Use the Laplace transform to solve the following initial value problem: x = 7x + 2y, y = -5x+ e2t x(0) = 0, y(0) = 0 Let X(s) = [{x(t)}, and Y(s) = Cty(t) }. Find the expressions you obtain by taking the Laplace transform of both differential equations and solving for Y(s) and X(s): X( s) = Y(s) = Find the partial fraction decomposition of X(s) and Y(s) and their inverse Laplace transforms to find the solution of the system of DEs: x(t) = y( t) =