\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (2 x y+2 x^{2}\right ) y^{\prime } = x^{2}+2 x y+2 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{x} = y^{3} x^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = 2 \sqrt {2 x +y-3}-2
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = 2 \sqrt {2 x +y-3}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}-y+x y^{\prime } = \sqrt {x y+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime }+3 y = \frac {28 \,{\mathrm e}^{2 x}}{y^{3}}
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \left (x -y+3\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
|
|
\[
{}y^{\prime }+2 x = 2 \sqrt {y+x^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y^{\prime } = x \left (1+\frac {2 y}{x^{2}}+\frac {y^{2}}{x^{4}}\right )
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1}{y}-\frac {y}{2 x}
\] |
[[_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] |
✓ |
|
|
\[
{}2 x y+y^{2}+\left (x^{2}+2 x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}2 x y^{3}+4 x^{3}+3 x^{2} y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}2-2 x +3 y^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}4 x^{3} y+\left (x^{4}-y^{4}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}1+\ln \left (x y\right )+\frac {x y^{\prime }}{y} = 0
\] |
[[_homogeneous, ‘class G‘], _exact] |
✓ |
|
|
\[
{}1+{\mathrm e}^{y}+x \,{\mathrm e}^{y} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}{\mathrm e}^{y}+\left (x \,{\mathrm e}^{y}+1\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_exponential_symmetries], _exact] |
✓ |
|
|
\[
{}1+y^{4}+x y^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y+\left (y^{4}-3 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}\frac {2 y}{x}+\left (4 x^{2} y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}3 y+3 y^{2}+\left (2 x +4 x y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 x \left (y+1\right )-y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 y^{3}+\left (4 x^{3} y^{3}-3 x y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}4 x y+\left (3 x^{2}+5 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}6+12 x^{2} y^{2}+\left (7 x^{3} y+\frac {x}{y}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}x y^{\prime } = 2 y-6 x^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime } = 2 y^{2}-6 y
\] |
[_separable] |
✓ |
|
|
\[
{}4 y^{2}-x^{2} y^{2}+y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \sqrt {x +y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}x y y^{\prime }-y^{2} = \sqrt {x^{4}+x^{2} y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}-2 x y+x^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
|
|
\[
{}4 x y-6+x^{2} y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{2}-6+x^{2} y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{3}+y^{3}+x y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}3 y-x^{3}+x y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}3 x y^{3}-y+x y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2+2 x^{2}-2 x y+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\left (y^{2}-4\right ) y^{\prime } = y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1}{x y-3 x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {3 y}{x +1}-y^{2}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\sin \left (y\right )+\left (x +1\right ) \cos \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y y^{\prime } = 2 y^{2}+2 x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +2 y}{x +2 y+3}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +2 y}{2 x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = x y^{2}+3 y^{2}+x +3
\] |
[_separable] |
✓ |
|
|
\[
{}1-\left (x +2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{2}+1-y^{\prime } = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }-3 y = 12 \,{\mathrm e}^{2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}x y y^{\prime } = y^{2}+x y+x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x y^{3} y^{\prime } = y^{4}-x^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = 4 y-\frac {16 \,{\mathrm e}^{4 x}}{y^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
|
|
\[
{}2 y-6 x +\left (x +1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{2}+\left (x^{2} y+10 y^{4}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
|
|
\[
{}\left (y-x +3\right )^{2} \left (y^{\prime }-1\right ) = 1
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{2}-y^{2} \cos \left (x \right )+y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y^{3}-y^{3} \cos \left (x \right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{4 x +3 y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \tan \left (6 x +3 y+1\right )-2
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{4 x +3 y}
\] |
[_separable] |
✓ |
|
|
\[
{}2 x -y-y^{\prime } y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+2 y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {x}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}3 y \left (t^{2}+y\right )+t \left (t^{2}+6 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {2 y}{x}-3
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+2 y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\left (x -4\right ) y^{3}}{x^{3} \left (y-2\right )}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x y+y^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 x -3 y+\left (2 y-3 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+2 y = x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = y^{{1}/{5}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y \sqrt {t}
\] |
[_separable] |
✓ |
|
|
\[
{}t y^{\prime } = y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y \tan \left (t \right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \sqrt {y^{2}-1}
\] |
[_quadrature] |
✓ |
|
|
\[
{}t y^{\prime }+y = t^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_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] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y+1}{t +1}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2+y}{2 t +1}
\] |
[_separable] |
✓ |
|
|
\[
{}\frac {3}{t^{2}} = \left (\frac {1}{\sqrt {y}}+\sqrt {y}\right ) y^{\prime }
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+k y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{2 y+10 t}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{3 y+2 t}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {5^{-t}}{y^{2}}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = t^{2} y^{2}+y^{2}-t^{2}-1
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}-3 y+2
\] |
[_quadrature] |
✓ |
|
|
\[
{}4 \left (x -1\right )^{2} y^{\prime }-3 \left (y+3\right )^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y^{3}+1
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{3}-1
