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Mathematica |
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\[
{} x^{\prime } = 2 t x
\]
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\[
{} x^{\prime }+\frac {{\mathrm e}^{-t} x}{t} = t
\]
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\[
{} x^{\prime } = \left (t +x\right )^{2}
\]
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\[
{} x^{\prime } = a x+b
\]
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\[
{} x^{\prime }+p \left (t \right ) x = 0
\]
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\[
{} x^{\prime } = \frac {2 x}{3 t}+\frac {2 t}{x}
\]
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\[
{} x^{\prime } = x \left (1+x \,{\mathrm e}^{t}\right )
\]
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\[
{} x^{\prime } = -\frac {x}{t}+\frac {1}{t x^{2}}
\]
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\[
{} t^{2} y^{\prime }+2 t y-y^{2} = 0
\]
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\[
{} x^{\prime } = a x+b x^{3}
\]
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\[
{} w^{\prime } = t w+t^{3} w^{3}
\]
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\[
{} x^{3}+3 t x^{2} x^{\prime } = 0
\]
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\[
{} t^{3}+\frac {x}{t}+\left (x^{2}+\ln \left (t \right )\right ) x^{\prime } = 0
\]
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\[
{} x^{\prime } = -\frac {\sin \left (x\right )-x \sin \left (t \right )}{t \cos \left (x\right )+\cos \left (t \right )}
\]
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\[
{} x+3 t x^{2} x^{\prime } = 0
\]
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\[
{} x^{2}-t^{2} x^{\prime } = 0
\]
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\[
{} t \cot \left (x\right ) x^{\prime } = -2
\]
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\[
{} x^{\prime }+5 x = \operatorname {Heaviside}\left (t -2\right )
\]
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\[
{} x^{\prime }+x = \sin \left (2 t \right )
\]
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\[
{} x^{\prime } = 2 x+\operatorname {Heaviside}\left (t -1\right )
\]
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\[
{} x^{\prime } = x-2 \operatorname {Heaviside}\left (t -1\right )
\]
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\[
{} x^{\prime } = -x+\operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (t -2\right )
\]
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\[
{} x^{\prime }+3 x = \delta \left (t -1\right )+\operatorname {Heaviside}\left (t -4\right )
\]
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\[
{} y^{\prime }+y = 1+x
\]
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\[
{} 2 x y y^{\prime }+x^{2}+y^{2} = 0
\]
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\[
{} x y^{\prime }+y = x^{3} y^{3}
\]
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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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\[
{} y^{\prime }+2 y = 6 \,{\mathrm e}^{x}+4 x \,{\mathrm e}^{-2 x}
\]
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\[
{} {y^{\prime }}^{2}-4 y = 0
\]
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\[
{} y^{\prime }+y = 2 x \,{\mathrm e}^{-x}
\]
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\[
{} y^{\prime }+y = 2 x \,{\mathrm e}^{-x}
\]
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\[
{} y^{\prime } = x^{2} \sin \left (y\right )
\]
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\[
{} y^{\prime } = \frac {y^{2}}{x -2}
\]
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\[
{} y^{\prime } = y^{{1}/{3}}
\]
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\[
{} 3 x +2 y+\left (y+2 x \right ) y^{\prime } = 0
\]
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\[
{} y^{2}+3+\left (2 x y-4\right ) y^{\prime } = 0
\]
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\[
{} 2 x y+1+\left (x^{2}+4 y\right ) y^{\prime } = 0
\]
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\[
{} 3 x^{2} y+2-\left (x^{3}+y\right ) y^{\prime } = 0
\]
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\[
{} 6 x y+2 y^{2}-5+\left (3 x^{2}+4 x y-6\right ) y^{\prime } = 0
\]
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\[
{} y \sec \left (x \right )^{2}+\sec \left (x \right ) \tan \left (x \right )+\left (\tan \left (x \right )+2 y\right ) y^{\prime } = 0
\]
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\[
{} \frac {x}{y^{2}}+x +\left (\frac {x^{2}}{y^{3}}+y\right ) y^{\prime } = 0
\]
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\[
{} \frac {\left (2 s-1\right ) s^{\prime }}{t}+\frac {s-s^{2}}{t^{2}} = 0
\]
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\[
{} \frac {2 y^{{3}/{2}}+1}{\sqrt {x}}+\left (3 \sqrt {x}\, \sqrt {y}-1\right ) y^{\prime } = 0
\]
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\[
{} 2 x y-3+\left (x^{2}+4 y\right ) y^{\prime } = 0
\]
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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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\[
{} 2 y \sin \left (x \right ) \cos \left (x \right )+y^{2} \sin \left (x \right )+\left (\sin \left (x \right )^{2}-2 \cos \left (x \right ) y\right ) y^{\prime } = 0
\]
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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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\[
{} \left (3 x +8\right ) \left (y^{2}+4\right )-4 y \left (x^{2}+5 x +6\right ) y^{\prime } = 0
\]
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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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\[
{} x^{2}+2 y^{2}+\left (4 x y-y^{2}\right ) y^{\prime } = 0
\]
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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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\[
{} \cos \left (x \right )^{2}-\cos \left (x \right ) y-\left (\sin \left (x \right )+1\right ) y^{\prime } = 0
\]
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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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\[
{} 2 x \left (y+1\right )-\left (x^{2}+1\right ) y^{\prime } = 0
\]
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\[
{} r^{\prime }+r \tan \left (t \right ) = \cos \left (t \right )^{2}
\]
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