\[
\boxed{
{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left( x \right) -4\,x{\frac {\rm d}{{\rm d}x}}y \left( x \right) + \left( 4\,{x}^{2}-3 \right) y \left( x \right) -{{\rm e}^{{x}^{2}}}=0}
\]