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Mathematica |
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\[
{}r^{\prime }+r \tan \left (t \right ) = \cos \left (t \right )
\] |
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\[
{}\cos \left (t \right ) r^{\prime }+r \sin \left (t \right )-\cos \left (t \right )^{4} = 0
\] |
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\[
{}\cos \left (x \right )^{2}-y \cos \left (x \right )-\left (\sin \left (x \right )+1\right ) y^{\prime } = 0
\] |
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\[
{}y \sin \left (2 x \right )-\cos \left (x \right )+\left (1+\sin \left (x \right )^{2}\right ) y^{\prime } = 0
\] |
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\[
{}y^{\prime }-\frac {y}{x} = -\frac {y^{2}}{x}
\] |
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\[
{}x y^{\prime }+y = -2 x^{6} y^{4}
\] |
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\[
{}y^{\prime }+\left (4 y-\frac {8}{y^{3}}\right ) x = 0
\] |
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\[
{}x^{\prime }+\frac {\left (t +1\right ) x}{2 t} = \frac {t +1}{t x}
\] |
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\[
{}x y^{\prime }-2 y = 2 x^{4}
\] |
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\[
{}y^{\prime }+3 x^{2} y = x^{2}
\] |
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\[
{}{\mathrm e}^{x} \left (y-3 \left (1+{\mathrm e}^{x}\right )^{2}\right )+\left (1+{\mathrm e}^{x}\right ) y^{\prime } = 0
\] |
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\[
{}2 x \left (1+y\right )-\left (x^{2}+1\right ) y^{\prime } = 0
\] |
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\[
{}r^{\prime }+r \tan \left (t \right ) = \cos \left (t \right )^{2}
\] |
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\[
{}x^{\prime }-x = \sin \left (2 t \right )
\] |
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\[
{}y^{\prime }+\frac {y}{2 x} = \frac {x}{y^{3}}
\] |
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\[
{}x y^{\prime }+y = \left (x y\right )^{{3}/{2}}
\] |
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\[
{}y^{\prime }+y = \left \{\begin {array}{cc} 2 & 0\le x <1 \\ 0 & 1\le x \end {array}\right .
\] |
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\[
{}y^{\prime }+y = \left \{\begin {array}{cc} 5 & 0\le x <10 \\ 1 & 10\le x \end {array}\right .
\] |
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\[
{}y^{\prime }+y = \left \{\begin {array}{cc} {\mathrm e}^{-x} & 0\le x <2 \\ {\mathrm e}^{-2} & 2\le x \end {array}\right .
\] |
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\[
{}\left (x +2\right ) y^{\prime }+y = \left \{\begin {array}{cc} 2 x & 0\le x <2 \\ 4 & 2\le x \end {array}\right .
\] |
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\[
{}a y^{\prime }+b y = k \,{\mathrm e}^{-\lambda x}
\] |
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\[
{}y^{\prime }+y = 2 \sin \left (x \right )+5 \sin \left (2 x \right )
\] |
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\[
{}\cos \left (y\right ) y^{\prime }+\frac {\sin \left (y\right )}{x} = 1
\] |
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\[
{}\left (1+y\right ) y^{\prime }+x \left (2 y+y^{2}\right ) = x
\] |
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\[
{}y^{\prime } = \left (1-x \right ) y^{2}+\left (2 x -1\right ) y-x
\] |
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\[
{}y^{\prime } = -y^{2}+x y+1
\] |
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\[
{}y^{\prime } = -8 x y^{2}+4 x \left (4 x +1\right ) y-8 x^{3}-4 x^{2}+1
\] |
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\[
{}6 x^{2} y-\left (x^{3}+1\right ) y^{\prime } = 0
\] |
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\[
{}\left (3 x^{2} y^{2}-x \right ) y^{\prime }+2 x y^{3}-y = 0
\] |
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\[
{}y-1+x \left (1+x \right ) y^{\prime } = 0
\] |
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\[
{}x^{2}-2 y+x y^{\prime } = 0
\] |
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\[
{}3 x -5 y+\left (x +y\right ) y^{\prime } = 0
\] |
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\[
{}y^{2} {\mathrm e}^{2 x}+\left (y \,{\mathrm e}^{2 x}-2 y\right ) y^{\prime } = 0
\] |
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\[
{}8 x^{3} y-12 x^{3}+\left (x^{4}+1\right ) y^{\prime } = 0
\] |
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\[
{}2 x^{2}+x y+y^{2}+2 x^{2} y^{\prime } = 0
\] |
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\[
{}y^{\prime } = \frac {4 y^{2} x^{3}-3 x^{2} y}{x^{3}-2 x^{4} y}
\] |
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\[
{}\left (1+x \right ) y^{\prime }+x y = {\mathrm e}^{-x}
\] |
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\[
{}y^{\prime } = \frac {2 x -7 y}{3 y-8 x}
\] |
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\[
{}x^{2} y^{\prime }+x y = x y^{3}
\] |
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\[
{}\left (x^{3}+1\right ) y^{\prime }+6 x^{2} y = 6 x^{2}
\] |
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\[
{}y^{\prime } = \frac {2 x^{2}+y^{2}}{2 x y-x^{2}}
\] |
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\[
{}x^{2}+y^{2}-2 x y y^{\prime } = 0
\] |
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\[
{}8+2 y^{2}+\left (-x^{2}+1\right ) y y^{\prime } = 0
\] |
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\[
{}y^{2} {\mathrm e}^{2 x}-2 x +{\mathrm e}^{2 x} y y^{\prime } = 0
\] |
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\[
{}3 x^{2}+2 x y^{2}+\left (2 x^{2} y+6 y^{2}\right ) y^{\prime } = 0
\] |
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\[
{}4 x y y^{\prime } = 1+y^{2}
\] |
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\[
{}y^{\prime } = \frac {2 x +7 y}{2 x -2 y}
\] |
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\[
{}y^{\prime } = \frac {x y}{x^{2}+1}
\] |
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\[
{}y^{\prime }+y = \left \{\begin {array}{cc} 1 & 0\le x <2 \\ 0 & 0<x \end {array}\right .