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{3}+y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{3}-y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{3}-y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{3}+y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\sqrt {t}}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \sqrt {\frac {y}{t}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{t}}{y+1}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{\ln \left (y\right )}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y+3}{3 x +1}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x -y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{2 x -y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {3 y+1}{x +3}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y \cos \left (t \right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y^{2} \cos \left (t \right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y-2}{-2+x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +y+3}{3 x +3 y+1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x -y+2}{2 x -2 y-1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \left (x +y-4\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = \left (3 y+1\right )^{4}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 3 y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = -y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}-y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 16 y-8 y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 12+4 y-y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y f \left (t \right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-y = 10
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }-y = 2 \,{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-y = t^{2}-2 t
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}t y^{\prime }+y = t^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}t y^{\prime }+y = t
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-\frac {2 t y}{t^{2}+1} = 2
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-\frac {4 t y}{4 t^{2}+1} = 4 t
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = 2 x +\frac {x y}{x^{2}-1}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-\frac {3 t y}{t^{2}-4} = t
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-\frac {4 t y}{4 t^{2}-9} = t
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-\frac {9 x y}{9 x^{2}+49} = x
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+x y = x^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-x y = x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1}{x +y^{2}}
\] |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
|
|
\[
{}y^{\prime }-x = y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y-\left (x +3 y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}x^{\prime } = \frac {3 x t^{2}}{-t^{3}+1}
\] |
[_separable] |
✓ |
|
|
\[
{}p^{\prime } = t^{3}+\frac {p}{t}
\] |
[_linear] |
✓ |
|
|
\[
{}v^{\prime }+v = {\mathrm e}^{-s}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-y = 4 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+3 t^{2} y = {\mathrm e}^{-t^{3}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+2 t y = 2 t
\] |
[_separable] |
✓ |
|
|
\[
{}\left (t^{2}+4\right ) y^{\prime }+2 t y = 2 t
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime } = x+t +1
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{2 t}+2 y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{t} = \ln \left (t \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y = 5 \,{\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y = 2-{\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-5 y = t
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+3 y = 27 t^{2}+9
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+10 y = 2 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-3 y = 27 t^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-y = 2 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y = 4+3 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y = t
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{2}-\frac {y}{2 \sqrt {t}}+\left (2 t y-\sqrt {t}+1\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}\frac {t}{\sqrt {t^{2}+y^{2}}}+\frac {y y^{\prime }}{\sqrt {t^{2}+y^{2}}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y \cos \left (t y\right )+t \cos \left (t y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}3 t y^{2}+y^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\ln \left (t y\right )+\frac {t y^{\prime }}{y} = 0
\] |
[[_homogeneous, ‘class G‘], _exact] |
✓ |
|
|
\[
{}{\mathrm e}^{t y}+\frac {t \,{\mathrm e}^{t y} y^{\prime }}{y} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}-1+3 y^{2} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{2}+2 t y y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\frac {3 t^{2}}{y}-\frac {t^{3} y^{\prime }}{y^{2}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}-\frac {1}{y}+\left (\frac {t}{y^{2}}+3 y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
|
|
\[
{}2 t y+\left (t^{2}+y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}2 t y^{3}+\left (1+3 t^{2} y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
|
|
\[
{}\sin \left (y\right )^{2}+t \sin \left (2 y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}3 t^{2}+3 y^{2}+6 t y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
|
|
\[
{}-2 t y^{2} \sin \left (t^{2}\right )+2 y \cos \left (t^{2}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (3+t \right ) \cos \left (y+t \right )+\sin \left (y+t \right )+\left (3+t \right ) \cos \left (y+t \right ) y^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries], _exact] |
✓ |
|
|
\[
{}-\frac {y^{2} {\mathrm e}^{\frac {y}{t}}}{t^{2}}+1+{\mathrm e}^{\frac {y}{t}} \left (1+\frac {y}{t}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
|
|
\[
{}2 t \sin \left (\frac {y}{t}\right )-y \cos \left (\frac {y}{t}\right )+t \cos \left (\frac {y}{t}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
|
|
\[
{}2 t y^{2}+2 t^{2} y y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}1+\frac {y}{t^{2}}-\frac {y^{\prime }}{t} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}1+5 t -y-\left (t +2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}t^{2} y+t^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y \left (2 \,{\mathrm e}^{t}+4 t \right )+3 \left ({\mathrm e}^{t}+t^{2}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 t y+y^{2}-t^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}5 t y^{2}+y+\left (2 t^{3}-t \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\frac {9 t}{5}+2 y+\left (2 t +2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 t +\frac {19 y}{10}+\left (\frac {19 t}{10}+2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y = t y^{2}
\] |
[_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] |
✓ |
|
|
\[
