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\[
{} y^{\prime \prime }+\frac {2 {y^{\prime }}^{2}}{1-y} = 0
\]
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\[
{} x^{3} x^{\prime \prime }+1 = 0
\]
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\[
{} {y^{\prime \prime \prime }}^{2}+{y^{\prime \prime }}^{2} = 1
\]
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\[
{} y^{\prime \prime }+{y^{\prime }}^{2} = 1
\]
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\[
{} y^{\prime \prime } = 3 \sqrt {y}
\]
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\[
{} y y^{\prime \prime }+{y^{\prime }}^{2} = \frac {y y^{\prime }}{\sqrt {x^{2}+1}}
\]
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\[
{} y y^{\prime } y^{\prime \prime } = {y^{\prime }}^{3}+{y^{\prime \prime }}^{2}
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = \sinh \left (x \right )
\]
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\[
{} \left (x^{2}-1\right ) y^{\prime \prime }-6 y = 1
\]
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\[
{} m x^{\prime \prime } = f \left (x\right )
\]
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\[
{} m x^{\prime \prime } = f \left (x^{\prime }\right )
\]
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\[
{} \left (1+x \right )^{2} y^{\prime \prime }+\left (1+x \right ) y^{\prime }+y = 2 \cos \left (\ln \left (1+x \right )\right )
\]
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\[
{} x^{3} y^{\prime \prime }-x y^{\prime }+y = 0
\]
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\[
{} x y y^{\prime \prime }-x {y^{\prime }}^{2}-y y^{\prime } = 0
\]
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\[
{} 6 y^{\prime \prime } y^{\prime \prime \prime \prime }-5 {y^{\prime \prime \prime }}^{2} = 0
\]
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\[
{} y^{\prime \prime } = 2 y^{3}
\]
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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2} = y^{\prime }
\]
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\[
{} y^{\prime } = \sin \left (x y\right )
\]
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\[
{} y^{\prime } = t \ln \left (y^{2 t}\right )+t^{2}
\]
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\[
{} y^{\prime } = \ln \left (x y\right )
\]
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\[
{} y^{\prime \prime }+x^{2} y = 0
\]
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\[
{} y^{\prime \prime \prime }+x y = \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }+y y^{\prime } = 1
\]
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\[
{} y^{\left (5\right )}-y^{\prime \prime \prime \prime }+y^{\prime } = 2 x^{2}+3
\]
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\[
{} y^{\prime \prime }+y y^{\prime \prime \prime \prime } = 1
\]
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\[
{} y^{\prime \prime \prime }+x y = \cosh \left (x \right )
\]
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\[
{} \cos \left (x \right ) y^{\prime }+y \,{\mathrm e}^{x^{2}} = \sinh \left (x \right )
\]
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\[
{} y^{\prime \prime \prime }+x y = \cosh \left (x \right )
\]
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\[
{} \sinh \left (x \right ) {y^{\prime }}^{2}+3 y = 0
\]
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\[
{} 2 y^{\prime \prime }+3 y^{\prime }+4 x^{2} y = 1
\]
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\[
{} y^{\prime \prime \prime }+x y^{\prime \prime }-y^{2} = \sin \left (x \right )
\]
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\[
{} {y^{\prime }}^{2}+y {y^{\prime }}^{2} x = \ln \left (x \right )
\]
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\[
{} \sin \left (y^{\prime \prime }\right )+y y^{\prime \prime \prime \prime } = 1
\]
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\[
{} \sinh \left (x \right ) {y^{\prime }}^{2}+y^{\prime \prime } = x y
\]
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\[
{} {y^{\prime \prime \prime }}^{2}+\sqrt {y} = \sin \left (x \right )
\]
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\[
{} \left (x -3\right ) y^{\prime \prime }+y \ln \left (x \right ) = x^{2}
\]
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\[
{} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+\cot \left (x \right ) y = 0
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y = 0
\]
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\[
{} x y^{\prime \prime }+2 x^{2} y^{\prime }+\sin \left (x \right ) y = \sinh \left (x \right )
\]
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\[
{} \sin \left (x \right ) y^{\prime \prime }+x y^{\prime }+7 y = 1
\]
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\[
{} y^{\prime \prime }-\left (x -1\right ) y^{\prime }+x^{2} y = \tan \left (x \right )
\]
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\[
{} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (x^{2}+1\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\frac {k x}{y^{4}} = 0
\]
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\[
{} y^{\prime \prime }+2 x y^{\prime }+2 y = 0
\]
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\[
{} x y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y = 0
\]
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\[
{} y^{\prime \prime }+2 x^{2} y^{\prime }+4 x y = 2 x
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y = 1-2 x
\]
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\[
{} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+x^{2} y^{\prime }+2 \left (1-x \right ) y = 0
\]
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\[
{} y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 2 x
\]
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\[
{} \ln \left (x^{2}+1\right ) y^{\prime \prime }+\frac {4 x y^{\prime }}{x^{2}+1}+\frac {\left (-x^{2}+1\right ) y}{\left (x^{2}+1\right )^{2}} = 0
\]
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\[
{} x y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 0
\]
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\[
{} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y = \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }+\cot \left (x \right ) y^{\prime }-\csc \left (x \right )^{2} y = \cos \left (x \right )
\]
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\[
{} x \ln \left (x \right ) y^{\prime \prime }+2 y^{\prime }-\frac {y}{x} = 1
