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\[
{} y = x y^{\prime }+\sqrt {1-{y^{\prime }}^{2}}
\]
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\[
{} y = x y^{\prime }+\frac {1}{y^{\prime }}
\]
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\[
{} y = x y^{\prime }-\frac {1}{{y^{\prime }}^{2}}
\]
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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2}+{y^{\prime }}^{3} = 0
\]
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\[
{} {y^{\prime \prime }}^{2}+{y^{\prime }}^{2} = a^{2}
\]
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\[
{} y^{\prime } y^{\prime \prime \prime }-3 {y^{\prime \prime }}^{2} = 0
\]
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\[
{} y^{\prime \prime }+y = \frac {1}{\cos \left (2 x \right )^{{3}/{2}}}
\]
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\[
{} y y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
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\[
{} y^{\prime } = x +y^{2}
\]
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\[
{} x^{\prime \prime }+x-x^{3} = 0
\]
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\[
{} x^{\prime \prime }+x+x^{3} = 0
\]
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\[
{} x^{\prime \prime }+x^{\prime }+x-x^{3} = 0
\]
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\[
{} x^{\prime \prime }+x^{\prime }+x+x^{3} = 0
\]
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\[
{} x^{\prime \prime } = \left (2 \cos \left (x\right )-1\right ) \sin \left (x\right )
\]
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\[
{} y^{\prime } = x^{2}-y^{2}
\]
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\[
{} y^{\prime } = y^{2}-x^{2}
\]
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\[
{} y^{\prime } = x^{3}+y^{3}
\]
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\[
{} y^{\prime } = \frac {1}{\sqrt {15-x^{2}-y^{2}}}
\]
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\[
{} y^{\prime } = \frac {3 y}{\left (x -5\right ) \left (x +3\right )}+{\mathrm e}^{-x}
\]
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\[
{} y^{\prime } = \left (x y\right )^{{1}/{3}}
\]
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\[
{} y^{\prime } = \frac {y}{-x^{2}+4}+\sqrt {x}
\]
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\[
{} y^{\prime } = \frac {y}{-x^{2}+4}+\sqrt {x}
\]
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\[
{} x y \left (1-y\right )-2 y^{\prime } = 0
\]
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\[
{} y^{\prime } = \frac {y}{-x^{2}+1}+\sqrt {x}
\]
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\[
{} y^{\prime } = y^{2}
\]
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\[
{} y^{\prime } = y^{3}
\]
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\[
{} y^{\prime } = \frac {\sqrt {y}}{x}
\]
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\[
{} y^{\prime } = \frac {\sqrt {y}}{x}
\]
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\[
{} y^{\prime } = \frac {\sqrt {y}}{x}
\]
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\[
{} y^{\prime } = 3 x y^{{1}/{3}}
\]
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\[
{} y^{\prime } = 3 x y^{{1}/{3}}
\]
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\[
{} y^{\prime } = 3 x y^{{1}/{3}}
\]
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\[
{} y^{\prime } = 3 x y^{{1}/{3}}
\]
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\[
{} y^{\prime } = \sqrt {\left (y+2\right ) \left (-1+y\right )}
\]
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\[
{} y^{\prime } = \sqrt {\left (y+2\right ) \left (-1+y\right )}
\]
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\[
{} y^{\prime } = \frac {x y}{x^{2}+y^{2}}
\]
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\[
{} y^{\prime } = x \sqrt {1-y^{2}}
\]
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\[
{} y^{\prime } = x \sqrt {1-y^{2}}
\]
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\[
{} y^{\prime } = x \sqrt {1-y^{2}}
\]
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\[
{} y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\]
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\[
{} y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\]
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\[
{} y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\]
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\[
{} x \left (x -3\right ) y^{\prime \prime }+3 y^{\prime } = x^{2}
\]
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\[
{} x \left (x -3\right ) y^{\prime \prime }+3 y^{\prime } = x^{2}
\]
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\[
{} \sqrt {1-x}\, y^{\prime \prime }-4 y = \sin \left (x \right )
\]
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\[
{} \left (x^{2}-4\right ) y^{\prime \prime }+y \ln \left (x \right ) = x \,{\mathrm e}^{x}
\]
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\[
{} 2 y y^{\prime \prime }-{y^{\prime }}^{2} = 0
\]
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\[
{} y^{\prime }+2 y = \left \{\begin {array}{cc} 2 & 0\le x <1 \\ 1 & 1\le x \end {array}\right .
\]
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\[
{} y^{\prime \prime }-y^{\prime }-2 y = \left \{\begin {array}{cc} 1 & 2\le x <4 \\ 0 & \operatorname {otherwise} \end {array}\right .
\]
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\[
{} y^{\prime \prime }-2 y^{\prime } = \left \{\begin {array}{cc} 0 & 0\le x <1 \\ \left (x -1\right )^{2} & 1\le x \end {array}\right .
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = \left \{\begin {array}{cc} 0 & 0\le x <1 \\ x^{2}-2 x +3 & 1\le x \end {array}\right .
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+5 y = \left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right .
