(c) (10 points) Consider the following non-homogeneous linear system of differential equations (1) where y = (y1 (t), y2(t)) . Let Y denote the vector (Y1(s), Y2(s)) where Yk is the Laplace transform YK = [lyk (t) }(s) for k = 1, 2. By taking the Laplace transform of each component in the differential equation, obtain Y explicitly in terms of s. Hence, by applying the inverse Laplace transform to each component, or otherwise, find the solution to (1) with the initial conditions y (0) = 0