{}\cos \left (\frac {t}{y+t}\right )+{\mathrm e}^{\frac {2 y}{t}} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\frac {2}{t}+\frac {1}{y}+\frac {t y^{\prime }}{y^{2}} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 t +\left (y-3 t \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}2 y-3 t +t y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}t y-y^{2}+t \left (t -3 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}t^{2}+t y+y^{2}-t y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}t^{3}+y^{3}-t y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {t +4 y}{4 t +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}t -y+t y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y+\left (y+t \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 t^{2}-7 t y+5 y^{2}+t y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y+2 \sqrt {t^{2}+y^{2}}-t y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{2} = \left (t y-4 t^{2}\right ) y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y-\left (3 \sqrt {t y}+t \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (t^{2}-y^{2}\right ) y^{\prime }+y^{2}+t y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}t y y^{\prime }-t^{2} {\mathrm e}^{-\frac {y}{t}}-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1}{\frac {2 y \,{\mathrm e}^{-\frac {t}{y}}}{t}+\frac {t}{y}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}t \left (\ln \left (t \right )-\ln \left (y\right )\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {4 y^{2}-t^{2}}{2 t y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}t +y-t y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}t y^{\prime }-y-\sqrt {t^{2}+y^{2}} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}t^{3}+y^{2} \sqrt {t^{2}+y^{2}}-t y \sqrt {t^{2}+y^{2}}\, y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{3}-t^{3}-t y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}t y^{3}-\left (t^{4}+y^{4}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}t -2 y+1+\left (4 t -3 y-6\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}5 t +2 y+1+\left (2 t +y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 t -y+1-\left (6 t -2 y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 t +3 y+1+\left (4 t +6 y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-\frac {2 y}{x} = -x^{2} y
\] |
[_separable] |
✓ |
|
|
\[
{}1+y-t y^{\prime } = \ln \left (y^{\prime }\right )
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y = t \left (y^{\prime }+1\right )+2 y^{\prime }+1
\] |
[_linear] |
✓ |
|
|
\[
{}t^{{1}/{3}} y^{{2}/{3}}+t +\left (t^{{2}/{3}} y^{{1}/{3}}+y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}-t^{2}}{t y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y \sin \left (\frac {t}{y}\right )-\left (t +t \sin \left (\frac {t}{y}\right )\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 t^{5}}{5 y^{2}}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{t} = \frac {y^{2}}{t}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{8 y}}{t}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{5 t}}{y^{4}}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\left (4-7 x \right ) \left (2 y-3\right )}{\left (x -1\right ) \left (2 x -5\right )}
\] |
[_separable] |
✓ |
|
|
\[
{}3 t +\left (t -4 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y-t +\left (y+t \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y-x +y^{\prime } = 0
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{2}+\left (t y+t^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}r^{\prime } = \frac {r^{2}+t^{2}}{r t}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{\prime } = \frac {5 t x}{t^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime }+y = 5
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }+t y = t
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime }+\frac {x}{y} = y^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-y = t y^{3}
\] |
[_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] |
✓ |
|
|
\[
{}2 x -y-2+\left (2 y-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\cos \left (t -y\right )+\left (1-\cos \left (t -y\right )\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \sqrt {x -y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime }-4 y = t^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-y = {\mathrm e}^{4 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+4 y = {\mathrm e}^{-4 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+4 y = t \,{\mathrm e}^{-4 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y+3 y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \sqrt {x -y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \sqrt {x^{2}-y}-x
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \sqrt {1-y^{2}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y+1}{x -y}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = 1-\cot \left (y\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \left (3 x -y\right )^{{1}/{3}}-1
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime }+2 y = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+x y = 2 x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = y-x
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x}{2}-y+\frac {3}{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \left (y-1\right )^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \left (y-1\right ) x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \cos \left (x -y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = y-x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = x^{2}+2 x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y+1}{x -1}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = 2 x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = y+x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}x y^{\prime } = 2 x -y
\] |
[_linear] |
✓ |
|
|
\[
{}1+y^{2}+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}1+y^{2}+x y y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } \sin \left (x \right )-y \cos \left (x \right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}1+y^{2} = x y^{\prime }
\] |
[_separable] |
✓ |
|
|
\[
{}{\mathrm e}^{-y} y^{\prime } = 1
\] |
[_quadrature] |
✓ |
|
|
\[
{}y \ln \left (y\right )+x y^{\prime } = 1
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = a^{x +y}
\] |
[_separable] |
✓ |
|
|
\[
{}{\mathrm e}^{y} \left (x^{2}+1\right ) y^{\prime }-2 x \left (1+{\mathrm e}^{y}\right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \sin \left (x -y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = a x +b y+c
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x +y\right )^{2} y^{\prime } = a^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}a^{2}+y^{2}+2 x \sqrt {a x -x^{2}}\, y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}{\mathrm e}^{y} = {\mathrm e}^{4 y} y^{\prime }+1
\] |
[_quadrature] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime } = y-1
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 x \left (\pi +y\right )
