|
# |
ODE |
CAS classification |
Solved? |
|
\[
{}y^{\prime } = -y-\sin \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = y-\sin \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = -x +y+1
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = x -y+1
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = x^{2}-y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = x^{2}-y-2
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = y-x
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \sin \left (x \right ) y
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime } = 4 y
\] |
[_separable] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = 2 y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 1+x +y+x y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y \,{\mathrm e}^{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 4 x^{3} y-y
\] |
[_separable] |
✓ |
|
|
\[
{}\tan \left (x \right ) y^{\prime } = y
\] |
[_separable] |
✓ |
|
|
\[
{}-y+y^{\prime } x = 2 x^{2} y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-2 y = 3 \,{\mathrm e}^{2 x}
\] |
[[_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] |
✓ |
|
|
\[
{}y^{\prime } x +2 y = 3 x
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +5 y = 7 x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}2 y^{\prime } x +y = 10 \sqrt {x}
\] |
[_linear] |
✓ |
|
|
\[
{}3 y^{\prime } x +y = 12 x
\] |
[_linear] |
✓ |
|
|
\[
{}-y+y^{\prime } x = x
\] |
[_linear] |
✓ |
|
|
\[
{}2 y^{\prime } x -3 y = 9 x^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +y = 3 x y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x +3 y = 2 x^{5}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } x -3 y = x^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \left (1-y\right ) \cos \left (x \right )
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime }+y = \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x = 2 y+x^{3} \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = 1+x +y+x y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x = 3 y+x^{4} \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = 2 x y+3 x^{2} {\mathrm e}^{x^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +\left (2 x -3\right ) y = 4 x^{4}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}+4\right ) y^{\prime }+3 x y = x
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+3 x^{3} y = 6 x \,{\mathrm e}^{-\frac {3 x^{2}}{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}\frac {1-4 x y^{2}}{x^{\prime }} = y^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}\frac {x+y \,{\mathrm e}^{y}}{x^{\prime }} = 1
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}\frac {1+2 x y}{x^{\prime }} = y^{2}+1
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = 1+2 x y
\] |
[_linear] |
✓ |
|
|
\[
{}2 y^{\prime } x = y+2 x \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+p \left (x \right ) y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+p \left (x \right ) y = q \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}\frac {2 x^{{5}/{2}}-3 y^{{5}/{3}}}{2 x^{{5}/{2}} y^{{2}/{3}}}+\frac {\left (3 y^{{5}/{3}}-2 x^{{5}/{2}}\right ) y^{\prime }}{3 x^{{3}/{2}} y^{{5}/{3}}} = 0
\] |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
|
|
\[
{}x^{3}+3 y-y^{\prime } x = 0
\] |
[_linear] |
✓ |
|
|
\[
{}3 y+x^{4} y^{\prime } = 2 x y
\] |
[_separable] |
✓ |
|
|
\[
{}2 x^{2} y+x^{3} y^{\prime } = 1
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+3 y = 3 x^{2} {\mathrm e}^{-3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } x +3 y = \frac {3}{x^{{3}/{2}}}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+\left (x -1\right ) y = 1
\] |
[_linear] |
✓ |
|
|
\[
{}2 y+\left (x +1\right ) y^{\prime } = 3 x +3
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +y = 2 \,{\mathrm e}^{2 x}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (2 x +1\right ) y^{\prime }+y = \left (2 x +1\right )^{{3}/{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = 3 \left (y+7\right ) x^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x y+2 x}{x^{2}+1}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -y-\sin \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = y-\sin \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = -x +y+1
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = x -y+1
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = x^{2}-y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = x^{2}-y-2
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \sin \left (x \right ) y
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime } = 4 y
\] |
[_separable] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = 2 y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 1+x +y+x y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y \,{\mathrm e}^{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 4 x^{3} y-y
\] |
[_separable] |
✓ |
|
|
\[
{}\tan \left (x \right ) y^{\prime } = y
\] |
[_separable] |
✓ |
|
|
\[
{}-y+y^{\prime } x = 2 x^{2} y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-2 y = 3 \,{\mathrm e}^{2 x}
\] |
[[_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] |
✓ |
|
|
\[
{}y^{\prime } x +2 y = 3 x
\] |
[_linear] |
✓ |
|
|
\[
{}2 y^{\prime } x +y = 10 \sqrt {x}
\] |
[_linear] |
✓ |
|
|
\[
{}2 y^{\prime } x +y = 10 \sqrt {x}
\] |
[_linear] |
✓ |
|
|
\[
{}3 y^{\prime } x +y = 12 x
\] |
[_linear] |
✓ |
|
|
\[
{}-y+y^{\prime } x = x
\] |
[_linear] |
✓ |
|
|
\[
{}2 y^{\prime } x -3 y = 9 x^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +y = 3 x y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x +3 y = 2 x^{5}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } x -3 y = x^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \left (1-y\right ) \cos \left (x \right )
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime }+y = \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x = 2 y+x^{3} \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = 1+x +y+x y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x = 3 y+x^{4} \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = 2 x y+3 x^{2} {\mathrm e}^{x^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +\left (2 x -3\right ) y = 4 x^{4}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}+4\right ) y^{\prime }+3 x y = x
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+3 x^{3} y = 6 x \,{\mathrm e}^{-\frac {3 x^{2}}{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}\frac {2 x^{{5}/{2}}-3 y^{{5}/{3}}}{2 x^{{5}/{2}} y^{{2}/{3}}}+\frac {\left (3 y^{{5}/{3}}-2 x^{{5}/{2}}\right ) y^{\prime }}{3 x^{{3}/{2}} y^{{5}/{3}}} = 0
\] |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
|
|
\[
{}x^{3}+3 y-y^{\prime } x = 0
\] |
[_linear] |
✓ |
|
|
\[
{}3 y+x^{4} y^{\prime } = 2 x y
\] |
[_separable] |
✓ |
|
|
\[
{}2 x^{2} y+x^{3} y^{\prime } = 1
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+3 y = 3 x^{2} {\mathrm e}^{-3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } x +3 y = \frac {3}{x^{{3}/{2}}}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+\left (x -1\right ) y = 1
\] |
[_linear] |
✓ |
|
|
\[
{}2 y+\left (x +1\right ) y^{\prime } = 3 x +3
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +y = 2 \,{\mathrm e}^{2 x}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (2 x +1\right ) y^{\prime }+y = \left (2 x +1\right )^{{3}/{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = 3 \left (y+7\right ) x^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 3 \left (y+7\right ) x^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x y+2 x}{x^{2}+1}
\] |
[_separable] |
✓ |
|
|
\[
{}3 y+y^{\prime } = {\mathrm e}^{-2 t}+t
\] |
[[_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‘]] |
✓ |
|
|
\[
{}\frac {y}{t}+y^{\prime } = 3 \cos \left (2 t \right )
\] |
[_linear] |
✓ |
|
|
\[
{}-2 y+y^{\prime } = 3 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}2 y+t y^{\prime } = \sin \left (t \right )
\] |
[_linear] |
✓ |
|
|
\[
{}2 t y+y^{\prime } = 2 t \,{\mathrm e}^{-t^{2}}
\] |
[_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] |
✓ |
|
|
\[
{}y^{\prime }+y = 5 \sin \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y+2 y^{\prime } = 3 t^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}-y+y^{\prime } = 2 \,{\mathrm e}^{2 t} t
\] |
[[_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] |
✓ |
|
|
\[
{}\frac {2 y}{t}+y^{\prime } = \frac {\cos \left (t \right )}{t^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}-2 y+y^{\prime } = {\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}2 y+t y^{\prime } = \sin \left (t \right )
\] |
[_linear] |
✓ |
|
|
\[
{}4 t^{2} y+t^{3} y^{\prime } = {\mathrm e}^{-t}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (1+t \right ) y+t y^{\prime } = t
\] |
[_linear] |
✓ |
|
|
\[
{}-\frac {y}{2}+y^{\prime } = 2 \cos \left (t \right )
\] |
[[_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‘]] |
✓ |
|
|
\[
{}\left (1+t \right ) y+t y^{\prime } = 2 t \,{\mathrm e}^{-t}
\] |
[_linear] |
✓ |
|
|
\[
{}2 y+t y^{\prime } = \frac {\sin \left (t \right )}{t}
\] |
[_linear] |
✓ |
|
|
\[
{}\cos \left (t \right ) y+\sin \left (t \right ) y^{\prime } = {\mathrm e}^{t}
\] |
[_linear] |
✓ |
|
|
\[
{}\frac {y}{2}+y^{\prime } = 2 \cos \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}\frac {2 y}{3}+y^{\prime } = 1-\frac {t}{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}\frac {y}{4}+y^{\prime } = 3+2 \cos \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}-y+y^{\prime } = 1+3 \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}-\frac {3 y}{2}+y^{\prime } = 2 \,{\mathrm e}^{t}+3 t
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}\ln \left (t \right ) y+\left (t -3\right ) y^{\prime } = 2 t
\] |
[_linear] |
✓ |
|
|
\[
{}y+\left (t -4\right ) t y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\tan \left (t \right ) y+y^{\prime } = \sin \left (t \right )
\] |
[_linear] |
✓ |
|
|
\[
{}2 t y+\left (-t^{2}+4\right ) y^{\prime } = 3 t^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}2 t y+\left (-t^{2}+4\right ) y^{\prime } = 3 t^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y+\ln \left (t \right ) y^{\prime } = \cot \left (t \right )
\] |
[_linear] |
✓ |
|
|
\[
{}2 y+2 x y^{2}+\left (2 x +2 x^{2} y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\frac {y}{x}+6 x +\left (\ln \left (x \right )-2\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = -1+{\mathrm e}^{2 x}+y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{3}-2 y}{x}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = 3-6 x +y-2 x y
\] |
[_separable] |
✓ |
|
|
\[
{}x y+y^{\prime } x = 1-y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +2 y = \frac {\sin \left (x \right )}{x}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y = \frac {1}{{\mathrm e}^{x}+1}
\] |
[_linear] |
✓ |
|
|
\[
{}\left ({\mathrm e}^{x}+1\right ) y^{\prime } = y-y \,{\mathrm e}^{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{2 x}+3 y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}2 y+y^{\prime } = {\mathrm e}^{-x^{2}-2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}\left (1+t \right ) y+t y^{\prime } = {\mathrm e}^{2 t}
\] |
[_linear] |
✓ |
|
|
\[
{}3 t +2 y = -t y^{\prime }
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +y = x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \cos \left (x \right )-y \tan \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{2}-2 x^{2} y+2}{x^{3}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+3 x^{2} y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x +y \ln \left (x \right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x +3 y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+\frac {\left (x +1\right ) y}{x} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x +\left (1+\frac {1}{\ln \left (x \right )}\right ) y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x +\left (1+x \cot \left (x \right )\right ) y = 0
\] |
[_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] |
✓ |
|
|
\[
{}y^{\prime }+\left (\frac {1}{x}-1\right ) y = -\frac {2}{x}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = x \,{\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {2 x y}{x^{2}+1} = \frac {{\mathrm e}^{-x^{2}}}{x^{2}+1}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{x} = \frac {7}{x^{2}}+3
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {4 y}{x -1} = \frac {1}{\left (x -1\right )^{5}}+\frac {\sin \left (x \right )}{\left (x -1\right )^{4}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +\left (2 x^{2}+1\right ) y = x^{3} {\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +2 y = \frac {2}{x^{2}}+1
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y \tan \left (x \right ) = \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}2 y+\left (x +1\right ) y^{\prime } = \frac {\sin \left (x \right )}{x +1}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x -2\right ) \left (x -1\right ) y^{\prime }-\left (4 x -3\right ) y = \left (x -2\right )^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+2 \sin \left (x \right ) \cos \left (x \right ) y = {\mathrm e}^{-\sin \left (x \right )^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+3 x y = {\mathrm e}^{x}
\] |
[_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] |
✓ |
|
|
\[
{}y^{\prime } x +3 y = \frac {2}{x \left (x^{2}+1\right )}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{x} = \frac {2}{x^{2}}+1
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x -1\right ) y^{\prime }+3 y = \frac {1}{\left (x -1\right )^{3}}+\frac {\sin \left (x \right )}{\left (x -1\right )^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +2 y = 8 x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x -2 y = -x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = x
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x -1\right ) y^{\prime }+3 y = \frac {1+\left (x -1\right ) \sec \left (x \right )^{2}}{\left (x -1\right )^{3}}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x +2\right ) y^{\prime }+4 y = \frac {2 x^{2}+1}{x \left (x +2\right )^{3}}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }-2 x y = x \left (x^{2}-1\right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x -2 y = -1
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+2 x \left (1+y\right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +1\right ) \left (x -2\right ) y^{\prime }+y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 x y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +y}{x}
\] |
[_linear] |
✓ |
|
|
\[
{}6 x^{2} y^{2}+4 x^{3} y y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}3 y \cos \left (x \right )+4 x \,{\mathrm e}^{x}+2 x^{3} y+\left (3 \sin \left (x \right )+3\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\sin \left (x \right )-\sin \left (x \right ) y-2 \cos \left (x \right )+y^{\prime } \cos \left (x \right ) = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\left (2 x -1\right ) \left (-1+y\right )+\left (x +2\right ) \left (x -3\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y-y^{\prime } x = 0
\] |
[_separable] |
✓ |
|
|
\[
