\[
\boxed{
 \left\{ {\frac {\rm d}{{\rm d}t}}x \left( t \right) +{\frac {\rm d}{{\rm d}t}}y \left( t \right) -y \left( t \right) ={{\rm e}^{t}},2\,{\frac {\rm d}{{\rm d}t}}x \left( t \right) +{\frac {\rm d}{{\rm d}t}}y \left( t \right) +2\,y \left( t \right) =\cos \left( t \right)  \right\} }
\]