Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 17 - Second-Order Differential Equations - Review - Exercises - Page 1193: 8

Answer

$c_1cos2x+c_2sin2x-\frac{1}{4}xcos2x$

Work Step by Step

$y''+4y=sin2x$ which has characteristic equation $t^2+4=0$ with solutions $t=\pm 2i$ Particular solution: $Axcos2x+Bxsin2x$ giving $A=-1/4$ and $B=0$ General solution: $c_1cos2x+c_2sin2x-\frac{1}{4}xcos2x$
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