{}3 x^{2} y+2 x^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}5 x y+2 y+5+2 y^{\prime } x = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x y+x +2 y+1+\left (x +1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y+4 x y+2 y+\left (x^{2}+x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}-y+\left (x^{4}-x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}a \cos \left (x \right ) y-y^{2} \sin \left (x \right )+\left (b \cos \left (x \right ) y-x \sin \left (x \right ) y\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x^{4} y^{4}+x^{5} y^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+\sin \left (t \right ) y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+{\mathrm e}^{t^{2}} y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-2 t y = t
\] |
[_separable] |
✓ |
|
|
\[
{}2 t y+y^{\prime } = t
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y = \frac {1}{t^{2}+1}
\] |
[_linear] |
✓ |
|
|
\[
{}\cos \left (t \right ) y+y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\sqrt {t}\, \sin \left (t \right ) y+y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\frac {2 t y}{t^{2}+1}+y^{\prime } = \frac {1}{t^{2}+1}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y = t \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}t^{2} y+y^{\prime } = 1
\] |
[_linear] |
✓ |
|
|
\[
{}t^{2} y+y^{\prime } = t^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}\frac {t y}{t^{2}+1}+y^{\prime } = 1-\frac {t^{3} y}{t^{4}+1}
\] |
[_linear] |
✓ |
|
|
\[
{}\sqrt {t^{2}+1}\, y+y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-2 t y = t
\] |
[_separable] |
✓ |
|
|
\[
{}t y+y^{\prime } = 1+t
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y = \frac {1}{t^{2}+1}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-2 t y = 1
\] |
[_linear] |
✓ |
|
|
\[
{}t y+\left (t^{2}+1\right ) y^{\prime } = \left (t^{2}+1\right )^{{5}/{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}4 t y+\left (t^{2}+1\right ) y^{\prime } = t
\] |
[_separable] |
✓ |
|
|
\[
{}\frac {y}{t}+y^{\prime } = \frac {1}{t^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{\sqrt {t}} = {\mathrm e}^{\frac {\sqrt {t}}{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}\frac {y}{t}+y^{\prime } = \cos \left (t \right )+\frac {\sin \left (t \right )}{t}
\] |
[_linear] |
✓ |
|
|
\[
{}\tan \left (t \right ) y+y^{\prime } = \cos \left (t \right ) \sin \left (t \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \left (1+t \right ) \left (y+1\right )
\] |
[_separable] |
✓ |
|
|
\[
{}3 t y^{\prime } = \cos \left (t \right ) y
\] |
[_separable] |
✓ |
|
|
\[
{}2 t y^{3}+3 t^{2} y^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = t \left (y+1\right )
\] |
[_separable] |
✓ |
|
|
\[
{}\cos \left (t \right ) y+y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\sqrt {t}\, \sin \left (t \right ) y+y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\frac {2 t y}{t^{2}+1}+y^{\prime } = \frac {1}{t^{2}+1}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y = t \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}t^{2} y+y^{\prime } = 1
\] |
[_linear] |
✓ |
|
|
\[
{}t^{2} y+y^{\prime } = t^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}\frac {t y}{t^{2}+1}+y^{\prime } = 1-\frac {t^{3} y}{t^{4}+1}
\] |
[_linear] |
✓ |
|
|
\[
{}\sqrt {t^{2}+1}\, y+y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-2 t y = t
\] |
[_separable] |
✓ |
|
|
\[
{}t y+y^{\prime } = 1+t
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y = \frac {1}{t^{2}+1}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-2 t y = 1
\] |
[_linear] |
✓ |
|
|
\[
{}t y+\left (t^{2}+1\right ) y^{\prime } = \left (t^{2}+1\right )^{{5}/{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}4 t y+\left (t^{2}+1\right ) y^{\prime } = t
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y = \left \{\begin {array}{cc} 2 & 0\le t \le 1 \\ 0 & 1<t \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \left (1+t \right ) \left (y+1\right )
\] |
[_separable] |
✓ |
|
|
\[
{}3 t y^{\prime } = \cos \left (t \right ) y
\] |
[_separable] |
✓ |
|
|
\[
{}2 t y^{3}+3 t^{2} y^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 t \left (y+1\right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = t \left (y+1\right )
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x +y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 x y
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime }-1+y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\tan \left (x \right ) y^{\prime }-y = 1
\] |
[_separable] |
✓ |
|
|
\[
{}y+3+\cot \left (x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y+\sqrt {x^{2}+1}\, y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y = x y+x^{2} y^{\prime }
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x +2 y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x +y = y^{\prime } x
\] |
[_linear] |
✓ |
|
|
\[
{}y \,{\mathrm e}^{x}-2 x +{\mathrm e}^{x} y^{\prime } = 0
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}\frac {2}{y}-\frac {y}{x^{2}}+\left (\frac {1}{x}-\frac {2 x}{y^{2}}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x +\ln \left (x \right )-y = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y \left (x^{2}-1\right )+x \left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x +2 y = x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-x y = {\mathrm e}^{\frac {x^{2}}{2}} \cos \left (x \right )
\] |
[_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‘]] |
✓ |
|
|
\[
{}y x^{\prime }+\left (1+y \right ) x = {\mathrm e}^{y}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x -2 x^{4}-2 y = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{2} x^{\prime }+\left (y^{2}+2 y \right ) x = 1
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x = 5 y+x +1
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+y-2 x y-2 x^{2} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}2 y+\left (x +1\right ) y^{\prime } = \frac {{\mathrm e}^{x}}{x +1}
\] |
[_linear] |
✓ |
|
|
\[
{}\cos \left (\theta \right ) r^{\prime } = 2+2 r \sin \left (\theta \right )
\] |
[_linear] |
✓ |
|
|
\[
{}\sin \left (\theta \right ) r^{\prime }+1+r \tan \left (\theta \right ) = \cos \left (\theta \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y x^{\prime } = 2 y \,{\mathrm e}^{3 y}+x \left (3 y +2\right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y \cot \left (x \right )-\sec \left (x \right ) = 0
\] |
[_linear] |
✓ |
|
|
\[
{}2 y-x y-3+y^{\prime } x = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+\left (x^{2}-1\right )^{2}+4 y = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\left (1-x \right ) y^{\prime }-1-y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x \ln \left (x \right ) y^{\prime }+y-x = 0
\] |
[_linear] |
✓ |
|
|
\[
{}r^{\prime } = r \cot \left (\theta \right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+x +y \cot \left (x \right ) = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x = x^{4}+4 y
\] |
[_linear] |
✓ |
|
|
\[
{}2 y+y^{\prime } = 3 \,{\mathrm e}^{2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}2 x y-2 y+1+x \left (x -1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+P \left (x \right ) y = Q \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}4 y^{2} = x^{2} {y^{\prime }}^{2}
\] |
[_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] |
✓ |
|
|
\[
{}y^{2}-2 x y y^{\prime }+\left (x^{2}-1\right ) {y^{\prime }}^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{t}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \left (t^{2}+1\right ) y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 y+{\mathrm e}^{-3 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = 2 y+{\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = t -y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}2 y+t y^{\prime } = \sin \left (t \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \tan \left (t \right ) y+\sec \left (t \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 t y}{t^{2}+1}+t +1
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \tan \left (t \right ) y+\sec \left (t \right )^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}t y^{\prime } = y+t^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = -\tan \left (t \right ) y+\sec \left (t \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y}{1+t}
\] |
[_separable] |
✓ |
|
|
\[
{}t y^{\prime } = -y+t^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+4 \tan \left (2 t \right ) y = \tan \left (2 t \right )
\] |
[_separable] |
✓ |
|
|
\[
{}t \ln \left (t \right ) y^{\prime } = t \ln \left (t \right )-y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y}{-t^{2}+1}+3
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = -\cot \left (t \right ) y+6 \cos \left (t \right )^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}\frac {y^{\prime }}{\tan \left (x \right )}-\frac {y}{x^{2}+1} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 y^{\prime } x +3 x +y = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+4 x y = \left (-x^{2}+1\right )^{{3}/{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-y \cot \left (x \right )+\frac {1}{\sin \left (x \right )} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {x y}{a^{2}+x^{2}} = x
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{x} = 1
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-y \tan \left (x \right ) = 1
\] |
[_linear] |
✓ |
|
|
\[
{}\sin \left (x \right ) y^{\prime }+2 y \cos \left (x \right ) = 1
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = 2 x y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x \ln \left (x \right )}
\] |
[_separable] |
✓ |
|
|
\[
{}y-\left (x -2\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x \left (-1+y\right )}{x^{2}+3}
\] |
[_separable] |
✓ |
|
|
\[
{}y-y^{\prime } x = 3-2 x^{2} y^{\prime }
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{2} y-32}{-x^{2}+16}+32
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime }-y+c = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+x y = a x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-y = {\mathrm e}^{2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime }-4 x y = x^{7} \sin \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = 2 x^{3}
\] |
[_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] |
✓ |
|
|
\[
{}2 \cos \left (x \right )^{2} y^{\prime }+y \sin \left (2 x \right ) = 4 \cos \left (x \right )^{4}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{x \ln \left (x \right )} = 9 x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-y \tan \left (x \right ) = 8 \sin \left (x \right )^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}t x^{\prime }+2 x = 4 \,{\mathrm e}^{t}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \sin \left (x \right ) \left (y \sec \left (x \right )-2\right )
\] |
[_linear] |
✓ |
|
|
\[
{}1-\sin \left (x \right ) y-y^{\prime } \cos \left (x \right ) = 0
\] |
[_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‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{2 x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 x y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x \ln \left (x \right )}
\] |
[_separable] |
✓ |
|
|
\[
{}y-\left (x -1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x \left (-1+y\right )}{x^{2}+3}
\] |
[_separable] |
✓ |
|
|
\[
{}y-y^{\prime } x = 3-2 x^{2} y^{\prime }
\] |
[_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] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+x y = a x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y = 4 \,{\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = 5 x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime }-4 x y = x^{7} \sin \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = 2 x^{3}
\] |
[_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] |
✓ |
|
|
\[
{}2 \cos \left (x \right )^{2} y^{\prime }+y \sin \left (2 x \right ) = 4 \cos \left (x \right )^{4}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{x \ln \left (x \right )} = 9 x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-y \tan \left (x \right ) = 8 \sin \left (x \right )^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}t x^{\prime }+2 x = 4 \,{\mathrm e}^{t}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \sin \left (x \right ) \left (y \sec \left (x \right )-2\right )
\] |
[_linear] |
✓ |
|
|
\[
{}1-\sin \left (x \right ) y-y^{\prime } \cos \left (x \right ) = 0
\] |
[_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‘]] |
✓ |
|
|
\[
{}y^{\prime }+\frac {m y}{x} = \ln \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = 4 x
\] |
[_linear] |
✓ |
|
|
\[
{}\sin \left (x \right ) y^{\prime }-y \cos \left (x \right ) = \sin \left (2 x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}x^{\prime }+\frac {2 x}{4-t} = 5
\] |
[_linear] |
✓ |
|
|
\[
{}y-{\mathrm e}^{x}+y^{\prime } = 0
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-2 y = \left \{\begin {array}{cc} 1 & x \le 1 \\ 0 & 1<x \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-2 y = \left \{\begin {array}{cc} 1-x & x <1 \\ 0 & 1\le x \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{x} = \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{-2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = 2 \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}-y+y^{\prime } x = x^{2} \ln \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y \left (x^{2}-y^{2}\right )-x \left (x^{2}-y^{2}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}3 y-2 x +\left (3 x -2\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y-2 x}{x}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y = x^{2}+2
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-y \tan \left (x \right ) = x
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x = x +y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-3 y = {\mathrm e}^{3 x}+{\mathrm e}^{-3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } x +2 y = \left (3 x +2\right ) {\mathrm e}^{3 x}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } \cos \left (x \right )+\sin \left (x \right ) y = 1
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-y = x^{3}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = x
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = \tan \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y \tan \left (x \right ) = \cot \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y \ln \left (x \right ) = x^{-x}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +y = x
\] |
[_linear] |
✓ |
|
|
\[
{}-y+y^{\prime } x = x^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +n y = x^{n}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x -n y = x^{n}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{3}+x \right ) y^{\prime }+y = x
\] |
[_linear] |
✓ |
|
|
\[
{}\cot \left (x \right ) y^{\prime }+y = x
\] |
[_linear] |
✓ |
|
|
\[
