You are given a homogeneous system of first-order linear differential equations and two vector-valued functions, 1)...

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You are given a homogeneous system of first-order linear differential equations and two vector-valued functions, 1) and 2). a. Show that the given functions are solutions of the given system of differential equations. b. Show that i = cx(1) + C2x(2) is also a solution of the given system for any values of c 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)". %3D e. Find W[1) (2](t). f. Show that the Wronskian, W[x(1) (2)](t), found in e is a solution of Abel's equation: W' = (P11(t) + P22(t))W. i' = ( -3t *(2) 2t %3D %3D You are given a homogeneous system of first-order linear differential equations and two vector-valued functions, 1) and 2). a. Show that the given functions are solutions of the given system of differential equations. b. Show that i = cx(1) + C2x(2) is also a solution of the given system for any values of c 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)". %3D e. Find W[1) (2](t). f. Show that the Wronskian, W[x(1) (2)](t), found in e is a solution of Abel's equation: W' = (P11(t) + P22(t))W. i' = ( -3t *(2) 2t %3D %3D

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