\[
\boxed{
 \left\{ 3\,{\frac {\rm d}{{\rm d}t}}x \left( t \right) +7\,{\frac {\rm d}{{\rm d}t}}y \left( t \right) +34\,x \left( t \right) +38\,y \left( t \right) ={{\rm e}^{t}},4\,{\frac {\rm d}{{\rm d}t}}x \left( t \right) +9\,{\frac {\rm d}{{\rm d}t}}y \left( t \right) +44\,x \left( t \right) +49\,y \left( t \right) =t \right\} }
\]