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime } = y+x \cos \left (\frac {y}{x}\right )^{2}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x -y+x y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime } = y \left (\ln \left (y\right )-\ln \left (x \right )\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = x^{2}-x y+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x y^{\prime } = y+\sqrt {y^{2}-x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime } = y^{2}+x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}4 x -3 y+\left (2 y-3 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y-x +\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x +y-2+\left (1-x \right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x +y-2+\left (x -y+4\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x +y+\left (x -y-2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x +3 y-5+\left (3 x +2 y-5\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}8 x +4 y+1+\left (4 x +2 y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x -2 y-1+\left (3 x -6 y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x +y+\left (y-1+x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x y^{\prime } \left (x -y^{2}\right )+y^{3} = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}4 y^{6}+x^{3} = 6 x y^{5} y^{\prime }
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y \left (1+\sqrt {x^{2} y^{4}+1}\right )+2 x y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
|
|
\[
{}x +y^{3}+3 \left (y^{3}-x \right ) y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}y^{\prime }+2 y = {\mathrm e}^{-x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2}-x y^{\prime } = y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-2 x y = 2 x \,{\mathrm e}^{x^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = {\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime }-2 y = x^{3} \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}\left (2 x -y^{2}\right ) y^{\prime } = 2 y
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{2 y \ln \left (y\right )+y-x}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime }+y = 2 x
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = 2 x y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}3 x y^{2} y^{\prime }-2 y^{3} = x^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (x^{3}+{\mathrm e}^{y}\right ) y^{\prime } = 3 x^{2}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime }+3 x y = y \,{\mathrm e}^{x^{2}}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-y \cos \left (x \right ) = y^{2} \cos \left (x \right )
\] |
[_separable] |
✓ |
|
|
\[
{}x \left (2 x^{2}+y^{2}\right )+y \left (x^{2}+2 y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\frac {x y}{\sqrt {x^{2}+1}}+2 x y-\frac {y}{x}+\left (\sqrt {x^{2}+1}+x^{2}-\ln \left (x \right )\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}3 x^{2} y+y^{3}+\left (x^{3}+3 x y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}x^{2}+y-x y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x +y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}3 y^{2}-x +\left (2 y^{3}-6 x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}x^{2}+y^{2}+1-2 x y y^{\prime } = 0
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}x -x y+\left (y+x^{2}\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+3 x y y^{\prime }+2 y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-\left (2 x +y\right ) y^{\prime }+x^{2}+x y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}{y^{\prime }}^{3} = y {y^{\prime }}^{2}-x^{2} y^{\prime }+x^{2} y
\] |
[_quadrature] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-y^{\prime } y+{\mathrm e}^{x} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{\frac {y^{\prime }}{y}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y = \left (y^{\prime }-1\right ) {\mathrm e}^{y^{\prime }}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y = y^{\prime } \left (1+y^{\prime } \cos \left (y^{\prime }\right )\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y = 2 x y^{\prime }+\ln \left (y^{\prime }\right )
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }-y^{2}+\left (2 x +1\right ) y = x^{2}+2 x
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Riccati] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = x^{2} y^{2}+x y+1
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-y^{2} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y^{{2}/{3}}+a
\] |
[_quadrature] |
✓ |
|
|
\[
{}\left (y^{\prime }-1\right )^{2} = y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-y^{\prime } y+{\mathrm e}^{x} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime } = \left (x -y\right )^{2}+1
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
|
|
\[
{}x^{3}-3 x y^{2}+\left (y^{3}-3 x^{2} y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}5 x y-4 y^{2}-6 x^{2}+\left (y^{2}-8 x y+\frac {5 x^{2}}{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}y-x y^{2} \ln \left (x \right )+x y^{\prime } = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1}{2 x -y^{2}}
\] |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
|
|
\[
{}x y y^{\prime }-y^{2} = x^{4}
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\frac {1}{x^{2}-x y+y^{2}} = \frac {y^{\prime }}{2 y^{2}-x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (2 x -1\right ) y^{\prime }-2 y = \frac {1-4 x}{x^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}x -y+3+\left (3 x +y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } \left (3 x^{2}-2 x \right )-y \left (6 x -2\right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{2} y^{\prime }-y^{3} = \frac {x^{4}}{3}
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
|
|
\[
{}x^{2}+y^{2}-x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x -y+2+\left (x -y+3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y^{2}+y-x y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (x -2 x y-y^{2}\right ) y^{\prime }+y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
|
|
\[
{}y^{\prime }-1 = {\mathrm e}^{x +2 y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}2 x^{5}+4 x^{3} y-2 x y^{2}+\left (y^{2}+2 x^{2} y-x^{4}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}x^{2} y^{n} y^{\prime } = 2 x y^{\prime }-y
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}\left (3 x +3 y+a^{2}\right ) y^{\prime } = 4 x +4 y+b^{2}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x -y^{2}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{\prime }+y = y^{2} \ln \left (x \right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}\left (5 x -7 y+1\right ) y^{\prime }+y-1+x = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x +y+1+\left (2 x +2 y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{3}+2 \left (x^{2}-x y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 \left (y+2\right )^{2}}{\left (y-1+x \right )^{2}}
\] |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{4}}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y^{3} \sin \left (x \right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y^{\prime } = \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 4 \sqrt {x y}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
|
|
\[
{}y^{\prime } = x \left (y-y^{2}\right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \left (1-12 x \right ) y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {3-2 x}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}r^{\prime } = \frac {r^{2}}{\theta }