{}\cot \left (x \right ) y^{\prime }+y = \tan \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}\tan \left (x \right ) y^{\prime }+y = \cot \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}\tan \left (x \right ) y^{\prime } = y-\cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = \sin \left (2 x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } \cos \left (x \right )+y = \sin \left (2 x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\sin \left (x \right ) y = \sin \left (2 x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}\sin \left (x \right ) y^{\prime }+y = \sin \left (2 x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}\sqrt {x^{2}+1}\, y^{\prime }+y = 2 x
\] |
[_linear] |
✓ |
|
|
\[
{}\sqrt {x^{2}+1}\, y^{\prime }-y = 2 \sqrt {x^{2}+1}
\] |
[_linear] |
✓ |
|
|
\[
{}\sqrt {\left (x +a \right ) \left (x +b \right )}\, \left (2 y^{\prime }-3\right )+y = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\sqrt {\left (x +a \right ) \left (x +b \right )}\, y^{\prime }+y = \sqrt {x +a}-\sqrt {x +b}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x = y
\] |
[_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] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\cot \left (x \right ) y^{\prime } = y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-2 x y = 2 x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x = x y+y
\] |
[_separable] |
✓ |
|
|
\[
{}\left (1-x \right ) y^{\prime } = x y
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime } = \left (x^{2}+1\right ) y
\] |
[_separable] |
✓ |
|
|
\[
{}y+y \cos \left (x y\right )+\left (x +x \cos \left (x y\right )\right ) y^{\prime } = 0
\] |
[_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] |
✓ |
|
|
\[
{}y^{\prime } x -3 y = x^{4}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y = \frac {1}{1+{\mathrm e}^{2 x}}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+2 x y = \cot \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y = 2 x \,{\mathrm e}^{-x}+x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = 2 x \csc \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}2 y-x^{3} = y^{\prime } x
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +y = x \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y+x^{2} = y^{\prime } x
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +y = x^{2} \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = {\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+2 x y = 4 x^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}2 x y+x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\ln \left (x \right ) y^{\prime }+\frac {x +y}{x} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}1+y \cos \left (x \right )-\sin \left (x \right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\left (2 x +3\right ) y^{\prime } = y+\sqrt {2 x +3}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = 1+3 y \tan \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}\left (\cos \left (x \right )+1\right ) y^{\prime } = \sin \left (x \right ) \left (\sin \left (x \right )+\sin \left (x \right ) \cos \left (x \right )-y\right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \left (\sin \left (x \right )^{2}-y\right ) \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime }-y = x \left (x +1\right )^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y+2}{x +1}
\] |
[_separable] |
✓ |
|
|
\[
{}y-1-x y+y^{\prime } x = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x y+2 x^{3} y+x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\sin \left (x \right ) y+\cos \left (x \right )^{2}-y^{\prime } \cos \left (x \right ) = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\left (\cos \left (x \right )+1\right ) y^{\prime }+\sin \left (x \right ) \left (\sin \left (x \right )+\sin \left (x \right ) \cos \left (x \right )-y\right ) = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = x +\sin \left (x \right )+y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = x^{2}+3 \cosh \left (x \right )+2 y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = a +b x +c y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = a \cos \left (b x +c \right )+k y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = a \sin \left (b x +c \right )+k y
\] |
[[_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] |
✓ |
|
|
\[
{}y^{\prime } = x \left ({\mathrm e}^{-x^{2}}+a y\right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = x^{2} \left (a \,x^{3}+b y\right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = a \,x^{n} y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \sin \left (x \right ) \cos \left (x \right )+y \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{\sin \left (x \right )}+y \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = y \cot \left (x \right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 1-y \cot \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = x \csc \left (x \right )-y \cot \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \left (2 \csc \left (2 x \right )+\cot \left (x \right )\right ) y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \sec \left (x \right )-y \cot \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x} \sin \left (x \right )+y \cot \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\csc \left (x \right )+2 y \cot \left (x \right ) = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = 4 \csc \left (x \right ) x \sec \left (x \right )^{2}-2 y \cot \left (2 x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = 2 \cot \left (x \right )^{2} \cos \left (2 x \right )-2 y \csc \left (2 x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = 4 \csc \left (x \right ) x \left (\sin \left (x \right )^{3}+y\right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = 4 \csc \left (x \right ) x \left (1-\tan \left (x \right )^{2}+y\right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = y \sec \left (x \right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+\tan \left (x \right ) = \left (1-y\right ) \sec \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = y \tan \left (x \right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \cos \left (x \right )+y \tan \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \cos \left (x \right )-y \tan \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \sec \left (x \right )-y \tan \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \sin \left (2 x \right )+y \tan \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \sin \left (2 x \right )-y \tan \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \sin \left (x \right )+2 y \tan \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = 2+2 \sec \left (2 x \right )+2 y \tan \left (2 x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \csc \left (x \right )+3 y \tan \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \left (a +\cos \left (\ln \left (x \right )\right )+\sin \left (\ln \left (x \right )\right )\right ) y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 6 \,{\mathrm e}^{2 x}-y \tanh \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = f \left (x \right ) f^{\prime }\left (x \right )+f^{\prime }\left (x \right ) y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = f \left (x \right )+g \left (x \right ) y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \sin \left (x \right ) \left (2 \sec \left (x \right )^{2}-y\right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = y \sec \left (x \right )+\left (\sin \left (x \right )-1\right )^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \sec \left (x \right )^{2}+y \sec \left (x \right ) \operatorname {Csx} \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +x +y = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +x^{2}-y = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x = x^{3}-y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x = 1+x^{3}+y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x = x^{m}+y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x = x \sin \left (x \right )-y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x = x^{2} \sin \left (x \right )+y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x = x^{n} \ln \left (x \right )-y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x = \sin \left (x \right )-2 y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x = a y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x = 1+x +a y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x = a x +b y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x = a \,x^{2}+b y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x = a +b \,x^{n}+c y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +2+\left (3-x \right ) y = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +x +\left (a x +2\right ) y = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +\left (b x +a \right ) y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x = x^{3}+\left (-2 x^{2}+1\right ) y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x = a x -\left (-b \,x^{2}+1\right ) y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +x +\left (-a \,x^{2}+2\right ) y = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime } = x^{3} \left (4+3 x \right )+y
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime } = \left (x +1\right )^{4}+2 y
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime } = {\mathrm e}^{x} \left (x +1\right )^{n +1}+n y
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x +a \right ) y^{\prime } = b x +y
\] |
[_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] |
✓ |
|
|
\[
{}2 y^{\prime } x = 2 x^{3}-y
\] |
[_linear] |
✓ |
|
|
\[
{}\left (1-2 x \right ) y^{\prime } = 16+32 x -6 y
\] |
[_linear] |
✓ |
|
|
\[
{}2 \left (1-x \right ) y^{\prime } = 4 x \sqrt {1-x}+y
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = -y+a
\] |
[_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] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+\left (1-2 x \right ) y = x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = a +b x y
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = \left (b x +a \right ) y
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+x \left (x +2\right ) y = x \left (1-{\mathrm e}^{-2 x}\right )-2
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+2 x \left (1-x \right ) y = {\mathrm e}^{x} \left (2 \,{\mathrm e}^{x}-1\right )
\] |
[_linear] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = 1-x^{2}+y
\] |
[_linear] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+1 = x y
\] |
[_linear] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = 5-x y
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+a +x y = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+a -x y = 0
\] |
[_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] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }-x^{2}+x y = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+x^{2}+x y = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = x \left (x^{2}+1\right )-x y
\] |
[_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] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = 2 x \left (x -y\right )
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = 2 x \left (x^{2}+1\right )^{2}+2 x y
\] |
[_linear] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+\cos \left (x \right ) = 2 x y
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = \tan \left (x \right )-2 x y
\] |
[_linear] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = a +4 x y
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = \left (2 b x +a \right ) y
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = 1+x^{2}-y \,\operatorname {arccot}\left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}\left (a^{2}+x^{2}\right ) y^{\prime } = b +x y
\] |
[_linear] |
✓ |
|
|
\[
{}\left (a^{2}+x^{2}\right ) y^{\prime } = \left (b +y\right ) \left (x +\sqrt {a^{2}+x^{2}}\right )
\] |
[_separable] |
✓ |
|
|
\[
{}x \left (1-x \right ) y^{\prime } = a +\left (x +1\right ) y
\] |
[_linear] |
✓ |
|
|
\[
{}x \left (1-x \right ) y^{\prime } = 2+2 x y
\] |
[_linear] |
✓ |
|
|
\[
{}x \left (1-x \right ) y^{\prime } = 2 x y-2
\] |
[_linear] |
✓ |
|
|
\[
{}x \left (x +1\right ) y^{\prime } = \left (1-2 x \right ) y
\] |
[_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] |
✓ |
|
|
\[
{}x \left (1-x \right ) y^{\prime }+2-3 x y+y = 0
\] |
[_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] |
✓ |
|
|
\[
{}\left (x -2\right ) \left (x -3\right ) y^{\prime }+x^{2}-8 y+3 x y = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x +a \right )^{2} y^{\prime } = 2 \left (x +a \right ) \left (b +y\right )
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime }+k y = 0
\] |
[_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] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime } = y
\] |
[_separable] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime }+x \cot \left (x \right )-1+2 x^{2} y \cot \left (x \right ) = 0
\] |
[_linear] |
✓ |
|
|
\[
{}2 \left (-x^{2}+1\right ) y^{\prime } = \sqrt {-x^{2}+1}+\left (x +1\right ) y
\] |
[_linear] |
✓ |
|
|
\[
{}x \left (1-2 x \right ) y^{\prime }+1+\left (1-4 x \right ) y = 0
\] |
[_linear] |
✓ |
|
|
\[
{}2 x \left (1-x \right ) y^{\prime }+x +\left (1-2 x \right ) y = 0
\] |
[_linear] |
✓ |
|
|
\[
{}2 \left (x^{2}+x +1\right ) y^{\prime } = 1+8 x^{2}-\left (2 x +1\right ) y
\] |
[_linear] |
✓ |
|
|
\[
{}4 \left (x^{2}+1\right ) y^{\prime }-4 x y-x^{2} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x \left (a x +1\right ) y^{\prime }+a -y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{3} y^{\prime } = a +b \,x^{2} y
\] |
[_linear] |
✓ |
|
|
\[
{}x^{3} y^{\prime } = 3-x^{2}+x^{2} y
\] |
[_linear] |
✓ |
|
|
\[
{}x \left (x^{2}+1\right ) y^{\prime } = a \,x^{2}+y
\] |
[_linear] |
✓ |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime } = a \,x^{2}+y
\] |
[_linear] |
✓ |
|
|
\[
{}x \left (x^{2}+1\right ) y^{\prime } = a \,x^{3}+y
\] |
[_linear] |
✓ |
|
|
\[
{}x \left (x^{2}+1\right ) y^{\prime } = a -x^{2} y
\] |
[_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] |
✓ |
|
|
\[
{}x \left (x^{2}+1\right ) y^{\prime } = 2-4 x^{2} y
\] |
[_linear] |
✓ |
|
|
\[
{}x \left (x^{2}+1\right ) y^{\prime } = x -\left (5 x^{2}+3\right ) y
\] |
[_linear] |
✓ |
|
|
\[
{}x \left (-x^{3}+1\right ) y^{\prime } = 2 x -\left (-4 x^{3}+1\right ) y
\] |
[_linear] |
✓ |
|
|
\[
{}x \left (-2 x^{3}+1\right ) y^{\prime } = 2 \left (-x^{3}+1\right ) y
\] |
[_separable] |
✓ |
|
|
\[
{}x^{5} y^{\prime } = 1-3 x^{4} y
\] |
[_linear] |
✓ |
|
|
\[
{}x^{n} y^{\prime } = a +b \,x^{n -1} y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } \sqrt {x^{2}+1} = 2 x -y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } \sqrt {a^{2}+x^{2}}+x +y = \sqrt {a^{2}+x^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (1-4 \cos \left (x \right )^{2}\right ) y^{\prime } = \tan \left (x \right ) \left (1+4 \cos \left (x \right )^{2}\right ) y
\] |
[_separable] |
✓ |
|
|
\[
{}\left (1-\sin \left (x \right )\right ) y^{\prime }+y \cos \left (x \right ) = 0
\] |
[_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] |
✓ |
|
|
\[
{}\left (\operatorname {a0} +\operatorname {a1} \sin \left (x \right )^{2}\right ) y^{\prime }+\operatorname {a2} x \left (\operatorname {a3} +\operatorname {a1} \sin \left (x \right )^{2}\right )+\operatorname {a1} y \sin \left (2 x \right ) = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x -{\mathrm e}^{x}\right ) y^{\prime }+x \,{\mathrm e}^{x}+\left (1-{\mathrm e}^{x}\right ) y = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x \ln \left (x \right ) y^{\prime } = a x \left (1+\ln \left (x \right )\right )-y
