\[ \boxed { \left \{ {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) =ay \left ( t \right ) ,{\frac {\rm d}{{\rm d}t}}y \left ( t \right ) =-ax \left ( t \right ) \right \} } \]
Mathematica: cpu = 0.039505 (sec), leaf count = 39 \[ \left \{\left \{x(t)\to c_2 \sin (a t)+c_1 \cos (a t),y(t)\to c_2 \cos (a t)-c_1 \sin (a t)\right \}\right \} \]
Maple: cpu = 0.047 (sec), leaf count = 35 \[ \left \{ \left \{ x \left ( t \right ) ={\it \_C1}\,\sin \left ( at \right ) +{\it \_C2}\,\cos \left ( at \right ) ,y \left ( t \right ) =\cos \left ( at \right ) {\it \_C1}-\sin \left ( at \right ) {\it \_C2} \right \} \right \} \]