\[
\boxed{
{\it d4y} \left( x \right) +2\,{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left( x \right) -3\,{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left( x \right) -4\,{\frac {\rm d}{{\rm d}x}}y \left( x \right) +4\,y \left( x \right) -32\,\sin \left( 2\,x \right) +24\,\cos \left( 2\,x \right) =0}
\]