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: 9

Answer

$y=e^{2x}(c_{1}cos3x+c_{2}sin3x)$

Work Step by Step

$y''-4y'+13y=0$ Use auxiliary equation $r^{2}-4r+13=0$ $r^{2}-4r+13=0$ $r=\frac{-(-4)\sqrt ((-4)^{2}-4(1)(13))}{2(1)}$ $r=\frac{4±\sqrt (16-52)}{2}$ $r=\frac{4±\sqrt (-36)}{2}$ $r=\frac{4±6i}{2}$ $r= 2±3i$ $r_{1}=2-3i$ $r_{2}=2+3i$ $α=2$, $β=3$ Formula 11 $y=e^{αx}(c_{1}cosβx+c_{2}sinβx)$ $y=e^{2x}(c_{1}cos3x+c_{2}sin3x)$
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