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