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