\[
\boxed{
{\it d4y} \left( x \right) +4\,ax{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left( x \right) +6\,{a}^{2}{x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left( x \right) +4\,{a}^{3}{x}^{3}{\frac {\rm d}{{\rm d}x}}y \left( x \right) +{a}^{4}{x}^{4}y \left( x \right) =0}
\]