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