Solve the following ODEs using Laplace transforms: (a) y(i) + 2(1)-y(t)-2y(t) = 0 given y(0) = y(0) = 0 and (0) = 6 (b) y(t) + 4y(1) + 4y(t) = e' given y(0) = y(0) = 0 (c) (1) - 2y(t) + y(t) = e2t given y(0) = y(0) = -1 (d) () +2y(t) + y(t) = 3te given y(0) = 4, y(0) = 2 (e) (1) + 2y(1) + 2y(t) = 5 sin t given y(0) = y(0) = 0 (f) (1) + 6y(1) +9y(t) = 1212e-31 given y(0) = y(0) = 0