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