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In this problem we outline a different derivation of

Elementary Differential Equations and Boundary Value Problems | 10th Edition | ISBN: 9780470458310 | Authors: William E. Boyce ISBN: 9780470458310 168

Solution for problem 28 Chapter 3.3

Elementary Differential Equations and Boundary Value Problems | 10th Edition

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Elementary Differential Equations and Boundary Value Problems | 10th Edition | ISBN: 9780470458310 | Authors: William E. Boyce

Elementary Differential Equations and Boundary Value Problems | 10th Edition

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Problem 28

In this problem we outline a different derivation of Eulers formula.(a) Show that y1(t) = cost and y2(t) = sin t are a fundamental set of solutions ofy+ y = 0; that is, show that they are solutions and that their Wronskian is not zero.(b) Show (formally) that y = eit is also a solution of y+ y = 0. Therefore,eit = c1 cost + c2 sin t (i)for some constants c1 and c2. Why is this so?(c) Set t = 0 in Eq. (i) to show that c1 = 1.(d) Assuming that Eq. (14) is true, differentiate Eq. (i) and then set t = 0 to conclude thatc2 = i. Use the values of c1 and c2 in Eq. (i) to arrive at Eulers formula.

Step-by-Step Solution:
Step 1 of 3

Lecture 16: Rates of Change & Higher Derivatives (Sections 3.4 & 3.5) Recall the following: Average Rate of Change y = f(x) x1 2 Instantaneous Rate of Change

Step 2 of 3

Chapter 3.3, Problem 28 is Solved
Step 3 of 3

Textbook: Elementary Differential Equations and Boundary Value Problems
Edition: 10
Author: William E. Boyce
ISBN: 9780470458310

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In this problem we outline a different derivation of