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

Chapter 7, Problem 2

(choose chapter or problem)

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.x_ = _1 1 4 2 _ x; x(1) = _ 1 4 _e3t , x(2) = _11 _e2t