(a) Show that e4t x Y are solutions of the homogeneous system dx dt dt e4t and X Y Y = of this system for which x(0) = 5 and y(0) = 1. || || x + 3y 3x+y. (b) Show in two ways that the given solutions of the system in part (a) are linearly independent on every closed interval, and write the general solution of this system. (c) Find the particular solution x(t) y(t) e-2t -e-2t