\[ \left \{-\text {A0} y'(t)+\text {a1} x''(t)+\text {b1} x'(t)+\text {c1} x(t)=\text {B0} e^{i \omega t},\text {A0} x'(t)+\text {a2} y''(t)+\text {b2} y'(t)+\text {c2} y(t)=0\right \} \] ✓ Mathematica : cpu = 0.404543 (sec), leaf count = 5546
DSolve[{c1*x[t] + b1*Derivative[1][x][t] - A0*Derivative[1][y][t] + a1*Derivative[2][x][t] == B0*E^(I*omega*t), c2*y[t] + A0*Derivative[1][x][t] + b2*Derivative[1][y][t] + a2*Derivative[2][y][t] == 0},{x[t], y[t]},t]
\[\text {Expression too large to display}\]
✓ Maple : cpu = 0.855 (sec), leaf count = 1579
dsolve({a1*diff(diff(x(t),t),t)+b1*diff(x(t),t)+c1*x(t)-A*diff(y(t),t) = B*exp(I*omega*t), a2*diff(diff(y(t),t),t)+b2*diff(y(t),t)+c2*y(t)+A*diff(x(t),t) = 0})
\[\text {Expression too large to display}\]