\] |
[_linear] |
✓ |
|
|
\[
{}1-y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x +a \right ) \left (x +b \right ) y^{\prime } = x y
\] |
[_separable] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} = x^{2} y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}+y y^{\prime } = \left (x +y\right ) x
\] |
[_quadrature] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-\left (1+2 x y\right ) y^{\prime }+2 x y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-\left (x -y\right ) y y^{\prime }-x y^{3} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-x y \left (x^{2}+y^{2}\right ) y^{\prime }+x^{4} y^{4} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )-y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x {y^{\prime }}^{2}-\left (2 x +3 y\right ) y^{\prime }+6 y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}x {y^{\prime }}^{2}+\left (1-x \right ) y y^{\prime }-y^{2} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}x {y^{\prime }}^{2}+\left (1-x^{2} y\right ) y^{\prime }-x y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2} = y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2} = \left (x -y\right )^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-y^{\prime } x +y \left (1-y\right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+3 x y y^{\prime }+2 y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+4 x y y^{\prime }-5 y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-5 x y y^{\prime }+6 y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }-y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}4 x^{2} {y^{\prime }}^{2}-4 x y y^{\prime } = 8 x^{3}-y^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}\right ) y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x^{2}-y^{2}\right ) y^{\prime }-x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}-\left (x^{2}-y^{2}\right ) y^{\prime }-x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (3 x^{2}-2 y^{2}\right ) y^{\prime }-6 x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}-\left (2 x +y^{2}\right ) {y^{\prime }}^{2}+\left (x^{2}-y^{2}+2 x y^{2}\right ) y^{\prime }-\left (x^{2}-y^{2}\right ) y^{2} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}-\left (x^{2}+x y+y^{2}\right ) {y^{\prime }}^{2}+x y \left (x^{2}+x y+y^{2}\right ) y^{\prime }-x^{3} y^{3} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}x {y^{\prime }}^{3}-\left (x +x^{2}+y\right ) {y^{\prime }}^{2}+\left (x^{2}+y+x y\right ) y^{\prime }-x y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y \ln \left (y^{\prime }\right )+y^{\prime }-y \ln \left (y\right )-x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-\frac {2 y}{x +1} = \left (x +1\right )^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {x y}{x^{2}+1} = \frac {1}{2 x \left (x^{2}+1\right )}
\] |
[_linear] |
✓ |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y = a \,x^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{\left (-x^{2}+1\right )^{{3}/{2}}} = \frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = \frac {\sin \left (2 x \right )}{2}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+y = \arctan \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}\frac {y-y^{\prime } x}{y^{2}+y^{\prime }} = \frac {y-y^{\prime } x}{1+x^{2} y^{\prime }}
\] |
[_separable] |
✓ |
|
|
\[
{}7 y-3+\left (2 x +1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x +y = x^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}x^{\prime }+2 x y = {\mathrm e}^{-y^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}r^{\prime } = \left (r+{\mathrm e}^{-\theta }\right ) \tan \left (\theta \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-\frac {2 x y}{x^{2}+1} = 1
\] |
[_linear] |
✓ |
|
|
\[
{}\tan \left (\theta \right ) r^{\prime }-r = \tan \left (\theta \right )^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}2 y+y^{\prime } = 3 \,{\mathrm e}^{-2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}2 y+y^{\prime } = \frac {3 \,{\mathrm e}^{-2 x}}{4}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}2 y+y^{\prime } = \sin \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = {\mathrm e}^{2 x}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = \frac {\sin \left (2 x \right )}{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +y = x \sin \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}-y+y^{\prime } x = x^{2} \sin \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-y = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}2 y-x y \ln \left (x \right )-2 x \ln \left (x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+a y = k \,{\mathrm e}^{b x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+a y = b \sin \left (k x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = {\mathrm e}^{-\sin \left (x \right )}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +a y+b \,x^{n} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+2 x y-\cos \left (x \right ) = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } \cos \left (x \right )+y+\left (1+\sin \left (x \right )\right ) \cos \left (x \right ) = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y \tan \left (x \right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{a x}+a y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } x = y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-x y = x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+3 x y = 1
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+2 x y-x \,{\mathrm e}^{-x^{2}} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}2 y^{\prime } x +y = 2 x^{{5}/{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } \cos \left (x \right )+y = \cos \left (x \right )^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{\sqrt {x^{2}+1}} = \frac {1}{x +\sqrt {x^{2}+1}}
\] |
[_linear] |
✓ |
|
|
\[
{}\left ({\mathrm e}^{x}+1\right ) y^{\prime }+2 y \,{\mathrm e}^{x} = \left ({\mathrm e}^{x}+1\right ) {\mathrm e}^{x}
\] |
[_linear] |
✓ |
|
|
\[
{}x \ln \left (x \right ) y^{\prime }+y = \ln \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = x y+2 x \sqrt {-x^{2}+1}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y \tanh \left (x \right ) = 2 \,{\mathrm e}^{x}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = \sin \left (2 x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}x^{\prime } = \cos \left (y \right )-x \tan \left (y \right )
\] |
[_linear] |
✓ |
|
|
\[
{}x^{\prime }+x-{\mathrm e}^{y} = 0
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}x^{\prime } = \frac {3 y^{{2}/{3}}-x}{3 y}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x -1\right ) y^{\prime }+y-\frac {1}{x^{2}}+\frac {2}{x^{3}} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime }-x y = \frac {1}{x}
\] |
[_linear] |
✓ |
|
|
\[
{}y+2 x -y^{\prime } x = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\sin \left (x \right )^{2} y^{\prime }+\sin \left (x \right )^{2}+\left (x +y\right ) \sin \left (2 x \right ) = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\sin \left (\theta \right ) \cos \left (\theta \right ) r^{\prime }-\sin \left (\theta \right )^{2} = r \cos \left (\theta \right )^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}3 x^{2} y+x^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}-y+y^{\prime } x = x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x = x y+y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 3 x^{2} y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x = y
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime } = 3 x t^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x^{3} \left (1-y\right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x^{2} \left (1+y\right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 y-2 t y
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+\sin \left (x \right )-y = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\left (t^{2}+1\right ) y^{\prime } = t y-y
\] |
[_separable] |
✓ |
|
|
\[
{}3 t = {\mathrm e}^{t} y^{\prime }+\ln \left (t \right ) y
\] |
[_linear] |
✓ |
|
|
\[
{}3 r = r^{\prime }-\theta ^{3}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-y-{\mathrm e}^{3 x} = 0
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x}+2 x +1
\] |
[_linear] |
✓ |
|
|
\[
{}r^{\prime }+r \tan \left (\theta \right ) = \sec \left (\theta \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +2 y = \frac {1}{x^{3}}
\] |
[_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] |
✓ |
|
|
\[
{}y^{\prime } x +3 y+3 x^{2} = \frac {\sin \left (x \right )}{x}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x y-x = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }-x^{2} y = \left (x +1\right ) \sqrt {-x^{2}+1}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{x} = x \,{\mathrm e}^{x}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+4 y-{\mathrm e}^{-x} = 0
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}t^{2} x^{\prime }+3 t x = t^{4} \ln \left (t \right )+1
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {3 y}{x}+2 = 3 x
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } \cos \left (x \right )+\sin \left (x \right ) y = 2 x \cos \left (x \right )^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}\sin \left (x \right ) y^{\prime }+y \cos \left (x \right ) = x \sin \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y \sqrt {1+\sin \left (x \right )^{2}} = x
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {3 y}{x} = x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}x^{\prime } = \alpha -\beta \cos \left (\frac {\pi t}{12}\right )-k x
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2} y+x^{4} \cos \left (x \right )-x^{3} y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x^{{10}/{3}}-2 y+y^{\prime } x = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-4 y = 32 x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+\frac {3 y}{x} = x^{2}-4 x +3
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-y = {\mathrm e}^{2 x}
\] |
[[_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‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+2 x y = \sinh \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{1-x}+2 x -x^{2} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{1-x}+x -x^{2} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = 1+x y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-\frac {2 y}{x}-x^{2} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {2 y}{x}-x^{3} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}2 y+y^{\prime } = {\mathrm e}^{3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}-y+y^{\prime } x = x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+2 x y = x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y \tanh \left (x \right ) = 2 \sinh \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x -2 y = x^{3} \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime } = x^{2} y
\] |
[_separable] |
✓ |
|
|
\[
{}-y+y^{\prime } x = x^{3}+3 x^{2}-2 x
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y \tan \left (x \right ) = \sin \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}-y+y^{\prime } x = x^{3} \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+3 x y = 5 x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = 5 \,{\mathrm e}^{\cos \left (x \right )}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = 1+x y
\] |
[_linear] |
✓ |
|
|
\[
{}y+\left (x^{2}-4 x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-y \tan \left (x \right ) = \cos \left (x \right )-2 x \sin \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = x \left (1+y\right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x +2 y = 3 x -1
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{x} = \sin \left (2 x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}\left (-x^{3}+1\right ) y^{\prime }+x^{2} y = x^{2} \left (-x^{3}+1\right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{x} = \sin \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\left (\frac {1}{x}-\frac {2 x}{-x^{2}+1}\right ) y = \frac {1}{-x^{2}+1}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x y = \left (x^{2}+1\right )^{{3}/{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-5 y = \left (x -1\right ) \sin \left (x \right )+\left (x +1\right ) \cos \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-5 y = 3 \,{\mathrm e}^{x}-2 x +1
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-5 y = x^{2} {\mathrm e}^{x}-x \,{\mathrm e}^{5 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-y = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-y = x \,{\mathrm e}^{2 x}+1
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-y = \sin \left (x \right )+\cos \left (2 x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+\frac {4 y}{x} = x^{4}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{x} = x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x = 2 y
\] |
[_separable] |
✓ |
|
|
\[
{}4 y+y^{\prime } x = 0
\] |
[_separable] |
✓ |
|
|
\[
{}1+2 y+\left (-x^{2}+4\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}1+y-\left (x +1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}1+2 y-\left (4-x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x +2 y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y = 2+2 x
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-y = x y
\] |
[_separable] |
✓ |
|
|
\[
{}-3 y-\left (x -2\right ) {\mathrm e}^{x}+y^{\prime } x = 0
\] |
[_linear] |
✓ |
|
|
\[
{}i^{\prime }-6 i = 10 \sin \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}r^{\prime }+2 r \cos \left (\theta \right )+\sin \left (2 \theta \right ) = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x = y \left (1-x \tan \left (x \right )\right )+x^{2} \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x = 2 y+x^{3} {\mathrm e}^{x}
\] |
[_linear] |
✓ |
|
|
\[
{}L i^{\prime }+R i = E \sin \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+x y y^{\prime }-6 y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x {y^{\prime }}^{2}+\left (y-1-x^{2}\right ) y^{\prime }-x \left (-1+y\right ) = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } x = 1-x +2 y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+x y = \frac {1}{x^{3}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+4 x y = 8 x^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x -3 x y = 1
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}2 y^{\prime } x -y = 2 x \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+x y = 10 \sin \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = 1
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x -2 y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}3 y^{\prime } x +5 y = 10
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x = 2 y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x = y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-y = x
