(1) In this problem you will justify the reduction of order. Consider the problem (*) ay"+by+cy = f(x) (a) Suppose that

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1 In This Problem You Will Justify The Reduction Of Order Consider The Problem Ay By Cy F X A Suppose That 1 (50.95 KiB) Viewed 28 times

(1) In this problem you will justify the reduction of order. Consider the problem (*) ay"+by+cy = f(x) (a) Suppose that y₁ solve the homogeneous problem ay"+by+cy=0 Assume that y = uy₁ is the solution to (*) and show that it can be rewritten in the form P(x)u" + Q(x)u' = f(x) Where P(x) = ay₁ and Q(x) = 2ay₁ +by₁. (b) Set u' (c) Attempt to solve the problem = v and show that the result is a linear first order equation w.r.t v. y" - 2y + y = e Using the method of undetermined coefficients. Explain why this method doesn't work. (d) Apply the reduction of order to the problem in (c) and find a solution.