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x}{1+2 y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 x y^{2}+4 x^{3} y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x^{2} {\mathrm e}^{-3 y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \left (1+y^{2}\right ) \tan \left (2 x \right )
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = y-x y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 y^{2}+x y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 \left (x +1\right ) \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {t y \left (4-y\right )}{3}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {t y \left (4-y\right )}{t +1}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {a y+b}{c y+d}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }+4 y = t +{\mathrm e}^{-2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-2 y = t^{2} {\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y = t \,{\mathrm e}^{-t}+1
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-2 y = 3 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+2 t y = 16 t \,{\mathrm e}^{-t^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (t^{2}+1\right ) y^{\prime }+4 t y = \frac {1}{\left (t^{2}+1\right )^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}2 y^{\prime }+y = 3 t
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}t y^{\prime }-y = t^{3} {\mathrm e}^{-t}
\] |
[_linear] |
✓ |
|
|
\[
{}2 y^{\prime }+y = 3 t^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+2 y = t \,{\mathrm e}^{-2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}t y^{\prime }+4 y = t^{2}-t +1
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-2 y = {\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}2 y^{\prime }-y = {\mathrm e}^{\frac {t}{3}}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}3 y^{\prime }-2 y = {\mathrm e}^{-\frac {\pi t}{2}}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}t y^{\prime }+\left (t +1\right ) y = 2 t \,{\mathrm e}^{-t}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {4 y}{3} = 1-\frac {t}{4}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-\frac {3 y}{2} = 3 t +3 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-6 y = t^{6} {\mathrm e}^{6 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}2 y^{\prime }+y = 3 t^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}t \left (-4+t \right ) y^{\prime }+y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (-t^{2}+4\right ) y^{\prime }+2 t y = 3 t^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (-t^{2}+4\right ) y^{\prime }+2 t y = 3 t^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {t -y}{2 t +5 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {t}{2}+\frac {\sqrt {t^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {4 t}{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 t y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y^{3} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = t y \left (3-y\right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y \left (3-t y\right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = -y \left (3-t y\right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}2 x +3+\left (2 y-2\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 x +4 y+\left (2 x -2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x y^{2}+2 y+\left (2 x^{2} y+2 x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {4 x +2 y}{2 x +3 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {4 x -2 y}{2 x -3 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\frac {x}{\left (y^{2}+x^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (y^{2}+x^{2}\right )^{{3}/{2}}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 x -y+\left (2 y-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{2 x}+y-1
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y+\left (2 x y-{\mathrm e}^{-2 y}\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
|
|
\[
{}3 x y+y^{2}+\left (x y+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } y = x +1
\] |
[_separable] |
✓ |
|
|
\[
{}\frac {\left (3 x^{3}-x y^{2}\right ) y^{\prime }}{3 x^{2} y+y^{3}} = 1
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (x -1\right ) y^{\prime } = y \left (y+1\right )
\] |
[_separable] |
✓ |
|
|
\[
{}\sqrt {x^{2}-y^{2}}+y = x y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y y^{\prime } = \left (x +y\right )^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {4 y-7 x}{5 x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y^{\prime }-4 \sqrt {y^{2}-x^{2}} = y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{4}+2 x y^{3}-3 x^{2} y^{2}-2 x^{3} y}{2 x^{2} y^{2}-2 x^{3} y-2 x^{4}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (y+x \,{\mathrm e}^{\frac {x}{y}}\right ) y^{\prime } = y \,{\mathrm e}^{\frac {x}{y}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y y^{\prime } = y^{2}+x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}t y^{\prime }+y = t^{2} y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _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] |
✓ |
|
|
\[
{}3 t y^{\prime }+9 y = 2 t y^{{5}/{3}}
\] |
[[_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] |
✓ |
|
|
\[
{}\left (3 x-y \right ) x^{\prime }+9 y -2 x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}1 = \left (3 \,{\mathrm e}^{y}-2 x \right ) y^{\prime }
\] |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
|
|
\[
{}y^{\prime }-4 \,{\mathrm e}^{x} y^{2} = y
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
|
|
\[
{}\frac {\sqrt {x}\, y^{\prime }}{y} = 1
\] |
[_separable] |
✓ |
|
|
\[
{}5 x y^{2}+5 y+\left (5 x^{2} y+5 x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (2-x \right ) y^{\prime } = y+2 \left (2-x \right )^{5}
\] |
[_linear] |
✓ |
|
|
\[
{}x^{\prime } = \frac {2 x y +x^{2}}{3 y^{2}+2 x y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}4 x y y^{\prime } = 8 x^{2}+5 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+y-y^{{1}/{4}} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}\sqrt {-x^{2}+1}\, y^{\prime }+\sqrt {1-y^{2}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x y}{y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y \left (1+\ln \left (y\right )-\ln \left (x \right )\right )}{x}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{2}+x^{2} y^{\prime } = x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}\left (x +y\right ) y^{\prime } = y-x
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}3 y-7 x +7 = \left (3 x -7 y-3\right ) y^{\prime }
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x +2 y+1\right ) y^{\prime } = 4 y+2 x +3
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 \left (y+2\right )^{2}}{\left (y-1+x \right )^{2}}
\] |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
|
|
\[
{}\left (x +y\right )^{2} y^{\prime } = a^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }-4 y = \sqrt {y}\, x^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = 2 x y-x^{3}+x