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } x = y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x -2 y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}2 y+y^{\prime } = 3 x -6
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } x = y
\] |
[_separable] |
✓ |
|
|
\[
{}3 y^{\prime } x -2 y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x +y = 2 x
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\sin \left (x \right ) y = x
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-2 x y = {\mathrm e}^{x}
\] |
[_linear] |
✓ |
|
|
\[
{}2 y+y^{\prime } = 3 x
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = 1-x y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = 1-x y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = 1-x y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = 1-x y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{5}+y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{5}+y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = y-\cos \left (\frac {\pi x}{2}\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = y-\cos \left (\frac {\pi x}{2}\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = 1-\frac {y}{x}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = 1-\frac {y}{x}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = x^{2}-2 y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } x = 4 y
\] |
[_separable] |
✓ |
|
|
\[
{}n^{\prime }+n = n t \,{\mathrm e}^{t +2}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = y-x y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y \,{\mathrm e}^{-x^{2}}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y+\frac {y}{x \ln \left (x \right )}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+3 x^{2} y = x^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = x^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+x y = 1
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = 2 y+x^{2}+5
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}-y+y^{\prime } x = x^{2} \sin \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +2 y = 3
\] |
[_separable] |
✓ |
|
|
\[
{}4 y+y^{\prime } x = x^{3}-x
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime }-x y = x^{2}+x
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+x \left (x +2\right ) y = {\mathrm e}^{x}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +\left (x +1\right ) y = {\mathrm e}^{-x} \sin \left (2 x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } \cos \left (x \right )+\sin \left (x \right ) y = 1
\] |
[_linear] |
✓ |
|
|
\[
{}\cos \left (x \right )^{2} \sin \left (x \right ) y^{\prime }+\cos \left (x \right )^{3} y = 1
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime }+\left (x +2\right ) y = 2 x \,{\mathrm e}^{-x}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x +2\right )^{2} y^{\prime } = 5-8 y-4 x y
\] |
[_linear] |
✓ |
|
|
\[
{}r^{\prime }+r \sec \left (t \right ) = \cos \left (t \right )
\] |
[_linear] |
✓ |
|
|
\[
{}p^{\prime }+2 t p = p+4 t -2
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x +\left (3 x +1\right ) y = {\mathrm e}^{-3 x}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+2 y = \left (x +1\right )^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = x +5 y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = 2 x -3 y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } x +y = {\mathrm e}^{x}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +y = 4 x +1
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+4 x y = x^{3} {\mathrm e}^{x^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime }+y = \ln \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}x \left (x +1\right ) y^{\prime }+x y = 1
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-\sin \left (x \right ) y = 2 \sin \left (x \right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y \tan \left (x \right ) = \cos \left (x \right )^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}2 y+y^{\prime } = \left \{\begin {array}{cc} 1 & 0\le x \le 3 \\ 0 & 3<x \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y = \left \{\begin {array}{cc} 1 & 0\le x \le 1 \\ -1 & 1<x \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = \left \{\begin {array}{cc} x & 0\le x <1 \\ 0 & 1\le x \end {array}\right .
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+2 x y = \left \{\begin {array}{cc} x & 0\le x <1 \\ -x & 1\le x \end {array}\right .
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\left (\left \{\begin {array}{cc} 2 & 0\le x \le 1 \\ -\frac {2}{x} & 1<x \end {array}\right .\right ) y = 4 x
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\left (\left \{\begin {array}{cc} 1 & 0\le x \le 2 \\ 5 & 2<x \end {array}\right .\right ) y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-2 x y = 1
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-2 x y = -1
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y \,{\mathrm e}^{x} = 1
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime }-y = x^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}2 x^{2} y+x^{3} y^{\prime } = 10 \sin \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-\sin \left (x^{2}\right ) y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x -4 y = x^{6} {\mathrm e}^{x}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x -4 y = x^{6} {\mathrm e}^{x}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \sin \left (x \right ) y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \left (-1+y\right ) \left (x +1\right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-y = 2 x -3
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y = 2 x +1
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y-2 x y+x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } \left (y^{\prime }+y\right ) = \left (x +y\right ) x
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-3 x y y^{\prime }+2 y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+\frac {x +2 y}{x} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x = x +\frac {y}{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y \,{\mathrm e}^{x y}+x \,{\mathrm e}^{x y} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = \sin \left (x \right ) \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_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‘]] |
✓ |
|
|
\[
{}L y^{\prime }+R y = E \sin \left (\omega x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}L y^{\prime }+R y = E \,{\mathrm e}^{i \omega x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+a y = b \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x +y = 3 x^{3}-1
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y \,{\mathrm e}^{x} = 3 \,{\mathrm e}^{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-y \tan \left (x \right ) = {\mathrm e}^{\sin \left (x \right )}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = x \,{\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = {\mathrm e}^{-\sin \left (x \right )}
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+2 x y = 1
\] |
[_linear] |
✓ |
|
|
\[
{}2 y+y^{\prime } = b \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = x^{2} y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x = 2 y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 1+2 x y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = 4 x y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y \tan \left (x \right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-y \tan \left (x \right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+x y = x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y = \frac {1}{1+{\mathrm e}^{2 x}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y = 2 x \,{\mathrm e}^{-x}+x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}2 y-x^{3} = y^{\prime } x
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x -3 y = x^{4}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+2 x y = \cot \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = 2 x \csc \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y-x +x y \cot \left (x \right )+y^{\prime } x = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-2 x y = 6 x \,{\mathrm e}^{x^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{x} = x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+4 y = {\mathrm e}^{-x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+x y = 2 x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x = 2 x^{2} y+y \ln \left (x \right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } \sin \left (2 x \right ) = 2 y+2 \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y+y \cos \left (x y\right )+\left (x +x \cos \left (x y\right )\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}1+y+\left (1-x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x = 2 x -6 y
\] |
[_linear] |
✓ |
|
|
\[
{}2 x +3 y-1-4 \left (x +1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +y = x
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+y = x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = y
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+2 x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}-y+y^{\prime } x = 2 x
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime }-2 y = 3 x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}\frac {1}{y}-\frac {x y^{\prime }}{y^{2}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y = \cos \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = 2 x y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-y = x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } x = y
\] |
[_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] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+y^{\prime } x -y^{2}-y = 0
\] |
[_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] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-x^{2} y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-y^{\prime } x y \left (x +y\right )+x^{3} y^{3} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x {y^{\prime }}^{3}-\left (x +x^{2}+y\right ) {y^{\prime }}^{2}+\left (x^{2}+y+x y\right ) y^{\prime }-x y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}6 x {y^{\prime }}^{2}-\left (3 x +2 y\right ) y^{\prime }+y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2} = \left (x -y\right )^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}x {y^{\prime }}^{2}+\left (1-x \right ) y y^{\prime }-y^{2} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x \ln \left (x \right )}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = 5 x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}t x^{\prime }+2 x = 4 \,{\mathrm e}^{t}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = x +\frac {\sec \left (x \right ) y}{x}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y \left (1+\frac {a^{2} x}{\sqrt {a^{2} \left (x^{2}+1\right )}}\right )}{\sqrt {a^{2} \left (x^{2}+1\right )}}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y a x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = a x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = a x +b y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}c y^{\prime } = a x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}c y^{\prime } = a x +b y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \sin \left (x \right )+y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \cos \left (x \right )+\frac {y}{x}
\] |
[_linear] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} = \frac {y^{2}}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = 2 \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+a y-c \,{\mathrm e}^{b x} = 0
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+a y-b \sin \left (c x \right ) = 0
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+2 x y-x \,{\mathrm e}^{-x^{2}} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y \cos \left (x \right )-{\mathrm e}^{2 x} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y \cos \left (x \right )-\frac {\sin \left (2 x \right )}{2} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y \cos \left (x \right )-{\mathrm e}^{-\sin \left (x \right )} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y \tan \left (x \right )-\sin \left (2 x \right ) = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-\left (a +\cos \left (\ln \left (x \right )\right )+\sin \left (\ln \left (x \right )\right )\right ) y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+f^{\prime }\left (x \right ) y-f \left (x \right ) f^{\prime }\left (x \right ) = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+f \left (x \right ) y-g \left (x \right ) = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +y-x \sin \left (x \right ) = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x -y-\frac {x}{\ln \left (x \right )} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x -y-x^{2} \sin \left (x \right ) = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x -y-\frac {x \cos \left (\ln \left (\ln \left (x \right )\right )\right )}{\ln \left (x \right )} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +a y+b \,x^{n} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}2 y^{\prime } x -y-2 x^{3} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+y-x = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime }-y+x^{2} {\mathrm e}^{x -\frac {1}{x}} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime }-\left (x -1\right ) y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x y-1 = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x y-x \left (x^{2}+1\right ) = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+2 x y-2 x^{2} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }-x y+a = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+2 x y-\cos \left (x \right ) = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}-5 x +6\right ) y^{\prime }+3 x y-8 y+x^{2} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x \left (x^{2}+1\right ) y^{\prime }+x^{2} y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x \left (x^{2}-1\right ) y^{\prime }-\left (2 x^{2}-1\right ) y+a \,x^{3} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\left (2 x^{4}-x \right ) y^{\prime }-2 \left (x^{3}-1\right ) y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } \sqrt {a^{2}+x^{2}}+y-\sqrt {a^{2}+x^{2}}+x = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x \ln \left (x \right ) y^{\prime }+y-a x \left (1+\ln \left (x \right )\right ) = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } \cos \left (x \right )+y+\left (1+\sin \left (x \right )\right ) \cos \left (x \right ) = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\sin \left (x \right ) \cos \left (x \right ) y^{\prime }-y-\sin \left (x \right )^{3} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\left (a \sin \left (x \right )^{2}+b \right ) y^{\prime }+a y \sin \left (2 x \right )+A x \left (a \sin \left (x \right )^{2}+c \right ) = 0
\] |
[_linear] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )-y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}+y \left (y-x \right ) y^{\prime }-x y^{3} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+3 x y y^{\prime }+2 y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+3 x y y^{\prime }+3 y^{2} = 0
\] |
