\[
\boxed{
{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left( x \right) - \left( 4\,{a}^{2}{b}^{2}{x}^{2}{{\rm e}^{2\,b{x}^{2}}}-1 \right) y \left( x \right) =0}
\]