\[ \left \{x'(t)=a y(t),y'(t)=-a x(t)\right \} \] ✓ Mathematica : cpu = 0.0091996 (sec), leaf count = 39
DSolve[{Derivative[1][x][t] == a*y[t], Derivative[1][y][t] == -(a*x[t])},{x[t], y[t]},t]
\[\{\{x(t)\to c_1 \cos (a t)+c_2 \sin (a t),y(t)\to c_2 \cos (a t)-c_1 \sin (a t)\}\}\] ✓ Maple : cpu = 0.039 (sec), leaf count = 35
dsolve({diff(x(t),t) = a*y(t), diff(y(t),t) = -a*x(t)})
\[\{x \left (t \right ) = c_{1} \sin \left (a t \right )+c_{2} \cos \left (a t \right ), y \left (t \right ) = \cos \left (a t \right ) c_{1}-\sin \left (a t \right ) c_{2}\}\]