In all the exercises, show your working and give your final answer correct to four decimal places if required. 1. Using Laplace transforms, solve for x only in the following pair of simultaneous differential equations [8] dy 22- y+x+ dt dx - sin t = 0 dt dy 3 +x-y+2 -e = 0 dx dt dt given that x(0) = y(0) = 0. 2. Given f(x) = -x if -1