Solve by using Laplace transforms dx/dt - 2y = cos2t, dy/dt + 2x = sin2t, x = 1, y = 0, at t = 0.
We have a system of equations,
x′ (t) – 2y (t) = cos 2t ...(1)
2x (t) + y′ (t) = sin 2t ...(2)
where we have x (0) = 1 and y (0) = 0
Taking Laplace transforms on both sides of Eqns. (1) and (2), we have