[_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] |
✓ |
|
|
\[
{}\left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}\right ) y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-a x y y^{\prime }+2 a y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}-\left (x^{2}+x y+y^{2}\right ) {y^{\prime }}^{2}+\left (x^{3} y+x^{2} y^{2}+x y^{3}\right ) y^{\prime }-x^{3} y^{3} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y \ln \left (y^{\prime }\right )+y^{\prime }-y \ln \left (y\right )-x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}g \left (x \right ) y^{\prime } = f_{1} \left (x \right ) y+f_{0} \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = a \ln \left (x \right )^{n} y-a b x \ln \left (x \right )^{n +1} y+b \ln \left (x \right )+b
\] |
[_linear] |
✓ |
|
|
\[
{}y+x +y^{\prime } x = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = \sec \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +\left (x +1\right ) y = {\mathrm e}^{x}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-\frac {2 y}{x +1} = \left (x +1\right )^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{3}+x \right ) y^{\prime }+4 x^{2} y = 2
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+\left (1-2 x \right ) y = x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{2} \left (3 y-6 y^{\prime } x \right )-x \left (y-2 y^{\prime } x \right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{3} y-y^{4}+\left (x y^{3}-x^{4}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x -y+2 x^{2} y-x^{3} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-x^{2} y = x^{5}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{\left (-x^{2}+1\right )^{{3}/{2}}} = \frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+y = \arctan \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = \frac {\sin \left (2 x \right )}{2}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (2 y^{\prime } x -y\right )^{2} = 8 x^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}-\left (2 x +y^{2}\right ) {y^{\prime }}^{2}+\left (x^{2}-y^{2}+2 x y^{2}\right ) y^{\prime }-\left (x^{2}-y^{2}\right ) y^{2} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right ) = y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-2 \left (x y+2 y^{\prime }\right ) y^{\prime }+y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime } = \frac {2 x}{t}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime }+2 x = t^{2}+4 t +7
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}2 t x^{\prime } = x
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime } = \frac {2 x}{1+t}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime } {\mathrm e}^{2 t}+2 x \,{\mathrm e}^{2 t} = {\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}x^{\prime } = 2 t^{3} x-6
\] |
[_linear] |
✓ |
|
|
\[
{}7 t^{2} x^{\prime } = 3 x-2 t
\] |
[_linear] |
✓ |
|
|
\[
{}x^{\prime } = -\frac {2 x}{t}+t
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}x^{\prime }+2 t x = {\mathrm e}^{-t^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}t x^{\prime } = -x+t^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}\theta ^{\prime } = -a \theta +{\mathrm e}^{b t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}\left (t^{2}+1\right ) x^{\prime } = -3 t x+6 t
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime }+\frac {5 x}{t} = 1+t
\] |
[_linear] |
✓ |
|
|
\[
{}x^{\prime } = \left (a +\frac {b}{t}\right ) x
\] |
[_separable] |
✓ |
|
|
\[
{}R^{\prime }+\frac {R}{t} = \frac {2}{t^{2}+1}
\] |
[_linear] |
✓ |
|
|
\[
{}N^{\prime } = N-9 \,{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}\cos \left (\theta \right ) v^{\prime }+v = 3
\] |
[_separable] |
✓ |
|
|
\[
{}R^{\prime } = \frac {R}{t}+t \,{\mathrm e}^{-t}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+a y = \sqrt {1+t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}x^{\prime } = 2 t x
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime }+\frac {{\mathrm e}^{-t} x}{t} = t
\] |
[_linear] |
✓ |
|
|
\[
{}x^{\prime }+p \left (t \right ) x = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{3}+3 t x^{2} x^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y = x +1
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+3 y = 3 x^{2} {\mathrm e}^{-3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+4 x y = 8 x
\] |
[_separable] |
✓ |
|
|
\[
{}2 y+y^{\prime } = 6 \,{\mathrm e}^{x}+4 x \,{\mathrm e}^{-2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y = 2 x \,{\mathrm e}^{-x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y = 2 x \,{\mathrm e}^{-x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}4 x y+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x y+2 x +y+2+\left (x^{2}+2 x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x +y-y^{\prime } x = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {3 y}{x} = 6 x^{2}
\] |
[_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] |
✓ |
|
|
\[
{}y^{\prime } x +\frac {\left (2 x +1\right ) y}{x +1} = x -1
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}+x -2\right ) y^{\prime }+3 \left (x +1\right ) y = x -1
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +x y+y-1 = 0
\] |
[_linear] |
✓ |
|
|
\[
{}r^{\prime }+r \tan \left (t \right ) = \cos \left (t \right )
\] |
[_linear] |
✓ |
|
|
\[
{}\cos \left (t \right ) r^{\prime }+r \sin \left (t \right )-\cos \left (t \right )^{4} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\cos \left (x \right )^{2}-y \cos \left (x \right )-\left (1+\sin \left (x \right )\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y \sin \left (2 x \right )-\cos \left (x \right )+\left (1+\sin \left (x \right )^{2}\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x -2 y = 2 x^{4}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+3 x^{2} y = x^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}{\mathrm e}^{x} \left (y-3 \left ({\mathrm e}^{x}+1\right )^{2}\right )+\left ({\mathrm e}^{x}+1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}2 x \left (1+y\right )-\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}r^{\prime }+r \tan \left (t \right ) = \cos \left (t \right )^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}x^{\prime }-x = \sin \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y = \left \{\begin {array}{cc} 2 & 0\le x <1 \\ 0 & 1\le x \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y = \left \{\begin {array}{cc} 5 & 0\le x <10 \\ 1 & 10\le x \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y = \left \{\begin {array}{cc} {\mathrm e}^{-x} & 0\le x <2 \\ {\mathrm e}^{-2} & 2\le x \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x +2\right ) y^{\prime }+y = \left \{\begin {array}{cc} 2 x & 0\le x <2 \\ 4 & 2\le x \end {array}\right .
\] |
[_linear] |
✓ |
|
|
\[
{}a y^{\prime }+b y = k \,{\mathrm e}^{-\lambda x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y = 2 \sin \left (x \right )+5 \sin \left (2 x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}6 x^{2} y-\left (x^{3}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y-1+x \left (x +1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2}-2 y+y^{\prime } x = 0
\] |
[_linear] |
✓ |
|
|
\[
{}{\mathrm e}^{2 x} y^{2}+\left ({\mathrm e}^{2 x} y-2 y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}8 x^{3} y-12 x^{3}+\left (x^{4}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime }+x y = {\mathrm e}^{-x}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime }+6 x^{2} y = 6 x^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {x y}{x^{2}+1}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y = \left \{\begin {array}{cc} 1 & 0\le x <2 \\ 0 & 0<x \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x +2\right ) y^{\prime }+y = \left \{\begin {array}{cc} 2 x & 0\le x \le 2 \\ 4 & 2<x \end {array}\right .
\] |
[_linear] |
✓ |
|
|
\[
{}x^{\prime } {\mathrm e}^{3 t}+3 x \,{\mathrm e}^{3 t} = {\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}x^{\prime } = t^{3} \left (-x+1\right )
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime } = x t^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x = k y
\] |
[_separable] |
✓ |
|
|
\[
{}i^{\prime } = p \left (t \right ) i
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{x} = x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}x^{\prime }+t x = 4 t
\] |
[_separable] |
✓ |
|
|
\[
{}z^{\prime } = z \tan \left (y \right )+\sin \left (y \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+{\mathrm e}^{-x} y = 1
\] |
[_linear] |
✓ |
|
|
\[
{}x^{\prime }+x \tanh \left (t \right ) = 3
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+2 y \cot \left (x \right ) = 5
\] |
[_linear] |
✓ |
|
|
\[
{}x^{\prime }+5 x = t
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}x^{\prime }+\left (a +\frac {1}{t}\right ) x = b
\] |
[_linear] |
✓ |
|
|
\[
{}T^{\prime } = -k \left (T-\mu -a \cos \left (\omega \left (t -\phi \right )\right )\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}1+y \,{\mathrm e}^{x}+x \,{\mathrm e}^{x} y+\left (x \,{\mathrm e}^{x}+2\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +y = x^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}x^{\prime }+3 x = {\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}\sin \left (x \right ) y+y^{\prime } \cos \left (x \right ) = 1
\] |
[_linear] |
✓ |
|
|
\[
{}x^{\prime } = x+\sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}-\left (x^{2}+y^{2}\right ) y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime }+5 x = 10 t +2
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}x^{\prime }-x \cot \left (t \right ) = 4 \sin \left (t \right )
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+2 x y-\cos \left (x \right ) = 0
\] |
[_linear] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )-y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } \cos \left (x \right )+y \,{\mathrm e}^{x^{2}} = \sinh \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}5 y^{\prime }-x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = \frac {\sin \left (2 x \right )}{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y-y^{\prime } x = 0
\] |
[_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] |
✓ |
|
|
\[
{}r^{\prime }+r \tan \left (t \right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y+x +y^{\prime } x = 0
\] |
[_linear] |
✓ |
|
|
\[
{}t -s+t s^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x +2 y+1-\left (2 x -3\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-\frac {2 y}{x +1} = \left (x +1\right )^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-\frac {a y}{x} = \frac {x +1}{x}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (-x^{2}+x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y-a \,x^{3} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}s^{\prime } \cos \left (t \right )+s \sin \left (t \right ) = 1
\] |
[_linear] |
✓ |
|
|
\[
{}s^{\prime }+s \cos \left (t \right ) = \frac {\sin \left (2 t \right )}{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-\frac {n y}{x} = {\mathrm e}^{x} x^{n}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {n y}{x} = a \,x^{-n}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{-x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+\frac {\left (1-2 x \right ) y}{x^{2}}-1 = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y = y^{\prime } x +y^{\prime }
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y}{x}-\sqrt {3}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }-x y-\alpha = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{x} = {\mathrm e}^{x}
\] |
[_linear] |
✓ |
|
|
\[
{}-y+y^{\prime } x = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{x} = 1
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+2 x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 y^{\prime } x -y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-2 x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y = x^{2}+2 x -1
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}x \ln \left (x \right ) y^{\prime }-\left (1+\ln \left (x \right )\right ) y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -x y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = x y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {3 y}{\left (x -5\right ) \left (x +3\right )}+{\mathrm e}^{-x}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = x y+\frac {1}{x^{2}+1}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \cos \left (x \right )+\frac {y}{x}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\tan \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{-x^{2}+4}+\sqrt {x}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{-x^{2}+4}+\sqrt {x}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = y \cot \left (x \right )+\csc \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x y+x
\] |
[_separable] |
✓ |
|
|
\[
{}y-x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1-x y}{x^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = x y+2
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_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] |
✓ |
|
|
\[
{}y^{\prime } = y \cot \left (x \right )+\sin \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y-y^{\prime } x = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2}-y+y^{\prime } x = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y \left (2 x -1\right )+x \left (x +1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{-x^{2}+1}+\sqrt {x}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{-x^{2}+1}+\sqrt {x}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{-x^{2}+1}+\sqrt {x}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y+1}{1+t}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = t^{4} y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y+1}{t}
\] |
[_separable] |
✓ |
|
|
\[
{}v^{\prime } = t^{2} v-2-2 v+t^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}w^{\prime } = \frac {w}{t}
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime } = -t x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = t y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y+t +1
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = 2 y-t
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \left (1+t \right ) y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = t^{2}+t^{2} y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = t +t y
\] |
[_separable] |
✓ |
|
|
\[
{}v^{\prime } = 2 V \left (t \right )-2 v
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = -4 y+9 \,{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = -4 y+3 \,{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = -3 y+4 \cos \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = 2 y+\sin \left (2 t \right )
\] |
[[_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‘]] |
✓ |
|
|
\[
{}-2 y+y^{\prime } = 3 \,{\mathrm e}^{-2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y = \cos \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+3 y = \cos \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}-2 y+y^{\prime } = 7 \,{\mathrm e}^{2 t}
\] |
[[_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‘]] |
✓ |
|
|
\[
