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