\[ \left \{x'(t)=a x(t)-y(t),y'(t)=a y(t)+x(t)\right \} \] ✓ Mathematica : cpu = 0.0044125 (sec), leaf count = 51
DSolve[{Derivative[1][x][t] == a*x[t] - y[t], Derivative[1][y][t] == x[t] + a*y[t]},{x[t], y[t]},t]
\[\left \{\left \{x(t)\to c_1 e^{a t} \cos (t)-c_2 e^{a t} \sin (t),y(t)\to c_2 e^{a t} \cos (t)+c_1 e^{a t} \sin (t)\right \}\right \}\] ✓ Maple : cpu = 0.047 (sec), leaf count = 37
dsolve({diff(x(t),t) = a*x(t)-y(t), diff(y(t),t) = x(t)+a*y(t)})
\[\{x \left (t \right ) = {\mathrm e}^{a t} \left (c_{1} \sin \left (t \right )+c_{2} \cos \left (t \right )\right ), y \left (t \right ) = {\mathrm e}^{a t} \left (\sin \left (t \right ) c_{2}-\cos \left (t \right ) c_{1}\right )\}\]