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