\[
\boxed{
{x}^{4}{\it d4y} \left( x \right) -2\,n \left( n+1 \right) {x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left( x \right) +4\,n \left( n+1 \right) x{\frac {\rm d}{{\rm d}x}}y \left( x \right) + \left( a{x}^{4}+n \left( n+1 \right)  \left( n+3 \right)  \left( n-2 \right)  \right) y \left( x \right) =0}
\]