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