Question

verify that the given functions are solutions of the homogeneous linear systempute the wronskian of the solution set. on the basis of this calculation, can you assert that the set of solutions forms a fundamental set?if the given solutions form a fundamental set, state the general solution of the linear homogeneous system. express the general solution as the product , where is a square matrix whose columns are the solutions forming the fundamental set and c is a column vector of arbitrary constants.if the solutions form a fundamental set, impose the given initial condition and find the unique solution of the initial value problem.

Answer 1

Given functions:

f1(x) = e^2x

f2(x) = e^-x

The homogeneous linear system is:

y' = Ay

where A = [2 -1]

The Wronskian of the solution set is:

W(f1, f2) = e^3x - e^-x

Since the Wronskian is not equal to 0