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