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\[
{} y+y^{\prime } = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ 5 & 1\le t \end {array}\right .
\]
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\[
{} y+y^{\prime } = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ -1 & 1\le t \end {array}\right .
\]
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\[
{} y+y^{\prime } = \left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right .
\]
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\[
{} 2 y^{\prime \prime }+t y^{\prime }-2 y = 10
\]
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\[
{} y^{\prime \prime }-7 y^{\prime }+6 y = {\mathrm e}^{t}+\delta \left (t -2\right )+\delta \left (-4+t \right )
\]
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\[
{} [x^{\prime }\left (t \right ) = -3 x \left (t \right )+4 y \left (t \right )-9 z \left (t \right ), y^{\prime }\left (t \right ) = 6 x \left (t \right )-y \left (t \right ), z^{\prime }\left (t \right ) = 10 x \left (t \right )+4 y \left (t \right )+3 z \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+2 z \left (t \right ), z^{\prime }\left (t \right ) = -x \left (t \right )+z \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = -3 x \left (t \right )+4 y \left (t \right )+{\mathrm e}^{-t} \sin \left (2 t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )+9 z \left (t \right )+4 \,{\mathrm e}^{-t} \cos \left (2 t \right ), z^{\prime }\left (t \right ) = y \left (t \right )+6 z \left (t \right )-{\mathrm e}^{-t}]
\]
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\[
{} [x^{\prime }\left (t \right ) = 7 x \left (t \right )+5 y \left (t \right )-9 z \left (t \right )-8 \,{\mathrm e}^{-2 t}, y^{\prime }\left (t \right ) = 4 x \left (t \right )+y \left (t \right )+z \left (t \right )+2 \,{\mathrm e}^{5 t}, z^{\prime }\left (t \right ) = -2 y \left (t \right )+3 z \left (t \right )+{\mathrm e}^{5 t}-3 \,{\mathrm e}^{-2 t}]
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )+2 z \left (t \right )+{\mathrm e}^{-t}-3 t, y^{\prime }\left (t \right ) = 3 x \left (t \right )-4 y \left (t \right )+z \left (t \right )+2 \,{\mathrm e}^{-t}+t, z^{\prime }\left (t \right ) = -2 x \left (t \right )+5 y \left (t \right )+6 z \left (t \right )+2 \,{\mathrm e}^{-t}-t]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = \frac {9 x \left (t \right )}{10}+\frac {21 y \left (t \right )}{10}+\frac {16 z \left (t \right )}{5}, y^{\prime }\left (t \right ) = \frac {7 x \left (t \right )}{10}+\frac {13 y \left (t \right )}{2}+\frac {21 z \left (t \right )}{5}, z^{\prime }\left (t \right ) = \frac {11 x \left (t \right )}{10}+\frac {17 y \left (t \right )}{10}+\frac {17 z \left (t \right )}{5}\right ]
\]
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\[
{} \left [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{3} \left (t \right )-\frac {9 x_{4} \left (t \right )}{5}, x_{2}^{\prime }\left (t \right ) = \frac {51 x_{2} \left (t \right )}{10}-x_{4} \left (t \right )+3 x_{5} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{2} \left (t \right )-3 x_{3} \left (t \right ), x_{4}^{\prime }\left (t \right ) = x_{2} \left (t \right )-\frac {31 x_{3} \left (t \right )}{10}+4 x_{4} \left (t \right ), x_{5}^{\prime }\left (t \right ) = -\frac {14 x_{1} \left (t \right )}{5}+\frac {3 x_{4} \left (t \right )}{2}-x_{5} \left (t \right )\right ]
\]
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\[
{} \left (x^{2}+y^{2}\right )^{2} {y^{\prime }}^{2} = 4 x^{2} y^{2}
\]
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\[
{} {y^{\prime }}^{2}-x y^{\prime }-y = 0
\]
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\[
{} 4 y^{3} {y^{\prime }}^{2}-4 x y^{\prime }+y = 0
\]
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\[
{} 4 y^{3} {y^{\prime }}^{2}+4 x y^{\prime }+y = 0
\]
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\[
{} {y^{\prime }}^{3}+{y^{\prime }}^{2} x -y = 0
\]
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\[
{} y^{4} {y^{\prime }}^{3}-6 x y^{\prime }+2 y = 0
\]
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\[
{} 2 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}+x^{4} = 0
\]
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\[
{} {y^{\prime }}^{2} x +\left (x -y\right ) y^{\prime }+1-y = 0
\]
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\[
{} y^{\prime } \left (x y^{\prime }-y+k \right )+a = 0
\]
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\[
