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ODE |
Mathematica |
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\[
{}3 x^{2} y^{2}-y^{3}+2 x +\left (2 x^{3} y-3 x y^{2}+1\right ) y^{\prime } = 0
\] |
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\[
{}2 y \sin \left (x \right ) \cos \left (x \right )+y^{2} \sin \left (x \right )+\left (\sin \left (x \right )^{2}-2 y \cos \left (x \right )\right ) y^{\prime } = 0
\] |
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\[
{}y \,{\mathrm e}^{x}+2 \,{\mathrm e}^{x}+y^{2}+\left ({\mathrm e}^{x}+2 x y\right ) y^{\prime } = 0
\] |
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\[
{}\frac {3-y}{x^{2}}+\frac {\left (y^{2}-2 x \right ) y^{\prime }}{x y^{2}} = 0
\] |
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\[
{}\frac {1+8 x y^{{2}/{3}}}{x^{{2}/{3}} y^{{1}/{3}}}+\frac {\left (2 x^{{4}/{3}} y^{{2}/{3}}-x^{{1}/{3}}\right ) y^{\prime }}{y^{{4}/{3}}} = 0
\] |
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\[
{}4 x +3 y^{2}+2 x y y^{\prime } = 0
\] |
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\[
{}y^{2}+2 x y-x^{2} y^{\prime } = 0
\] |
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\[
{}y+x \left (x^{2}+y^{2}\right )^{2}+\left (y \left (x^{2}+y^{2}\right )^{2}-x \right ) y^{\prime } = 0
\] |
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\[
{}4 x y+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
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\[
{}x y+2 x +y+2+\left (x^{2}+2 x \right ) y^{\prime } = 0
\] |
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\[
{}2 r \left (s^{2}+1\right )+\left (r^{4}+1\right ) s^{\prime } = 0
\] |
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\[
{}\csc \left (y\right )+\sec \left (x \right ) y^{\prime } = 0
\] |
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\[
{}\tan \left (\theta \right )+2 r \theta ^{\prime } = 0
\] |
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\[
{}\left ({\mathrm e}^{v}+1\right ) \cos \left (u \right )+{\mathrm e}^{v} \left (1+\sin \left (u \right )\right ) v^{\prime } = 0
\] |
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\[
{}\left (x +4\right ) \left (1+y^{2}\right )+y \left (x^{2}+3 x +2\right ) y^{\prime } = 0
\] |
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\[
{}x +y-x y^{\prime } = 0
\] |
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\[
{}2 x y+3 y^{2}-\left (2 x y+x^{2}\right ) y^{\prime } = 0
\] |
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\[
{}v^{3}+\left (u^{3}-u v^{2}\right ) v^{\prime } = 0
\] |
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\[
{}x \tan \left (\frac {y}{x}\right )+y-x y^{\prime } = 0
\] |
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\[
{}\left (2 s^{2}+2 s t +t^{2}\right ) s^{\prime }+s^{2}+2 s t -t^{2} = 0
\] |
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\[
{}x^{3}+y^{2} \sqrt {x^{2}+y^{2}}-x y \sqrt {x^{2}+y^{2}}\, y^{\prime } = 0
\] |
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\[
{}\sqrt {x +y}+\sqrt {x -y}+\left (\sqrt {x -y}-\sqrt {x +y}\right ) y^{\prime } = 0
\] |
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\[
{}y+2+y \left (x +4\right ) y^{\prime } = 0
\] |
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\[
{}8 \cos \left (y\right )^{2}+\csc \left (x \right )^{2} y^{\prime } = 0
\] |
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\[
{}\left (3 x +8\right ) \left (4+y^{2}\right )-4 y \left (x^{2}+5 x +6\right ) y^{\prime } = 0
\] |
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\[
{}x^{2}+3 y^{2}-2 x y y^{\prime } = 0
\] |
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\[
{}2 x -5 y+\left (4 x -y\right ) y^{\prime } = 0
\] |
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\[
{}3 x^{2}+9 x y+5 y^{2}-\left (6 x^{2}+4 x y\right ) y^{\prime } = 0
\] |
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\[
{}x +2 y+\left (2 x -y\right ) y^{\prime } = 0
\] |
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\[
{}3 x -y-\left (x +y\right ) y^{\prime } = 0
\] |
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\[
{}x^{2}+2 y^{2}+\left (-y^{2}+4 x y\right ) y^{\prime } = 0
\] |
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\[
{}2 x^{2}+2 x y+y^{2}+\left (2 x y+x^{2}\right ) y^{\prime } = 0
\] |
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\[
{}y^{\prime }+\frac {3 y}{x} = 6 x^{2}
\] |
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\[
{}x^{4} y^{\prime }+2 x^{3} y = 1
\] |
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\[
{}y^{\prime }+3 y = 3 x^{2} {\mathrm e}^{-3 x}
\] |
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\[
{}y^{\prime }+4 x y = 8 x
\] |
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\[
{}x^{\prime }+\frac {x}{t^{2}} = \frac {1}{t^{2}}
\] |
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\[
{}\left (u^{2}+1\right ) v^{\prime }+4 v u = 3 u
\] |
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\[
{}x y^{\prime }+\frac {\left (2 x +1\right ) y}{1+x} = x -1
\] |
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\[
{}\left (x^{2}+x -2\right ) y^{\prime }+3 \left (1+x \right ) y = x -1
\] |
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\[
{}x y^{\prime }+x y+y-1 = 0
\] |
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\[
{}y+\left (x y^{2}+x -y\right ) y^{\prime } = 0
\] |
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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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