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x -2 x y-y^{2}\right ) y^{\prime }+y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
|
|
\[
{}x y^{\prime }+y = x y^{2} \ln \left (x \right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}x -y^{2}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}}{3}+\frac {2}{3 x^{2}}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
|
|
\[
{}y^{\prime }+y^{2}+\frac {y}{x}-\frac {4}{x^{2}} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}+\frac {1}{x^{4}}
\] |
[_rational, [_Riccati, _special]] |
✓ |
|
|
\[
{}\left (y-x \right ) \sqrt {x^{2}+1}\, y^{\prime } = \left (1+y^{2}\right )^{{3}/{2}}
\] |
[‘y=_G(x,y’)‘] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x -y^{2}}{2 y \left (x +y^{2}\right )}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}\left (\left (x +y\right ) x +a^{2}\right ) y^{\prime } = y \left (x +y\right )+b^{2}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}\frac {x +y^{\prime } y}{\sqrt {x^{2}+y^{2}+1}}+\frac {y-x y^{\prime }}{y^{2}+x^{2}} = 0
\] |
[[_1st_order, _with_linear_symmetries], _exact] |
✓ |
|
|
\[
{}\frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{3}+2 \left (x^{2}-x y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}\left (x^{2} y^{2}-1\right ) y^{\prime }+2 x y^{3} = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}a x y^{\prime }+b y+x^{m} y^{n} \left (\alpha x y^{\prime }+\beta y\right ) = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}y^{\prime } = 2 x y-x^{3}+x
\] |
[_linear] |
✓ |
|
|
\[
{}y-x y^{2} \ln \left (x \right )+x y^{\prime } = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}y {y^{\prime }}^{2}+y^{\prime } \left (x -y\right )-x = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}-\left (y^{2}+x y+x^{2}\right ) {y^{\prime }}^{2}+\left (x^{3} y+x^{2} y^{2}+x y^{3}\right ) y^{\prime }-x^{3} y^{3} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y = 2 x y^{\prime }+y^{2} {y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime } = \sqrt {y-x}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \sqrt {y-x}+1
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \sqrt {y}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y \ln \left (y\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = y \ln \left (y\right )^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = -x +\sqrt {x^{2}+2 y}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y^{\prime } = -x -\sqrt {x^{2}+2 y}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-y^{\prime } y+{\mathrm e}^{x} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime } = 2 y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } y = {\mathrm e}^{2 x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = k y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x y}{y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}2 x y y^{\prime } = y^{2}+x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}}{x y-x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}\left (y \cos \left (y\right )-\sin \left (y\right )+x \right ) y^{\prime } = y
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}1+y^{2}+y^{2} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}x y y^{\prime } = y-1
\] |
[_separable] |
✓ |
|
|
\[
{}x^{5} y^{\prime }+y^{5} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 x y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y \tan \left (x \right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-y \tan \left (x \right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}1+y^{2}+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y \ln \left (y\right )-x y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-2 y+3 x}
\] |
[_separable] |
✓ |
|
|
\[
{}{\mathrm e}^{-y}+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}v^{\prime } = g -\frac {k v^{2}}{m}
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{2}-2 y^{2}+x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime }-3 x y-2 y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x \sin \left (\frac {y}{x}\right ) y^{\prime } = y \sin \left (\frac {y}{x}\right )+x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime } = y+2 x \,{\mathrm e}^{-\frac {y}{x}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x -y-\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y^{\prime } = 2 x +3 y
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime } = \sqrt {y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = 2 x y+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{3}+y^{3}-x y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \left (x +y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = \sin \left (x +1-y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +y+4}{x -y-6}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +y+4}{x +y-6}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x -2 y+\left (y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y-1+x}{x +4 y+2}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x +3 y-1-4 \left (x +1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1-x y^{2}}{2 x^{2} y}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2+3 x y^{2}}{4 x^{2} y}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y-x y^{2}}{x +x^{2} y}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}\left (x +\frac {2}{y}\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y+y \cos \left (x y\right )+\left (x +x \cos \left (x y\right )\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}-\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}1+y+\left (1-x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 x \left (1+\sqrt {x^{2}-y}\right ) = \sqrt {x^{2}-y}\, y^{\prime }
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
|
|
\[
{}\frac {x}{\left (y^{2}+x^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (y^{2}+x^{2}\right )^{{3}/{2}}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\frac {y-x y^{\prime }}{\left (x +y\right )^{2}}+y^{\prime } = 1
\] |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
|
|
\[
{}\frac {4 y^{2}-2 x^{2}}{4 x y^{2}-x^{3}}+\frac {\left (8 y^{2}-x^{2}\right ) y^{\prime }}{4 y^{3}-x^{2} y} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (3 x^{2}-y^{2}\right ) y^{\prime }-2 x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x y^{\prime }+y+3 x^{3} y^{4} y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}y+\left (x -2 y^{3} x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}x +3 y^{2}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}-y+x y^{\prime } = \left (1+y^{2}\right ) y^{\prime }
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
|
|
\[
{}y-x y^{\prime } = x y^{3} y^{\prime }
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +y\right ) y^{\prime } = y-x
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{2}-y+x y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}-y+x y^{\prime } = 2 x^{2}-3
