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 - 17.1 Exercises - Page 1172: 4

Answer

$y=c_{1}e^{2x}+c_{2}e^{6x}$

Work Step by Step

$y''-8y+12y=0$ Use auxiliary equation $r^{2}-8r+12=0$ $r^{2}-8r+12=0$ $(r-2)(r-6)=0$ $r=2,r=6$ By Theorem 4, $y=c_{1}e^{r_{1}x}+c_{2}e^{r_{2}x}$ $y=c_{1}e^{2x}+c_{2}e^{6x}$
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