Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 17 - Second-Order Differential Equations - 17.2 Nonhomogeneous Linear Equations - 17.2 Exercises: 6

Answer

$y=e^{-x}(c_{1}cos(2x)+c_{2}sin(2x))+\frac{1}{5}+\frac{1}{8}e^{x}$

Work Step by Step

$y''+2y'+5y=1+e^x$ $r^2+2r+5=0$ $r=-1+2i$ $y=e^{-x}(c_{1}cos(2x)+c_{2}sin(2x))$ $y=A+Be^x$ $y'=Be^x$ $y''=Be^x$ $Be^x+2Be^x+5A+5Be^x=1+e^x$ $A=\frac{1}{5}$ $B=\frac{1}{8}$ $y=e^{-x}(c_{1}cos(2x)+c_{2}sin(2x))+\frac{1}{5}+\frac{1}{8}e^{x}$
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