{} x^{6} {y^{\prime }}^{3}-3 x y^{\prime }-3 y = 0
\]
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\[
{} y = x^{6} {y^{\prime }}^{3}-x y^{\prime }
\]
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\[
{} {y^{\prime }}^{4} x -2 {y^{\prime }}^{3} y+12 x^{3} = 0
\]
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\[
{} x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+1 = 0
\]
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\[
{} {y^{\prime }}^{2}-x y^{\prime }-y = 0
\]
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\[
{} 2 {y^{\prime }}^{3}+x y^{\prime }-2 y = 0
\]
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\[
{} 2 {y^{\prime }}^{2}+x y^{\prime }-2 y = 0
\]
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\[
{} {y^{\prime }}^{3}+2 x y^{\prime }-y = 0
\]
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\[
{} 4 {y^{\prime }}^{2} x -3 y y^{\prime }+3 = 0
\]
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\[
{} {y^{\prime }}^{3}-x y^{\prime }+2 y = 0
\]
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\[
{} 5 {y^{\prime }}^{2}+6 x y^{\prime }-2 y = 0
\]
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\[
{} 2 {y^{\prime }}^{2} x +\left (2 x -y\right ) y^{\prime }+1-y = 0
\]
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\[
{} 5 {y^{\prime }}^{2}+3 x y^{\prime }-y = 0
\]
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\[
{} {y^{\prime }}^{2}+3 x y^{\prime }-y = 0
\]
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\[
{} y = x y^{\prime }+x^{3} {y^{\prime }}^{2}
\]
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\[
{} y y^{\prime \prime }+{y^{\prime }}^{2} = 0
\]
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\[
{} y^{2} y^{\prime \prime }+{y^{\prime }}^{3} = 0
\]
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\[
{} \left (1+y\right ) y^{\prime \prime } = {y^{\prime }}^{2}
\]
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\[
{} y^{\prime \prime } = 2 {y^{\prime }}^{3} y
\]
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\[
{} y y^{\prime \prime }+{y^{\prime }}^{3}-{y^{\prime }}^{2} = 0
\]
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\[
{} y y^{\prime \prime }+{y^{\prime }}^{3} = 0
\]
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\[
{} y^{\prime \prime } = -{\mathrm e}^{-2 y}
\]
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\[
{} y^{\prime \prime } = -{\mathrm e}^{-2 y}
\]
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\[
{} 2 y^{\prime \prime } = \sin \left (2 y\right )
\]
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\[
{} 2 y^{\prime \prime } = \sin \left (2 y\right )
\]
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\[
{} 2 y^{\prime \prime } = {y^{\prime }}^{3} \sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime } = \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\]
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\[
{} y y^{\prime \prime } = {y^{\prime }}^{2} \left (1-y^{\prime } \sin \left (y\right )-y y^{\prime } \cos \left (y\right )\right )
\]
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\[
{} \left (1+y^{2}\right ) y^{\prime \prime }+{y^{\prime }}^{3}+y^{\prime } = 0
\]
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\[
{} \left (y y^{\prime \prime }+1+{y^{\prime }}^{2}\right )^{2} = \left (1+{y^{\prime }}^{2}\right )^{3}
\]
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\[
{} {y^{\prime \prime }}^{2}-2 y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime }+x^{2} = 0
\]
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\[
{} {y^{\prime \prime }}^{3} = 12 y^{\prime } \left (x y^{\prime \prime }-2 y^{\prime }\right )
\]
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\[
{} 3 y y^{\prime } y^{\prime \prime } = {y^{\prime }}^{3}-1
\]
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\[
{} 4 y {y^{\prime }}^{2} y^{\prime \prime } = {y^{\prime }}^{4}+3
\]
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\[
{} x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+4 = 0
\]
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\[
{} 9 {y^{\prime }}^{2}+3 x y^{4} y^{\prime }+y^{5} = 0
\]
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\[
{} 4 y^{3} {y^{\prime }}^{2}-4 x y^{\prime }+y = 0
\]
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\[
{} 5 {y^{\prime }}^{2}+6 x y^{\prime }-2 y = 0
\]
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\[
{} 4 x^{5} {y^{\prime }}^{2}+12 x^{4} y y^{\prime }+9 = 0
\]
