\[
\boxed{
{\it d4y} \left( x \right) -12\,{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left( x \right) +12\,y \left( x \right) -16\,{x}^{4}{{\rm e}^{{x}^{2}}}=0}
\]