Solution: In 1 through 6 you are given a homogeneous system of firstorder linear

QUESTION:

In 1 through 6 you are given a homogeneous system of firstorder linear differential equations and two vector-valued functions, x(1) and x(2) . a. Show that the given functions are solutions of the given system of differential equations. b. Show that x = c1x(1) + c2x(2) is also a solution of the given system for any values of c1 and c2. c. Show that the given functions form a fundamental set of solutions of the given system. d. Find the solution of the given system that satisfies the initial condition x(0) = (1, 2) T . e. Find Wx(1) , x(2) (t). f. Show that the Wronskian, W = Wx(1) , x(2) , found in e is a solution of Abels equation: W = ( p11(t) + p22(t))W.tx_ = _3 2 2 2 _ x (t > 0); x(1) = _12 _t1, x(2) = _21 _t2