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In this problem we deal with the question of uniqueness of

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

Solution for problem 19 Chapter 2.8

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 19

In this problem we deal with the question of uniqueness of the solution of the integralequation (3)(t) =t0f[s, (s)] ds.(a) Suppose that and are two solutions of Eq. (3). Show that, for t 0,(t) (t) =t0{f[s, (s)] f[s, (s)]} ds.(b) Show that|(t) (t)| t0|f[s, (s)] f[s, (s)]| ds.(c) Use the result of to show that|(t) (t)| Kt0|(s) (s)| ds,where K is an upper bound for |f /y| in D. This is the same as Eq. (30), and the rest ofthe proof may be constructed as indicated in the text.2.

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Chapter 2.8, Problem 19 is Solved
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Textbook: Elementary Differential Equations and Boundary Value Problems
Edition: 10
Author: William E. Boyce
ISBN: 9780470458310

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In this problem we deal with the question of uniqueness of