Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 17 - Section 17.2 - Nonhomogeneous Linear Equations - 17.2 Exercise - Page 1167: 5



Work Step by Step

$y''-4y'+5y=e^{-x}$ $r^{2}-4r+5=0$ $r=2+i$ $y=Ae^{-x}$ $y'=-Ae^{-x}$ $y''=Ae^{-x}$ $Ae^{-x}-4(-Ae^{-x})+5Ae^{-x}=e^{-x}$ $A=\frac{1}{10}$ $y=e^{2x}(c_{1}cos(x)+c_{2}sin(x))+\frac{1}{10}e^{-x}$
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