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\[
{} y^{\prime \prime }+a \left (x y^{\prime }+y\right ) = 0
\]
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\[
{} a \,x^{2} y^{\prime \prime }+b x y^{\prime }+c y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+\frac {5 y}{4} = 0
\]
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\[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }-6 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-2 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+2 x y^{\prime }+4 y = 0
\]
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\[
{} 2 x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\]
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\[
{} 2 x^{2} y^{\prime \prime }+x y^{\prime }-3 y = 0
\]
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\[
{} 4 x^{2} y^{\prime \prime }+8 x y^{\prime }+17 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+5 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = \ln \left (x \right )
\]
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\[
{} x^{2} y^{\prime \prime }+7 x y^{\prime }+5 y = x
\]
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\[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 3 x^{2}+2 \ln \left (x \right )
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+4 y = \sin \left (\ln \left (x \right )\right )
\]
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\[
{} y^{\prime \prime }+y+\frac {y^{3}}{5} = \cos \left (w t \right )
\]
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\[
{} y^{\prime \prime }+\frac {y^{\prime }}{5}+y+\frac {y^{3}}{5} = \cos \left (w t \right )
\]
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\[
{} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y = 2 t^{3}
\]
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\[
{} t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = {\mathrm e}^{2 t} t^{2}
\]
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\[
{} \left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 2 \left (t -1\right )^{2} {\mathrm e}^{-t}
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 3 x^{{3}/{2}} \sin \left (x \right )
\]
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\[
{} \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = g \left (x \right )
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = g \left (x \right )
\]
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\[
{} t^{2} y^{\prime \prime }-2 y = 3 t^{2}-1
\]
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\[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{2} \ln \left (x \right )
\]
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\[
{} t^{2} y^{\prime \prime }-2 t y^{\prime }+2 y = 4 t^{2}
\]
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\[
{} t^{2} y^{\prime \prime }+7 t y^{\prime }+5 y = t
\]
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\[
{} t y^{\prime \prime }-\left (t +1\right ) y^{\prime }-y = {\mathrm e}^{2 t} t^{2}
\]
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\[
{} \left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 2 \left (t -1\right )^{2} {\mathrm e}^{-t}
\]
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\[
{} t y^{\prime \prime \prime }+\sin \left (t \right ) y^{\prime \prime }+8 y = \cos \left (t \right )
\]
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\[
{} t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+4 t^{2} y = 0
\]
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\[
{} y^{\prime \prime \prime }+t y^{\prime \prime }+t^{2} y^{\prime }+t^{2} y = \ln \left (t \right )
\]
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\[
{} \left (-4+x \right ) y^{\prime \prime \prime \prime }+\left (1+x \right ) y^{\prime \prime }+y \tan \left (x \right ) = 0
\]
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\[
{} \left (x^{2}-2\right ) y^{\left (6\right )}+x^{2} y^{\prime \prime }+3 y = 0
\]
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\[
{} t y^{\prime \prime \prime }+\sin \left (t \right ) y^{\prime \prime }+4 y = \cos \left (t \right )
\]
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\[
{} t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+7 t^{2} y = 0
\]
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\[
{} y^{\prime \prime \prime }+t y^{\prime \prime }+5 t^{2} y^{\prime }+2 t^{3} y = \ln \left (t \right )
\]
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\[
{} \left (x -1\right ) y^{\prime \prime \prime \prime }+\left (x +5\right ) y^{\prime \prime }+y \tan \left (x \right ) = 0
\]
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\[
{} \left (x^{2}-25\right ) y^{\left (6\right )}+x^{2} y^{\prime \prime }+5 y = 0
\]
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\[
{} x y^{\prime \prime \prime }-y^{\prime \prime } = 0
\]
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\[
{} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\]
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\[
{} y^{\prime \prime } = \frac {1}{\sqrt {y}}
\]
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\[
{} a^{3} y^{\prime \prime \prime } y^{\prime \prime } = \sqrt {1+c^{2} {y^{\prime \prime }}^{2}}
\]
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\[
{} y^{\prime \prime \prime } = \sqrt {1+{y^{\prime \prime }}^{2}}
\]
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\[
{} 2 \left (2 a -y\right ) y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
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\[
{} y^{\prime \prime }-x y^{\prime \prime \prime }+{y^{\prime \prime \prime }}^{3} = 0
\]
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\[
{} y y^{\prime \prime }+{y^{\prime }}^{2} = y^{2} \ln \left (y\right )
\]
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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2} = 0
\]
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\[
{} x y y^{\prime \prime }+{y^{\prime }}^{2} x -y y^{\prime } = 0
\]
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\[
{} n \,x^{3} y^{\prime \prime } = \left (y-x y^{\prime }\right )^{2}
\]
