We are given the following homogenous differential equation and pair of solutions on the given interval. xy" - 7xy + 15SY = 0; x,x, (0, o) We are asked to verify that the solutions are linearly independent. That is, there do not exist constants c, and ca, not both zero, such that c,x + c,x = 0. While this may be clear for these solu that are different powers of x, we have a formal test to verify the linear independence. Recall the definition of the Wronskian for the case of two functions f, and far each of which have a first derivative. W(f, f) = By Theorem 4.1.3, if W(f, f,) = 0 for every x in the interval of the solution, then solutions are linearly independent. Let f, (x) = x and f,(x) - x. Complete the Wronskian for these functions. W(x, x) - 3x

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