\[
\boxed{
{x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left( x \right) +2\,{x}^{2}f \left( x \right) {\frac {\rm d}{{\rm d}x}}y \left( x \right) + \left( {x}^{2} \left( {\frac {\rm d}{{\rm d}x}}f \left( x \right) + \left( f \left( x \right)  \right) ^{2}+a \right) -v \left( v-1 \right)  \right) y \left( x \right) =0}
\]