\[ \boxed { \left \{ {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) =x \left ( t \right ) \cos \left ( t \right ) ,{\frac {\rm d}{{\rm d}t}}y \left ( t \right ) =x \left ( t \right ) {{\rm e}^{-\sin \left ( t \right ) }} \right \} } \]
Mathematica: cpu = 0.074510 (sec), leaf count = 38 \[ \left \{\left \{x(t)\to c_1 e^{\sin (t)},y(t)\to c_1 \int _1^t e^{\sin (K[1])-\sin (K[1])} \, dK[1]+c_2\right \}\right \} \]
Maple: cpu = 0.093 (sec), leaf count = 18 \[ \left \{ \left \{ x \left ( t \right ) ={\it \_C2}\,{{\rm e}^{\sin \left ( t \right ) }},y \left ( t \right ) =t{\it \_C2}+{\it \_C1} \right \} \right \} \]