\[
\boxed{
{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left( x \right) - \left( 6\,{k}^{2} \left( \sin \left( x \right)  \right) ^{2}+a \right) {\frac {\rm d}{{\rm d}x}}y \left( x \right) +by \left( x \right) =0}
\]