\[ \boxed { \left \{ {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) =ax \left ( t \right ) -y \left ( t \right ) ,{\frac {\rm d}{{\rm d}t}}y \left ( t \right ) =x \left ( t \right ) +ay \left ( t \right ) \right \} } \]
Mathematica: cpu = 0.005001 (sec), leaf count = 51 \[ \left \{\left \{x(t)\to c_1 e^{a t} \cos (t)-c_2 e^{a t} \sin (t),y(t)\to c_1 e^{a t} \sin (t)+c_2 e^{a t} \cos (t)\right \}\right \} \]
Maple: cpu = 0.031 (sec), leaf count = 37 \[ \left \{ \left \{ x \left ( t \right ) ={{\rm e}^{at}} \left ( {\it \_C1} \,\sin \left ( t \right ) +{\it \_C2}\,\cos \left ( t \right ) \right ) ,y \left ( t \right ) ={{\rm e}^{at}} \left ( \sin \left ( t \right ) {\it \_C2}-\cos \left ( t \right ) {\it \_C1} \right ) \right \} \right \} \]