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime }+y = \sqrt {x y}\, y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}-y+x y^{\prime } = x^{2} y^{4} \left (x y^{\prime }+y\right )
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}x y^{\prime }+y+x^{2} y^{5} y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}2 x y^{2}-y+x y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y}{x}+\frac {x^{3}}{y}+x \tan \left (\frac {y}{x^{2}}\right )
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
|
|
\[
{}x y^{\prime }-3 y = x^{4}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y = 2 x \,{\mathrm e}^{-x}+x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}2 y-x^{3} = x y^{\prime }
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-2 x y = 6 x \,{\mathrm e}^{x^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y-2 x y-x^{2}+x^{2} y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{\prime }+y = y^{3} x^{4}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x y^{\prime }+y = x y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y-x y^{\prime } = y^{\prime } y^{2} {\mathrm e}^{y}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime }+2 = x^{3} \left (y-1\right ) y^{\prime }
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
|
|
\[
{}x y^{\prime } = 2 x^{2} y+y \ln \left (y\right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
|
|
\[
{}\left (1-x y\right ) y^{\prime } = y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}2 x +3 y+1+\left (2 y-3 x +5\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y^{\prime } = \sqrt {y^{2}+x^{2}}
\] |
|
✓ |
|
|
\[
{}y^{2} = \left (x^{3}-x y\right ) y^{\prime }
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{3} x^{2}+y = \left (x^{3} y^{2}-x \right ) y^{\prime }
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}x y^{\prime }+y = y^{2}+x^{2} y^{\prime }
\] |
[_separable] |
✓ |
|
|
\[
{}x y y^{\prime } = y^{2}+x^{2} y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y+x^{2} = x y^{\prime }
\] |
[_linear] |
✓ |
|
|
\[
{}6 x +4 y+3+\left (3 x +2 y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\cos \left (x +y\right ) = x \sin \left (x +y\right )+x \sin \left (x +y\right ) y^{\prime }
\] |
[[_1st_order, _with_linear_symmetries], _exact] |
✓ |
|
|
\[
{}y^{\prime } \ln \left (x -y\right ) = 1+\ln \left (x -y\right )
\] |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = {\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{2}-3 x y-2 x^{2} = \left (x^{2}-x y\right ) y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+2 x y = 4 x^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{4}+x^{6}-x^{3} y^{3} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime } = 1+\frac {y}{x}-\frac {y^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x y \,{\mathrm e}^{\frac {x^{2}}{y^{2}}}}{y^{2}+y^{2} {\mathrm e}^{\frac {x^{2}}{y^{2}}}+2 x^{2} {\mathrm e}^{\frac {x^{2}}{y^{2}}}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +2 y+2}{-2 x +y}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 x^{2} \ln \left (y\right )+\frac {x^{3} y^{\prime }}{y} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\frac {y-x}{\left (x +y\right )^{3}}-\frac {2 x y^{\prime }}{\left (x +y\right )^{3}} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x y^{2}+y+x y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}3 x^{2} y-y^{3}-\left (3 x y^{2}-x^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } = \frac {-3 x -2 y-1}{2 x +3 y-1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}{\mathrm e}^{x^{2} y} \left (1+2 x^{2} y\right )+x^{3} {\mathrm e}^{x^{2} y} y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}3 x y+y^{2}+\left (3 x y+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = y^{2}+x y+x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}x y^{\prime }+y = y^{2} \ln \left (x \right )
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}x^{2} y^{\prime }-y^{2} = 2 x y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}x^{\prime } = b \,{\mathrm e}^{x}
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime } = \left (x-1\right )^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime } = \sqrt {x^{2}-1}
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime } = 2 \sqrt {x}
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{\prime } = \tan \left (x\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}1+2 x+\left (-t^{2}+4\right ) x^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime } = \cos \left (\frac {x}{t}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}\left (t^{2}-x^{2}\right ) x^{\prime } = x t
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}{\mathrm e}^{3 t} x^{\prime }+3 x \,{\mathrm e}^{3 t} = 2 t
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}x^{\prime }+2 x = {\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}x^{\prime }+x \tan \left (t \right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}t^{3} x^{\prime }+\left (-3 t^{2}+2\right ) x = t^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}x^{\prime } = -\lambda x
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }+c y = a
\] |
[_quadrature] |
✓ |
|
|
\[
{}v^{\prime }+\frac {2 v}{u} = 3
\] |
[_linear] |
✓ |
|
|
\[
{}y-x y^{\prime } = b \left (1+x^{2} y^{\prime }\right )
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime } = k \left (A -n x\right ) \left (M -m x\right )
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{2} = x \left (y-x \right ) y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}2 x^{2} y+y^{3}-x^{3} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}2 a x +b y+\left (2 c y+b x +e \right ) y^{\prime } = g
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x +y^{\prime } y = m y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\frac {2 x}{y^{3}}+\left (\frac {1}{y^{2}}-\frac {3 x^{2}}{y^{4}}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime }+x y = x
\] |
[_separable] |
✓ |
|
|
\[
{}p^{\prime } = \frac {p+a \,t^{3}-2 p t^{2}}{t \left (-t^{2}+1\right )}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (T \ln \left (t \right )-1\right ) T = t T^{\prime }
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}\sqrt {t^{2}+T} = T^{\prime }
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
|
|
\[
{}y^{\prime } = \left (x +y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = x \left (y^{2} a +b \right )
\] |
[_separable] |
✓ |
|
|
\[
{}n^{\prime } = \left (n^{2}+1\right ) x
\] |
[_separable] |
✓ |
|
|
\[
{}v^{\prime }+\frac {2 v}{u} = 3 v
\] |
[_separable] |
✓ |
|
|
\[
{}\frac {y^{\prime }}{x} = y \sin \left (x^{2}-1\right )-\frac {2 y}{\sqrt {x}}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 1+\frac {2 y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}v^{\prime }+2 u v = 2 u
\] |
[_separable] |
✓ |
|
|
\[
{}1+v^{2}+\left (u^{2}+1\right ) v v^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}4 y {y^{\prime }}^{3}-2 x^{2} {y^{\prime }}^{2}+4 x y y^{\prime }+x^{3} = 16 y^{2}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{x} = -x^{2}+1