\] |
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\[
{}\left (x +2\right ) y^{\prime }+y = \left \{\begin {array}{cc} 2 x & 0\le x \le 2 \\ 4 & 2<x \end {array}\right .
\] |
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\[
{}x^{2} y^{\prime }+x y = \frac {y^{3}}{x}
\] |
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\[
{}5 x y+4 y^{2}+1+\left (2 x y+x^{2}\right ) y^{\prime } = 0
\] |
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\[
{}2 x +\tan \left (y\right )+\left (x -x^{2} \tan \left (y\right )\right ) y^{\prime } = 0
\] |
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\[
{}y^{2} \left (1+x \right )+y+\left (2 x y+1\right ) y^{\prime } = 0
\] |
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\[
{}2 x y^{2}+y+\left (2 y^{3}-x \right ) y^{\prime } = 0
\] |
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\[
{}4 x y^{2}+6 y+\left (5 x^{2} y+8 x \right ) y^{\prime } = 0
\] |
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\[
{}8 x^{2} y^{3}-2 y^{4}+\left (5 y^{2} x^{3}-8 x y^{3}\right ) y^{\prime } = 0
\] |
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\[
{}5 x +2 y+1+\left (2 x +y+1\right ) y^{\prime } = 0
\] |
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\[
{}3 x -y+1-\left (6 x -2 y-3\right ) y^{\prime } = 0
\] |
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\[
{}x -2 y-3+\left (2 x +y-1\right ) y^{\prime } = 0
\] |
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\[
{}10 x -4 y+12-\left (x +5 y+3\right ) y^{\prime } = 0
\] |
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\[
{}6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime } = 0
\] |
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\[
{}3 x -y-6+\left (x +y+2\right ) y^{\prime } = 0
\] |
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\[
{}2 x +3 y+1+\left (4 x +6 y+1\right ) y^{\prime } = 0
\] |
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\[
{}4 x +3 y+1+\left (x +y+1\right ) y^{\prime } = 0
\] |
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\[
{}y^{\prime }-y = {\mathrm e}^{3 t}
\] |
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\[
{}y^{\prime }+y = 2 \sin \left (t \right )
\] |
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\[
{}x^{\prime } = \sin \left (t \right )+\cos \left (t \right )
\] |
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\[
{}y^{\prime } = \frac {1}{x^{2}-1}
\] |
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\[
{}u^{\prime } = 4 t \ln \left (t \right )
\] |
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\[
{}z^{\prime } = x \,{\mathrm e}^{-2 x}
\] |
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\[
{}T^{\prime } = {\mathrm e}^{-t} \sin \left (2 t \right )
\] |
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\[
{}x^{\prime } = \sec \left (t \right )^{2}
\] |
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\[
{}y^{\prime } = x -\frac {1}{3} x^{3}
\] |
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\[
{}x^{\prime } = 2 \sin \left (t \right )^{2}
\] |
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\[
{}x V^{\prime } = x^{2}+1
\] |
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\[
{}x^{\prime } {\mathrm e}^{3 t}+3 x \,{\mathrm e}^{3 t} = {\mathrm e}^{-t}
\] |
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\[
{}x^{\prime } = -x+1
\] |
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\[
{}x^{\prime } = x \left (2-x\right )
\] |
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\[
{}x^{\prime } = \left (1+x\right ) \left (2-x\right ) \sin \left (x\right )
\] |
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\[
{}x^{\prime } = -x \left (-x+1\right ) \left (2-x\right )
\] |
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\[
{}x^{\prime } = x^{2}-x^{4}
\] |
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\[
{}x^{\prime } = t^{3} \left (-x+1\right )
\] |
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\[
{}y^{\prime } = \left (1+y^{2}\right ) \tan \left (x \right )
\] |
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\[
{}x^{\prime } = t^{2} x
\] |
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\[
{}x^{\prime } = -x^{2}
\] |
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\[
{}y^{\prime } = y^{2} {\mathrm e}^{-t^{2}}
\] |
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\[
{}x^{\prime }+p x = q
\] |
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\[
{}x y^{\prime } = k y
\] |
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\[
{}i^{\prime } = p \left (t \right ) i
\] |
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\[
{}x^{\prime } = \lambda x
\] |
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\[
{}m v^{\prime } = -m g +k v^{2}
\] |
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\[
{}x^{\prime } = k x-x^{2}
\] |
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\[
{}x^{\prime } = -x \left (k^{2}+x^{2}\right )
\] |
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\[
{}y^{\prime }+\frac {y}{x} = x^{2}
\] |
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\[
{}x^{\prime }+t x = 4 t
\] |
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\[
{}z^{\prime } = z \tan \left (y \right )+\sin \left (y \right )
\] |
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\[
{}y^{\prime }+{\mathrm e}^{-x} y = 1
\] |
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\[
{}x^{\prime }+x \tanh \left (t \right ) = 3
\] |
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\[
{}y^{\prime }+2 y \cot \left (x \right ) = 5
\] |
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