Detailed solution

(16 points) (CILO 2, 3, 4) Determine the Laplace Transform of the following: (a) eatsin (wt + 1/6) (b) te-[cos2 (t) - sin?(t)] (Additional Points) Name and write the equation used to solve item (a) (16 points) (CILO 1, 2, 3, 4) Determine the Inverse Laplace Transform of the following: 1 52 +75-4 (a) S($2-1) (b) (5-2) (52+4) (21 points) (CILO 1, 2, 3, 4) Determine the solution of the differential equation using Laplace and Inverse Laplace Transforms x"(t) + 9x(t) = 5sin (2t) when t = 0, x = 3, x' = 1 (Additional Points) Name the technique/s used to solve the inverse Laplace Transform of this differential equation