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