{}y^{\prime }+y = t^{3}+\sin \left (3 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-3 y = 2 t -{\mathrm e}^{4 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y = \cos \left (2 t \right )+3 \sin \left (2 t \right )+{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y}{t}+2
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {3 y}{t}+t^{5}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y}{1+t}+t^{2}
\] |
[_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] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y}{1+t}+2
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{1+t}+4 t^{2}+4 t
\] |
[_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] |
✓ |
|
|
\[
{}y^{\prime } = \sin \left (t \right ) y+4
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = t^{2} y+4
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{t^{2}}+4 \cos \left (t \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = y+4 \cos \left (t^{2}\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = -y \,{\mathrm e}^{-t^{2}}+\cos \left (t \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{\sqrt {t^{3}-3}}+t
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = a t y+4 \,{\mathrm e}^{-t^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = t^{r} y+4
\] |
[_linear] |
✓ |
|
|
\[
{}v^{\prime }+\frac {2 v}{5} = 3 \cos \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = -2 t y+4 \,{\mathrm e}^{-t^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+2 y = 3 \,{\mathrm e}^{-2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = y+{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = t y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 3 y+{\mathrm e}^{7 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {t y}{t^{2}+1}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -5 y+\sin \left (3 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = t +\frac {2 y}{1+t}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = -3 y+{\mathrm e}^{-2 t}+t^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}x^{\prime } = -t x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 y+\cos \left (4 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = 3 y+2 \,{\mathrm e}^{3 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+5 y = 3 \,{\mathrm e}^{-5 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = 2 t y+3 t \,{\mathrm e}^{t^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = t^{2} y+1+y+t^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y+1}{t}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+4 y = {\mathrm e}^{2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+3 x y = 6 x
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x -2\right ) y^{\prime } = 3+y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 3 x -\sin \left (x \right ) y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+x y = 4 x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+4 y = x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = x y-3 x -2 y+6
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 x -1+2 x y-y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x y-4 x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x y-4 x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x y-3 x -2 y+6
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 x -1+2 x y-y
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+3 x^{2} y = \sin \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = 1+x y+3 y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \sin \left (x \right ) y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x +\cos \left (x^{2}\right ) = 827 y
\] |
[_linear] |
✓ |
|
|
\[
{}2 y+y^{\prime } = 20 \,{\mathrm e}^{3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = 4 y+16 x
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-2 x y = x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x +3 y-10 x^{2} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+2 x y = \sin \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x = \sqrt {x}+3 y
\] |
[_linear] |
✓ |
|
|
\[
{}\sin \left (x \right ) y+y^{\prime } \cos \left (x \right ) = \cos \left (x \right )^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +\left (5 x +2\right ) y = \frac {20}{x}
\] |
[_linear] |
✓ |
|
|
\[
{}2 \sqrt {x}\, y^{\prime }+y = 2 x \,{\mathrm e}^{-\sqrt {x}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+5 y = {\mathrm e}^{-3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } x +3 y = 20 x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x = y+x^{2} \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = x \left (3+3 x^{2}-y\right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+6 x y = \sin \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+x y = \sqrt {x}\, \sin \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}-y+y^{\prime } x = x^{2} {\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}2 x \left (1+y\right )-y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x = 2 y-6 x^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}4 x y-6+x^{2} y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}3 y-x^{3}+y^{\prime } x = 0
\] |
[_linear] |
✓ |
|
|
\[
{}2+2 x^{2}-2 x y+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-3 y = 12 \,{\mathrm e}^{2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}2 y-6 x +\left (x +1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}2 y+y^{\prime } = \sin \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = x \left (6 y+{\mathrm e}^{x^{2}}\right )
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+3 x y = 6 \,{\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +3 y = {\mathrm e}^{2 x}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y = \sin \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {2 y}{x}-3
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y = \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } x +y = \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-y = \sin \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}2 y+y^{\prime } = x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = y+\frac {1}{-t +1}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = y \sqrt {t}
\] |
[_separable] |
✓ |
|
|
\[
{}t y^{\prime } = y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y \tan \left (t \right )
\] |
[_separable] |
✓ |
|
|
\[
{}t y^{\prime }+y = t^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}t^{3} y^{\prime }+t^{4} y = 2 t^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}2 y^{\prime }+t y = \ln \left (t \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y \sec \left (t \right ) = t
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{t -3} = \frac {1}{t -1}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (t -2\right ) y^{\prime }+\left (t^{2}-4\right ) y = \frac {1}{t +2}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{\sqrt {-t^{2}+4}} = t
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{\sqrt {-t^{2}+4}} = t
\] |
[_linear] |
✓ |
|
|
\[
{}t y^{\prime }+y = t \sin \left (t \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y \tan \left (t \right ) = \sin \left (t \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y+1}{1+t}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {2+y}{2 t +1}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {3+y}{3 x +1}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {3 y+1}{x +3}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \cos \left (t \right ) y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y f \left (t \right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y-2}{x -2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y f \left (t \right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-y = 2 \,{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-y = 2 \cos \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-y = t^{2}-2 t
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-y = 4 t \,{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}t y^{\prime }+y = t^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}t y^{\prime }+y = t
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +y = x \,{\mathrm e}^{x}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +y = {\mathrm e}^{-x}
\] |
[_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] |
✓ |
|
|
\[
{}y^{\prime }+y \cot \left (t \right ) = \cos \left (t \right )
\] |
[_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] |
✓ |
|
|
\[
{}y^{\prime }+2 y \cot \left (x \right ) = \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+x y = x^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-x y = x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-x = y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}x^{\prime } = \frac {3 x t^{2}}{-t^{3}+1}
\] |
[_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] |
✓ |
|
|
\[
{}t y^{\prime }+y = \cos \left (t \right )
\] |
[_linear] |
✓ |
|
|
\[
{}t y^{\prime }+y = 2 t \,{\mathrm e}^{t}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (1+{\mathrm e}^{t}\right ) y^{\prime }+{\mathrm e}^{t} y = t
\] |
[_linear] |
✓ |
|
|
\[
{}\left (t^{2}+4\right ) y^{\prime }+2 t y = 2 t
\] |
[_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] |
✓ |
|
|
\[
{}y^{\prime }+y = \left \{\begin {array}{cc} 4 & 0\le t <2 \\ 0 & 2\le t \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-y = \sin \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y = 5 \,{\mathrm e}^{2 t}
\] |
[[_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‘]] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{2} = 5 \cos \left (t \right )+2 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+4 y = 8 \cos \left (4 t \right )
\] |
[[_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‘]] |
✓ |
|
|
\[
{}y^{\prime }+y = 2 \cos \left (t \right )+t
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{2} = \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{2} = \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}t y^{\prime }+y = t \cos \left (t \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y = t
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y = \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y = \cos \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y \cos \left (t y\right )+t \cos \left (t y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y \sec \left (t \right )^{2}+2 t +\tan \left (t \right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}{\mathrm e}^{t y}+\frac {t \,{\mathrm e}^{t y} y^{\prime }}{y} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{2}+2 t y y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\frac {3 t^{2}}{y}-\frac {t^{3} y^{\prime }}{y^{2}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}-2 t y^{2} \sin \left (t^{2}\right )+2 y \cos \left (t^{2}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 t y^{2}+2 t^{2} y y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}1+\frac {y}{t^{2}}-\frac {y^{\prime }}{t} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}2 t y+3 t^{2}+\left (t^{2}-1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}t^{2} y+t^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y \left (2 \,{\mathrm e}^{t}+4 t \right )+3 \left ({\mathrm e}^{t}+t^{2}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 y-3 t +t y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}t -y+t y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}t +y-t y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-\frac {2 y}{x} = -x^{2} y
\] |
[_separable] |
✓ |
|
|
\[
{}y = t \left (y^{\prime }+1\right )+2 y^{\prime }+1
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {\left (4-7 x \right ) \left (2 y-3\right )}{\left (x -1\right ) \left (2 x -5\right )}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+3 y = -10 \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y-x +y^{\prime } = 0
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+t y = t
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime }+\frac {x}{y} = y^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}t r^{\prime }+r = t \cos \left (t \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y}{t -2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-4 y = t^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y = \cos \left (2 t \right )
\] |
[[_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‘]] |
✓ |
|
|
\[
{}y^{\prime } x +y = \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}2 y+y^{\prime } = {\mathrm e}^{x}
\] |
[[_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‘]] |
✓ |
|
|
\[
{}y^{\prime } = x \left (-1+y\right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = y-x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = x^{2}+2 x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1+y}{x -1}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = y+x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {y}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = 2 y-2 x^{2}-3
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } x = 2 x -y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } \sin \left (x \right )-y \cos \left (x \right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = a x +b y+c
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } x +y = a \left (1+x y\right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime } = -1+y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 2 x \left (\pi +y\right )
\] |
[_separable] |
✓ |
|
|
\[
{}x -y+y^{\prime } x = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x +y-2+\left (1-x \right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}2 y+y^{\prime } = {\mathrm e}^{-x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}x^{2}-y^{\prime } x = y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-2 x y = 2 x \,{\mathrm e}^{x^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = {\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } \cos \left (x \right )-\sin \left (x \right ) y = 2 x
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x -2 y = x^{3} \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-y \tan \left (x \right ) = \frac {1}{\cos \left (x \right )^{3}}
\] |
[_linear] |
✓ |
|
|
\[
{}x \ln \left (x \right ) y^{\prime }-y = 3 x^{3} \ln \left (x \right )^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = \cos \left (x \right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-y \,{\mathrm e}^{x} = 2 x \,{\mathrm e}^{{\mathrm e}^{x}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+x y \,{\mathrm e}^{x} = {\mathrm e}^{\left (1-x \right ) {\mathrm e}^{x}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-y \ln \left (2\right ) = 2^{\sin \left (x \right )} \left (\cos \left (x \right )-1\right ) \ln \left (2\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-y = -2 \,{\mathrm e}^{-x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } \sin \left (x \right )-y \cos \left (x \right ) = -\frac {\sin \left (x \right )^{2}}{x^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime } \cos \left (\frac {1}{x}\right )-y \sin \left (\frac {1}{x}\right ) = -1
\] |
[_linear] |
✓ |
|
|
\[
{}2 y^{\prime } x -y = 1-\frac {2}{\sqrt {x}}