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+5 y = \cos \left (x \right )+2 \delta \left (x -\pi \right )
\]
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\[
{} \left [y_{1}^{\prime }\left (x \right ) = \frac {2 y_{1} \left (x \right )}{x}-\frac {y_{2} \left (x \right )}{x^{2}}-3+\frac {1}{x}-\frac {1}{x^{2}}, y_{2}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )+1-6 x\right ]
\]
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\[
{} \left [y_{1}^{\prime }\left (x \right ) = \sin \left (x \right ) y_{1} \left (x \right )+\sqrt {x}\, y_{2} \left (x \right )+\ln \left (x \right ), y_{2}^{\prime }\left (x \right ) = \tan \left (x \right ) y_{1} \left (x \right )-{\mathrm e}^{x} y_{2} \left (x \right )+1\right ]
\]
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\[
{} \left [y_{1}^{\prime }\left (x \right ) = \sin \left (x \right ) y_{1} \left (x \right )+\sqrt {x}\, y_{2} \left (x \right )+\ln \left (x \right ), y_{2}^{\prime }\left (x \right ) = \tan \left (x \right ) y_{1} \left (x \right )-{\mathrm e}^{x} y_{2} \left (x \right )+1\right ]
\]
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\[
{} \left [y_{1}^{\prime }\left (x \right ) = {\mathrm e}^{-x} y_{1} \left (x \right )-\sqrt {1+x}\, y_{2} \left (x \right )+x^{2}, y_{2}^{\prime }\left (x \right ) = \frac {y_{1} \left (x \right )}{\left (x -2\right )^{2}}\right ]
\]
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\[
{} \left [y_{1}^{\prime }\left (x \right ) = {\mathrm e}^{-x} y_{1} \left (x \right )-\sqrt {1+x}\, y_{2} \left (x \right )+x^{2}, y_{2}^{\prime }\left (x \right ) = \frac {y_{1} \left (x \right )}{\left (x -2\right )^{2}}\right ]
\]
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\[
{} [y_{1}^{\prime }\left (x \right ) = 2 x y_{1} \left (x \right )-x^{2} y_{2} \left (x \right )+4 x, y_{2}^{\prime }\left (x \right ) = {\mathrm e}^{x} y_{1} \left (x \right )+3 \,{\mathrm e}^{-x} y_{2} \left (x \right )-\cos \left (3 x \right )]
\]
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\[
{} y^{\prime } = \frac {4 t}{1+3 y^{2}}
\]
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\[
{} y^{\prime } = -y^{2}
\]
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\[
{} y^{\prime } = \left (y+\frac {1}{2}\right ) \left (y+t \right )
\]
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\[
{} S^{\prime } = S^{3}-2 S^{2}+S
\]
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\[
{} y^{\prime } = t -y^{2}
\]
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\[
{} y^{\prime } = y^{2}-4 t
\]
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\[
{} y^{\prime } = \sin \left (y\right )
\]
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\[
{} w^{\prime } = \left (3-w\right ) \left (w+1\right )
\]
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\[
{} w^{\prime } = \left (3-w\right ) \left (w+1\right )
\]
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\[
{} y^{\prime } = 2 y^{3}+t^{2}
\]
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\[
{} y^{\prime } = \sqrt {y}
\]
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\[
{} y^{\prime } = y \left (y-1\right ) \left (y-3\right )
\]
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\[
{} y^{\prime } = y \left (y-1\right ) \left (y-3\right )
\]
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\[
{} y^{\prime } = y \left (y-1\right ) \left (y-3\right )
\]
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\[
{} y^{\prime } = y \left (y-1\right ) \left (y-3\right )
\]
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\[
{} y^{\prime } = 3 y \left (y-2\right )
\]
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\[
{} y^{\prime } = y^{2}-4 y-12
\]
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\[
{} y^{\prime } = y^{2}-4 y-12
\]
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\[
{} y^{\prime } = y^{2}-4 y-12
\]
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\[
{} y^{\prime } = y^{2}-4 y-12
\]
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\[
{} y^{\prime } = \cos \left (y\right )
\]
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\[
{} y^{\prime } = \cos \left (y\right )
\]
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\[
{} y^{\prime } = \cos \left (y\right )
\]
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\[
{} y^{\prime } = \cos \left (y\right )
\]
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\[
{} y^{\prime } = \cos \left (\frac {\pi y}{2}\right )
\]
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\[
{} y^{\prime } = -y \,{\mathrm e}^{-t^{2}}+\cos \left (t \right )
\]
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\[
{} y^{\prime } = t^{r} y+4
\]
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\[
{} y^{\prime } = \left (y-3\right ) \left (\sin \left (y\right ) \sin \left (t \right )+\cos \left (t \right )+1\right )
\]
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\[
{} y^{\prime } = 1-y^{2}
\]
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\[
{} y^{\prime } = \left (y-1\right ) \left (y-2\right ) \left (y-{\mathrm e}^{\frac {t}{2}}\right )
\]
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\[
{} y^{\prime } = 3-y^{2}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+9 y = 20 \operatorname {Heaviside}\left (t -2\right ) \sin \left (t -2\right )
\]
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\[
{} y^{\prime \prime }+y^{\prime }+5 y = \operatorname {Heaviside}\left (t -2\right ) \sin \left (4 t -8\right )
\]
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\[
{} y^{\prime \prime }+y^{\prime }+8 y = \left (1-\operatorname {Heaviside}\left (t -4\right )\right ) \cos \left (t -4\right )
\]
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\[
{} y^{\prime \prime }+y^{\prime }+3 y = \left (1-\operatorname {Heaviside}\left (t -2\right )\right ) {\mathrm e}^{-\frac {t}{10}+\frac {1}{5}} \sin \left (t -2\right )
\]
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\[
{} y^{2} y^{\prime \prime } = 8 x^{2}
\]
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\[
{} \sin \left (x +y\right )-y y^{\prime } = 0
\]
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\[
{} y^{\prime }-y^{2} = x
\]
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\[
{} y^{\prime }+\left (8-x \right ) y-y^{2} = -8 x
\]
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\[
{} x y^{\prime } = \left (x -y\right )^{2}
\]
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\[
{} y y^{\prime } = 3 \sqrt {x y^{2}+9 x}
\]
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