\[
\boxed{
{x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left( x \right) -2\,x{\frac {\rm d}{{\rm d}x}}y \left( x \right) -4\,y \left( x \right) -x\sin \left( x \right) - \left( a{x}^{2}+12\,a+4 \right) \cos \left( x \right) =0}
\]