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}-1\right ) y = x^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y = a \,x^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\sin \left (x \right ) y = y^{2} \sin \left (x \right )
\] |
[_separable] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }-x y = a x y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2}+\ln \left (y\right )+\frac {x y^{\prime }}{y} = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
|
|
\[
{}x \left (x -2 y\right ) y^{\prime }+x^{2}+2 y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}5 x y y^{\prime }-y^{2}-x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (x^{2}+3 x y-y^{2}\right ) y^{\prime }-3 y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x^{2}+2 x y\right ) y^{\prime }-3 x^{2}+2 x y-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}5 x y y^{\prime }-4 x^{2}-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (x^{2}-2 x y\right ) y^{\prime }+x^{2}-3 x y+2 y^{2} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}3 x^{2} y^{\prime }+2 x^{2}-3 y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
|
|
\[
{}\left (3 x +2 y-7\right ) y^{\prime } = 2 x -3 y+6
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (6 x -5 y+4\right ) y^{\prime } = 2 x -y+1
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (5 x -2 y+7\right ) y^{\prime } = x -3 y+2
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x -3 y+4\right ) y^{\prime } = 5 x -7 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x -3 y+4\right ) y^{\prime } = 2 x -6 y+7
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (5 x -2 y+7\right ) y^{\prime } = 10 x -4 y+6
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (2 x -2 y+5\right ) y^{\prime } = x -y+3
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (6 x -4 y+1\right ) y^{\prime } = 3 x -2 y+1
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (1-x \right ) y^{\prime }-y-1 = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y-x y^{\prime } = a \left (y^{2}+y^{\prime }\right )
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2}+y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{2}+\left (x y+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (4 y+3 x \right ) y^{\prime }+y-2 x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (y-3 x +3\right ) y^{\prime } = 2 y-x -4
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2}-4 x y-2 y^{2}+\left (y^{2}-4 x y-2 x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
|
|
\[
{}x +y^{\prime } y+\frac {-y+x y^{\prime }}{y^{2}+x^{2}} = 0
\] |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
|
|
\[
{}2 a x +b y+g +\left (2 c y+b x +e \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y-x y^{\prime }+\ln \left (x \right ) = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x y+1\right ) y-\left (1-x y\right ) x y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}a \left (x y^{\prime }+2 y\right ) = x y y^{\prime }
\] |
[_separable] |
✓ |
|
|
\[
{}y \left (2 x y+{\mathrm e}^{x}\right )-{\mathrm e}^{x} y^{\prime } = 0
\] |
[_Bernoulli] |
✓ |
|
|
\[
{}x^{2} y-2 x y^{2}-\left (x^{3}-3 x^{2} y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y \left (x y+2 x^{2} y^{2}\right )+x \left (x y-x^{2} y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}3 x^{2} y^{4}+2 x y+\left (2 x^{3} y^{3}-x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}y^{3}-2 x^{2} y+\left (2 x y^{2}-x^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}2 x^{2} y-3 y^{4}+\left (3 x^{3}+2 x y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}y^{2}+2 x^{2} y+\left (2 x^{3}-x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}x y^{\prime }-a y = x +1
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{-x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{x} = x^{2} y^{6}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = 3 x^{2} y^{{1}/{3}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}\left (x +y\right )^{2} y^{\prime } = a^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}-y+x y^{\prime } = \sqrt {y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime }+\frac {\left (-2 x +1\right ) y}{x^{2}} = 1
\] |
[_linear] |
✓ |
|
|
\[
{}2 x -y+1+\left (2 y-x -1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}x y^{\prime }+\frac {y^{2}}{x} = y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
|
|
\[
{}y^{\prime }+\frac {4 x y}{x^{2}+1} = \frac {1}{\left (x^{2}+1\right )^{3}}
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y = a \,x^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2}+y^{2}+1-2 x y y^{\prime } = 0
\] |
[_rational, _Bernoulli] |
✓ |
|
|
\[
{}x +y^{\prime } y = m \left (-y+x y^{\prime }\right )
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime }+1 = 2 \,{\mathrm e}^{y}
\] |
[_separable] |
✓ |
|
|
\[
{}y+\left (a \,x^{2} y^{n}-2 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}y^{\prime } y = a x
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +y\right ) y^{\prime }+x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}2 x y+\left (y^{2}-x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
|
|
\[
{}y-x y^{\prime } = b \left (1+x^{2} y^{\prime }\right )
\] |
[_separable] |
✓ |
|
|
\[
{}3 y+2 x +4-\left (4 x +6 y+5\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x^{3} y^{3}+x^{2} y^{2}+x y+1\right ) y+\left (x^{3} y^{3}-x^{2} y^{2}-x y+1\right ) x y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
|
|
\[
{}2 x^{2} y^{2}+y-\left (x^{3} y-3 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{2}+x^{2} y^{\prime } = x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
|
|
\[
{}y^{\prime }+\frac {n y}{x} = a \,x^{-n}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x -y\right )^{2} y^{\prime } = a^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}+2 x {y^{\prime }}^{2}-y^{2} {y^{\prime }}^{2}-2 x y^{2} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}{y^{\prime }}^{3} \left (x +2 y\right )+3 {y^{\prime }}^{2} \left (x +y\right )+\left (2 x +y\right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}4 y^{2} {y^{\prime }}^{2}+2 y^{\prime } x y \left (3 x +1\right )+3 x^{3} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y \left (y-x y^{\prime }\right ) = x +y^{\prime } y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = y^{2}+x^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
|
|
\[
{}x y^{2} \left ({y^{\prime }}^{2}+2\right ) = 2 y^{\prime } y^{3}+x^{3}
\] |
[_separable] |
✓ |
|
|
\[
{}\left (-y+x y^{\prime }\right ) \left (x +y^{\prime } y\right ) = h^{2} y^{\prime }
\] |
[_rational] |
✓ |
|
|
\[
{}\left ({y^{\prime }}^{2}-\frac {1}{a^{2}-x^{2}}\right ) \left (y^{\prime }-\sqrt {\frac {y}{x}}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}+y^{\prime } \left (3 x^{2}-2 y^{2}\right )-6 x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}-\left (y^{2}+x y+x^{2}\right ) {y^{\prime }}^{2}+\left (x^{3} y+x^{2} y^{2}+x y^{3}\right ) y^{\prime }-x^{3} y^{3} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y = 2 x y^{\prime }+y^{2} {y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
|