\[ \left \{x'(t)=a x(t)-y(t),y'(t)=a y(t)+x(t)\right \} \] ✓ Mathematica : cpu = 0.00576963 (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 = 0.035 (sec), leaf count = 38
\[ \left \{ \left \{ x \left ( t \right ) ={{\rm e}^{at}} \left ( {\it \_C2}\,\cos \left ( t \right ) +{\it \_C1}\,\sin \left ( t \right ) \right ) ,y \left ( t \right ) =-{{\rm e}^{at}} \left ( \cos \left ( t \right ) {\it \_C1}-\sin \left ( t \right ) {\it \_C2} \right ) \right \} \right \} \]