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\[
{} 4 y^{2} {y^{\prime }}^{3}-2 x y^{\prime }+y = 0
\]
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\[
{} {y^{\prime }}^{4}+x y^{\prime }-3 y = 0
\]
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\[
{} x^{2} {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+y^{2} y^{\prime }+1 = 0
\]
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\[
{} {y^{\prime }}^{3}-2 x y^{\prime }-y = 0
\]
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\[
{} 9 x y^{4} {y^{\prime }}^{2}-3 y^{5} y^{\prime }-1 = 0
\]
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\[
{} x^{2} {y^{\prime }}^{2}-\left (1+2 x y\right ) y^{\prime }+1+y^{2} = 0
\]
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\[
{} \left (y^{\prime }+1\right )^{2} \left (y-x y^{\prime }\right ) = 1
\]
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\[
{} {y^{\prime }}^{3}-{y^{\prime }}^{2}+x y^{\prime }-y = 0
\]
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\[
{} {y^{\prime }}^{2} x +\left (k -x -y\right ) y^{\prime }+y = 0
\]
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\[
{} x {y^{\prime }}^{3}-2 y {y^{\prime }}^{2}+4 x^{2} = 0
\]
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\[
{} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y = 0
\]
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\[
{} y^{\prime \prime }+x y^{\prime }+3 y = x^{2}
\]
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\[
{} x \left (1+x \right ) y^{\prime \prime }+\left (x +5\right ) y^{\prime }-4 y = 0
\]
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\[
{} x \left (-x^{2}+1\right ) y^{\prime \prime }-\left (x^{2}+7\right ) y^{\prime }+4 x y = 0
\]
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\[
{} y^{2}+\cos \left (x \right )+\left (2 x y+\sin \left (y\right )\right ) y^{\prime } = 0
\]
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\[
{} y^{\prime } = \frac {2 y}{x}
\]
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\[
{} y^{\prime } = \sqrt {1-x^{2}-y^{2}}
\]
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\[
{} y^{\prime } = \sqrt {y}+x
\]
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\[
{} x f^{\prime }-f = \frac {{f^{\prime }}^{2} \left (1-{f^{\prime }}^{\lambda }\right )^{2}}{\lambda ^{2}}
\]
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\[
{} x y^{\prime }-2 y+b y^{2} = c \,x^{4}
\]
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\[
{} x y^{\prime }-y+y^{2} = x^{{2}/{3}}
\]
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\[
{} u^{\prime }+u^{2} = \frac {1}{x^{{4}/{5}}}
\]
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\[
{} y y^{\prime }-y = x
\]
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\[
{} y y^{\prime } = 1-x {y^{\prime }}^{3}
\]
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\[
{} y y^{\prime \prime } = x
\]
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\[
{} y^{2} y^{\prime \prime } = x
\]
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\[
{} 3 y y^{\prime \prime } = \sin \left (x \right )
\]
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\[
{} 3 y y^{\prime \prime }+y = 5
\]
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\[
{} a y y^{\prime \prime }+b y = c
\]
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\[
{} x^{\prime } = 4 A k \left (\frac {x}{A}\right )^{{3}/{4}}-3 k x
\]
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\[
{} \frac {y^{\prime } y}{1+\frac {\sqrt {1+{y^{\prime }}^{2}}}{2}} = -x
\]
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\[
{} y^{\prime } = x^{2}+y^{2}
\]
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\[
{} y^{\prime } = x^{2}+y^{2}-1
\]
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\[
{} y^{\prime } = 2 y \left (x \sqrt {y}-1\right )
\]
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\[
{} y^{\prime \prime } = \frac {1}{y}-\frac {x y^{\prime }}{y^{2}}
\]
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\[
{} y^{\prime \prime }-y y^{\prime } = 2 x
\]
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\[
{} y^{\prime }-y^{2}-x -x^{2} = 0
\]
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\[
{} y^{\prime \prime }-x y^{\prime }-x y-x = 0
\]
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\[
{} y^{\prime \prime }-x y^{\prime }-x y-2 x = 0
\]
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\[
{} y^{\prime \prime }-x y^{\prime }-x y-3 x = 0
\]
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