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