Elementary Differential Equations and Boundary Value Problems 9th Edition

Published by Wiley
ISBN 10: 0-47038-334-8
ISBN 13: 978-0-47038-334-6

Chapter 4 - Higher Order Linear Equations - 4.3 The Method of Undetermined Coefficients - Problems - Page 238: 20


See solution.

Work Step by Step

$(D-a)(D-b)f=(D-a)\{{f}'-bf\}$ $(D-a)(D-b)f={f}''-b{f}'-af'+abf$ $(D-a)(D-b)f={f}''-(b+a){f}'+abf \;\;\;\;\;\;\;\;\;(1)$ $R.H.S=(D-b)(D-a)f=(D-b)\{{f}'-af\}$ $(D-b)(D-a)f={f}''-a{f}'-b{f}'+abf$ $(D-b)(D-a)f={f}''-(a+b){f}'+abf \;\;\;\;\;\;\;\;\;\;(2)$ So, $L.H.S=R.H.S$
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