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+y = \left (x^{2}+1\right ) {\mathrm e}^{x}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +y = 2 x
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } \sin \left (x \right )+y \cos \left (x \right ) = 1
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } \cos \left (x \right )-\sin \left (x \right ) y = -\sin \left (2 x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+3 x y = y \,{\mathrm e}^{x^{2}}
\] |
[_separable] |
✓ |
|
|
\[
{}\frac {x y}{\sqrt {x^{2}+1}}+2 x y-\frac {y}{x}+\left (\sqrt {x^{2}+1}+x^{2}-\ln \left (x \right )\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2}+y-y^{\prime } x = 0
\] |
[_linear] |
✓ |
|
|
\[
{}2 x^{2} y+2 y+5+\left (2 x^{3}+2 x \right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-2 y y^{\prime } = y^{2} \left ({\mathrm e}^{2 x}-1\right )
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+3 x y y^{\prime }+2 y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-\left (2 x +y\right ) y^{\prime }+x^{2}+x y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}x \sin \left (x \right ) y^{\prime }+\left (\sin \left (x \right )-x \cos \left (x \right )\right ) y = \sin \left (x \right ) \cos \left (x \right )-x
\] |
[_linear] |
✓ |
|
|
\[
{}2 x y \,{\mathrm e}^{x^{2}}-x \sin \left (x \right )+{\mathrm e}^{x^{2}} y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\left (2 x -1\right ) y^{\prime }-2 y = \frac {1-4 x}{x^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } \left (3 x^{2}-2 x \right )-y \left (6 x -2\right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = y-x y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+4 y = t +{\mathrm e}^{-2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}-2 y+y^{\prime } = t^{2} {\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y = t \,{\mathrm e}^{-t}+1
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{t} = 5+\cos \left (2 t \right )
\] |
[_linear] |
✓ |
|
|
\[
{}-2 y+y^{\prime } = 3 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}t y^{\prime }+2 y = \sin \left (t \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+2 t y = 16 t \,{\mathrm e}^{-t^{2}}
\] |
[_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‘]] |
✓ |
|
|
\[
{}-y+t y^{\prime } = t^{3} {\mathrm e}^{-t}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y = 5 \sin \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}2 y^{\prime }+y = 3 t^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-y = 2 \,{\mathrm e}^{2 t} t
\] |
[[_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] |
✓ |
|
|
\[
{}y^{\prime }+\frac {2 y}{t} = \frac {\cos \left (t \right )}{t^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}-2 y+y^{\prime } = {\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}t y^{\prime }+2 y = \sin \left (t \right )
\] |
[_linear] |
✓ |
|
|
\[
{}t^{3} y^{\prime }+4 t^{2} y = {\mathrm e}^{-t}
\] |
[_linear] |
✓ |
|
|
\[
{}t y^{\prime }+\left (1+t \right ) y = t
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{3} = 3 \cos \left (t \right )
\] |
[[_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‘]] |
✓ |
|
|
\[
{}t y^{\prime }+\left (1+t \right ) y = 2 t \,{\mathrm e}^{-t}
\] |
[_linear] |
✓ |
|
|
\[
{}t y^{\prime }+2 y = \frac {\sin \left (t \right )}{t}
\] |
[_linear] |
✓ |
|
|
\[
{}\sin \left (t \right ) y^{\prime }+\cos \left (t \right ) y = {\mathrm e}^{t}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{2} = 2 \cos \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+\frac {4 y}{3} = 1-\frac {t}{4}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{4} = 3+2 \cos \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-y = 1+3 \sin \left (t \right )
\] |
[[_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‘]] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{t} = 3 \cos \left (2 t \right )
\] |
[_linear] |
✓ |
|
|
\[
{}t y^{\prime }+2 y = \sin \left (t \right )
\] |
[_linear] |
✓ |
|
|
\[
{}2 y^{\prime }+y = 3 t^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}\left (t -3\right ) y^{\prime }+\ln \left (t \right ) y = 2 t
\] |
[_linear] |
✓ |
|
|
\[
{}\left (t -4\right ) t y^{\prime }+y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y \tan \left (t \right ) = \sin \left (t \right )
\] |
[_linear] |
✓ |
|
|
\[
{}\left (-t^{2}+4\right ) y^{\prime }+2 t y = 3 t^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (-t^{2}+4\right ) y^{\prime }+2 t y = 3 t^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}\ln \left (t \right ) y^{\prime }+y = \cot \left (t \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t \le 1 \\ 0 & 1<t \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+\left (\left \{\begin {array}{cc} 2 & 0\le t \le 1 \\ 1 & 1<t \end {array}\right .\right ) y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 x y^{2}+2 y+\left (2 x^{2} y+2 x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\frac {y}{x}+6 x +\left (\ln \left (x \right )-2\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{2 x}+y-1
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } x +\left (x +1\right ) y = x
\] |
[_linear] |
✓ |
|
|
\[
{}\frac {\sqrt {x}\, y^{\prime }}{y} = 1
\] |
[_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] |
✓ |
|
|
\[
{}y^{\prime } \cos \left (x \right ) = \sin \left (x \right ) y+\cos \left (x \right )^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = 2 x y-x^{3}+x
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {x y}{x^{2}+1} = \frac {1}{x \left (x^{2}+1\right )}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = k y+f \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = 2 x y-x^{3}+x
\] |
[_linear] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}-\left (x^{2}+x y+y^{2}\right ) {y^{\prime }}^{2}+\left (x^{3} y+x^{2} y^{2}+x y^{3}\right ) y^{\prime }-x^{3} y^{3} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } x = 2 y
\] |
[_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] |
✓ |
|
|
\[
{}y^{\prime } = 1+2 x y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x = 2 x +3 y
\] |
[_linear] |
✓ |
|
|
\[
{}2 x +3 y-1-4 \left (x +1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y+y \cos \left (x y\right )+\left (x +x \cos \left (x y\right )\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}-\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}1+y+\left (1-x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}-y+y^{\prime } x = 2 x^{2}-3
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{x} = \sin \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x -3 y = x^{4}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y = \frac {1}{1+{\mathrm e}^{2 x}}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+2 x y = \cot \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y = 2 x \,{\mathrm e}^{-x}+x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = 2 x \csc \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}2 y-x^{3} = y^{\prime } x
\] |
[_linear] |
✓ |
|
|
\[
{}y-x +x y \cot \left (x \right )+y^{\prime } x = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }-2 x y = 6 x \,{\mathrm e}^{x^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}x \ln \left (x \right ) y^{\prime }+y = 3 x^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}y-2 x y-x^{2}+x^{2} y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } \sin \left (2 x \right ) = 2 y+2 \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y+x^{2} = y^{\prime } x
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x +y = x^{2} \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = {\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+2 x y = 4 x^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = 1+3 y \tan \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}\frac {y-x}{\left (x +y\right )^{3}}-\frac {2 x y^{\prime }}{\left (x +y\right )^{3}} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x \left (x^{2}+1\right ) y^{\prime }+2 y = \left (x^{2}+1\right )^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}{\mathrm e}^{x^{2} y} \left (1+2 x^{2} y\right )+x^{3} {\mathrm e}^{x^{2} y} y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x y+y-1+y^{\prime } x = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x^{\prime }+x \cot \left (y \right ) = \sec \left (y \right )
\] |
[_linear] |
✓ |
|
|
\[
{}1+2 x+\left (-t^{2}+4\right ) x^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime } {\mathrm e}^{3 t}+3 x \,{\mathrm e}^{3 t} = 2 t
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}x^{\prime }+2 x = {\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}x^{\prime }+x \tan \left (t \right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}x^{\prime }-x \tan \left (t \right ) = 4 \sin \left (t \right )
\] |
[_linear] |
✓ |
|
|
\[
{}t^{3} x^{\prime }+\left (-3 t^{2}+2\right ) x = t^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}t x^{\prime }+x \ln \left (t \right ) = t^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}t x^{\prime }+x g \left (t \right ) = h \left (t \right )
\] |
[_linear] |
✓ |
|
|
\[
{}v^{\prime }+u^{2} v = \sin \left (u \right )
\] |
[_linear] |
✓ |
|
|
\[
{}v^{\prime }+\frac {2 v}{u} = 3
\] |
[_linear] |
✓ |
|
|
\[
{}y-y^{\prime } x = b \left (1+x^{2} y^{\prime }\right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+x y = x
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{x} = \sin \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}p^{\prime } = \frac {p+a \,t^{3}-2 p t^{2}}{t \left (-t^{2}+1\right )}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = \frac {\sin \left (2 x \right )}{2}
\] |
[_linear] |
✓ |
|
|
\[
{}v^{\prime }+\frac {2 v}{u} = 3 v
\] |
[_separable] |
✓ |
|
|
\[
{}\frac {y^{\prime }}{x} = y \sin \left (x^{2}-1\right )-\frac {2 y}{\sqrt {x}}
\] |
[_separable] |
✓ |
|
|
\[
{}v^{\prime }+2 v u = 2 u
\] |
[_separable] |
✓ |
|
|
\[
{}5 x^{\prime }+x = \sin \left (3 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+\frac {x y}{x^{2}+1} = \frac {1}{x \left (x^{2}+1\right )}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{x} = -x^{2}+1
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = \csc \left (x \right )^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+\frac {x y}{x^{2}+1} = \frac {1}{x \left (x^{2}+1\right )}
\] |
[_linear] |
✓ |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}-1\right ) y = x^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = \frac {\sin \left (2 x \right )}{2}
\] |
[_linear] |
✓ |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y = a \,x^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}-2 x y\right ) y^{\prime }+x^{2}-3 x y+2 y^{2} = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\left (1-x \right ) y^{\prime }-1-y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y-y^{\prime } x +\ln \left (x \right ) = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x -a y = x +1
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{-x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}\cos \left (x \right )^{2} y^{\prime }+y = \tan \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime }-n y = {\mathrm e}^{x} \left (x +1\right )^{n +1}
\] |
[_linear] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+2 x y = 4 x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {\left (1-2 x \right ) y}{x^{2}} = 1
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{\sqrt {-x^{2}+1}} = \frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {4 x y}{x^{2}+1} = \frac {1}{\left (x^{2}+1\right )^{3}}
\] |
[_linear] |
✓ |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y = a \,x^{3}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } \sqrt {a^{2}+x^{2}}+y = \sqrt {a^{2}+x^{2}}-x
\] |
[_linear] |
✓ |
|
|
\[
{}y-y^{\prime } x = b \left (1+x^{2} y^{\prime }\right )
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+\frac {n y}{x} = a \,x^{-n}
\] |
[_linear] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right ) = y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}+y^{\prime } \left (3 x^{2}-2 y^{2}\right )-6 x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}-\left (x^{2}+x y+y^{2}\right ) {y^{\prime }}^{2}+\left (x^{3} y+x^{2} y^{2}+x y^{3}\right ) y^{\prime }-x^{3} y^{3} = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y+x +y^{\prime } x = 0
\] |
[_linear] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }-2 x y = -x^{3}+x
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x -y-\cos \left (\frac {1}{x}\right ) = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+y = 1
\] |
[_separable] |
✓ |
|
|
\[
{}2 y+\left (x^{2}+1\right ) \arctan \left (x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = 2 \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}\cos \left (x \right )^{2} y^{\prime }+y = \tan \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}x \cos \left (x \right ) y^{\prime }+y \left (x \sin \left (x \right )+\cos \left (x \right )\right ) = 1
\] |
[_linear] |
✓ |
|
|
\[
{}y-x \sin \left (x^{2}\right )+y^{\prime } x = 0
\] |
[_linear] |
✓ |
|
|
\[
{}x \ln \left (x \right ) y^{\prime }+y = 2 \ln \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}\sin \left (x \right ) \cos \left (x \right ) y^{\prime } = y+\sin \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+3 x^{2} y = x^{5} {\mathrm e}^{x^{3}}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {\left (1-2 x \right ) y}{x^{2}} = 1
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = \sin \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}1+y+x^{2} y+\left (x^{3}+x \right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {x y}{x^{2}+1} = \frac {1}{2 x \left (x^{2}+1\right )}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{\left (-x^{2}+1\right )^{{3}/{2}}} = \frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right ) = y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } \left (y^{\prime }-y\right ) = \left (x +y\right ) x
\] |
[_quadrature] |
✓ |
|
|
\[
{}x {y^{\prime }}^{2}+\left (y-x \right ) y^{\prime }-y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}-y^{\prime } \left (x^{2}+x y+y^{2}\right )+x y \left (x +y\right ) = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}\left (y^{\prime }+y+x \right ) \left (y+x +y^{\prime } x \right ) \left (y^{\prime }+2 x \right ) = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+x y y^{\prime }-6 y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y = y^{\prime } \sin \left (x \right )+\cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}+y^{\prime } \left (3 x^{2}-2 y^{2}\right )-6 x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}4 {y^{\prime }}^{2} x^{2} \left (x -1\right )-4 y^{\prime } x y \left (4 x -3\right )+\left (16 x -9\right ) y^{2} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y-y^{\prime } x = b \left (1+x^{2} y^{\prime }\right )
\] |
[_separable] |
✓ |
|
|
\[
{}y-y^{\prime } x = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } \cos \left (x \right )+\sin \left (x \right ) y = 1
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = {\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}-\left (x^{2}+x y+y^{2}\right ) {y^{\prime }}^{2}+\left (x^{3} y+x^{2} y^{2}+x y^{3}\right ) y^{\prime }-x^{3} y^{3} = 0
\] |
[_quadrature] |
✓ |
|