\]
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\[
{} x y^{\prime \prime }+\left (6 x y^{2}+1\right ) y^{\prime }+2 y^{3}+1 = 0
\]
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\[
{} \frac {x y^{\prime \prime }}{y+1}+\frac {y y^{\prime }-x {y^{\prime }}^{2}+y^{\prime }}{\left (y+1\right )^{2}} = x \sin \left (x \right )
\]
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\[
{} \left (x \cos \left (y\right )+\sin \left (x \right )\right ) y^{\prime \prime }-x {y^{\prime }}^{2} \sin \left (y\right )+2 \left (\cos \left (y\right )+\cos \left (x \right )\right ) y^{\prime } = \sin \left (x \right ) y
\]
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\[
{} y y^{\prime \prime } \sin \left (x \right )+\left (\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y\right ) y^{\prime } = \cos \left (x \right )
\]
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\[
{} \left (1-y\right ) y^{\prime \prime }-{y^{\prime }}^{2} = 0
\]
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\[
{} \left (\cos \left (y\right )-y \sin \left (y\right )\right ) y^{\prime \prime }-{y^{\prime }}^{2} \left (2 \sin \left (y\right )+y \cos \left (y\right )\right ) = \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }+\frac {2 x y^{\prime }}{2 x -1}-\frac {4 x y}{\left (2 x -1\right )^{2}} = 0
\]
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\[
{} \left (x^{2}+2 x \right ) y^{\prime \prime }+\left (x^{2}+x +10\right ) y^{\prime } = \left (25-6 x \right ) y
\]
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\[
{} y^{\prime \prime }+\frac {y^{\prime }}{1+x}-\frac {\left (x +2\right ) y}{x^{2} \left (1+x \right )} = 0
\]
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\[
{} \left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x^{2}+4 x -3\right ) y^{\prime }+8 x y = 0
\]
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\[
{} \frac {\left (x^{2}-x \right ) y^{\prime \prime }}{x}+\frac {\left (3 x +1\right ) y^{\prime }}{x}+\frac {y}{x} = 3 x
\]
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\[
{} \left (2 \sin \left (x \right )-\cos \left (x \right )\right ) y^{\prime \prime }+\left (7 \sin \left (x \right )+4 \cos \left (x \right )\right ) y^{\prime }+10 \cos \left (x \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\frac {\left (x -1\right ) y^{\prime }}{x}+\frac {y}{x^{3}} = \frac {{\mathrm e}^{-\frac {1}{x}}}{x^{3}}
\]
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\[
{} y^{\prime \prime }+\left (5+2 x \right ) y^{\prime }+\left (4 x +8\right ) y = {\mathrm e}^{-2 x}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime } = \left \{\begin {array}{cc} 4 & 0\le t <1 \\ 6 & 1\le t \end {array}\right .
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }+2 y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ 1 & 1\le t <2 \\ -1 & 2\le t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t <2 \\ -1 & 2\le t \end {array}\right .
\]
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\[
{} y^{\prime \prime \prime }-5 y^{\prime \prime }+y^{\prime }-y = -t^{2}+2 t -10
\]
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\[
{} t^{2} y^{\prime \prime }-6 t y^{\prime }+\sin \left (2 t \right ) y = \ln \left (t \right )
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+\frac {y}{t} = t
\]
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\[
{} y^{\prime \prime }+t y^{\prime }-y \ln \left (t \right ) = \cos \left (2 t \right )
\]
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\[
{} t^{3} y^{\prime \prime }-2 t y^{\prime }+y = t^{4}
\]
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\[
{} [x^{\prime }\left (t \right ) = -3 x \left (t \right )-3 y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )+2 z \left (t \right )+29 \,{\mathrm e}^{-t}, z^{\prime }\left (t \right ) = 5 x \left (t \right )+y \left (t \right )+z \left (t \right )+39 \,{\mathrm e}^{t}]
\]
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\[
{} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\]
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\[
{} y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (1-\frac {1}{4 x^{2}}\right ) y = x
\]
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\[
{} x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+y^{\prime }-2 y = 0
\]
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\[
{} y^{\prime \prime }-x^{2} y = 0
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+n \left (n +1\right ) y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (-\nu ^{2}+x^{2}\right ) y = \sin \left (x \right )
\]
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\[
{} y {y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\]
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\[
{} x y \left (1-{y^{\prime }}^{2}\right ) = \left (x^{2}-y^{2}-a^{2}\right ) y^{\prime }
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }-a^{2} y = 0
\]
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\[
{} x \cos \left (\frac {y}{x}\right ) \left (x y^{\prime }+y\right ) = y \sin \left (\frac {y}{x}\right ) \left (x y^{\prime }-y\right )
\]
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\[
{} \frac {y-x y^{\prime }}{\sqrt {x^{2}+y^{2}}} = m
\]
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\[
{} y^{\prime }+\frac {n y}{x} = a \,x^{-n}
\]
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\[
{} x^{2}+y+\left (x -2 y\right ) y^{\prime } = 0
\]
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\[
{} y-3 x^{2}-\left (4 y-x \right ) y^{\prime } = 0
\]
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\[
{} \frac {y^{2}}{\left (x -y\right )^{2}}-\frac {1}{x}+\left (\frac {1}{y}-\frac {x^{2}}{\left (x -y\right )^{2}}\right ) y^{\prime } = 0
\]
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\[
{} 6 x y^{2}+4 x^{3}+3 \left (2 x^{2} y+y^{2}\right ) y^{\prime } = 0
\]
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\[
{} \frac {x}{\left (x +y\right )^{2}}+\frac {\left (y+2 x \right ) y^{\prime }}{\left (x +y\right )^{2}} = 0
\]
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\[
{} x +y y^{\prime } = \frac {y}{x^{2}+y^{2}}-\frac {x y^{\prime }}{x^{2}+y^{2}}
\]
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\[
{} y = 2 x y^{\prime }+{y^{\prime }}^{2}
\]
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\[
{} y = y {y^{\prime }}^{2}+2 x y^{\prime }
\]
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