\[
\boxed{
{x}^{2}{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left( x \right) -2\, \left( n+1 \right) x{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left( x \right) + \left( a{x}^{2}+6\,n \right) {\frac {\rm d}{{\rm d}x}}y \left( x \right) -2\,axy \left( x \right) =0}
\]