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Get Full Access to Elementary Differential Equations And Boundary Value Problems - 10 Edition - Chapter 2.8 - Problem 19
Get Full Access to Elementary Differential Equations And Boundary Value Problems - 10 Edition - Chapter 2.8 - Problem 19

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# In this problem we deal with the question of uniqueness of ISBN: 9780470458310 168

## Solution for problem 19 Chapter 2.8

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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##### ISBN: 9780470458310

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