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\[
{} y^{2} \left (x^{2} y^{\prime \prime }-x y^{\prime }+y\right ) = x^{3}
\]
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\[
{} x^{2} y^{2} y^{\prime \prime }-3 x y^{2} y^{\prime }+4 y^{3}+x^{6} = 0
\]
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\[
{} y^{\prime \prime } y^{\prime }-x^{2} y y^{\prime }-x y^{2} = 0
\]
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\[
{} x \left (y^{\prime } x^{2}+2 x y\right ) y^{\prime \prime }+4 {y^{\prime }}^{2} x +8 x y y^{\prime }+4 y^{2}-1 = 0
\]
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\[
{} x \left (x y+1\right ) y^{\prime \prime }+x^{2} {y^{\prime }}^{2}+\left (4 x y+2\right ) y^{\prime }+y^{2}+1 = 0
\]
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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2}-{y^{\prime }}^{4} = 0
\]
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\[
{} a^{2} y^{\prime \prime } = 2 x \sqrt {1+{y^{\prime }}^{2}}
\]
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\[
{} x^{2} y y^{\prime \prime }+x^{2} {y^{\prime }}^{2}-5 x y y^{\prime } = 4 y^{2}
\]
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\[
{} y \left (1-\ln \left (y\right )\right ) y^{\prime \prime }+\left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2} = 0
\]
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\[
{} 5 {y^{\prime \prime \prime }}^{2}-3 y^{\prime \prime } y^{\prime \prime \prime \prime } = 0
\]
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\[
{} 40 {y^{\prime \prime \prime }}^{3}-45 y^{\prime \prime } y^{\prime \prime \prime } y^{\prime \prime \prime \prime }+9 {y^{\prime \prime }}^{2} y^{\left (5\right )} = 0
\]
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\[
{} {y^{\prime \prime }}^{2}+2 x y^{\prime \prime }-y^{\prime } = 0
\]
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\[
{} {y^{\prime \prime }}^{2}-2 x y^{\prime \prime }-y^{\prime } = 0
\]
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\[
{} 2 x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+12 x y^{\prime }-12 y = 0
\]
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\[
{} y^{\prime \prime \prime }-\frac {3 y^{\prime \prime }}{x}+\frac {6 y^{\prime }}{x^{2}}-\frac {6 y}{x^{3}} = 0
\]
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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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\[
{} y^{\prime \prime }+\frac {2 y^{\prime }}{x}+y = 0
\]
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\[
{} \sin \left (x \right )^{2} y^{\prime \prime } = 2 y
\]
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\[
{} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = 0
\]
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\[
{} x y^{\prime \prime \prime }-y^{\prime \prime }+x y^{\prime }-y = 0
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime \prime }-x y^{\prime \prime }+y^{\prime } = 0
\]
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\[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 2 x^{3}
\]
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\[
{} y^{\prime \prime }+\frac {x y^{\prime }}{1-x}-\frac {y}{1-x} = x -1
\]
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\[
{} \left (x^{2}+2\right ) y^{\prime \prime \prime }-2 x y^{\prime \prime }+y^{\prime } \left (x^{2}+2\right )-2 x y = x^{4}+12
\]
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\[
{} y^{\prime \prime }+\frac {y}{x^{2} \ln \left (x \right )} = {\mathrm e}^{x} \left (\frac {2}{x}+\ln \left (x \right )\right )
\]
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\[
{} \left (2 x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }-8 y = 0
\]
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\[
{} \sin \left (x \right )^{2} y^{\prime \prime }+\sin \left (x \right ) \cos \left (x \right ) y^{\prime } = y
\]
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\[
{} y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {n \left (n +1\right ) y}{x^{2}} = 0
\]
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\[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x
\]
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\[
{} x^{2} y^{\prime \prime }-x y^{\prime }+2 y = x \ln \left (x \right )
\]
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\[
{} x^{2} y^{\prime \prime }-2 y = x^{2}+\frac {1}{x}
\]
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\[
{} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = x^{3}+3 x
\]
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\[
{} \left (1+x \right )^{2} y^{\prime \prime }+\left (1+x \right ) y^{\prime }+y = 4 \cos \left (\ln \left (1+x \right )\right )
\]
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\[
{} y^{\prime \prime }-\frac {y^{\prime }}{x}+\left (1-\frac {m^{2}}{x^{2}}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\frac {2 y^{\prime }}{x}+y = 0
\]
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\[
{} y^{\prime \prime }+\frac {2 p y^{\prime }}{x}+y = 0
\]
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\[
{} x y^{\prime \prime }-y^{\prime }-x^{3} y = 0
\]
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\[
{} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y = -3 \,{\mathrm e}^{x^{2}} \sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}} = 0
\]
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\[
{} y^{\prime \prime } = x +y^{2}
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y^{2} = 0
\]
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\[
{} y y^{\prime \prime }+{y^{\prime }}^{2} = 0
\]
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\[
{} x y^{\prime \prime } = {y^{\prime }}^{3}+y^{\prime }
\]
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\[
{} x^{2} y^{\prime \prime } = 2 x y^{\prime }+{y^{\prime }}^{2}
\]
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\[
{} 2 y y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2} = 0
\]
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\[
{} x y^{\prime \prime }+y^{\prime } = 4 x
\]
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