1. Using Laplace transforms, solve for x only in the following pair of simultaneous differential equations dy 2 -y+x+ dt dx sin t = 0 dt dx dy 3. +x-y+ 2 dt dt given that x(0) = y(0) = 0. 2. Given f(x) = -x if -1 < x < 1 and f(x) = f(x + 2). %3D %3D (a) Find the trigonometric Fourier series for f(x). Expand the series up to the fourth harmonic. (b) Let x = 1/2 and deduce a series for a/4. Present your final answer using the Sigma notation. %3D 3. Given -A SI