Calculus: Early Transcendentals 8th Edition

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

Chapter 17 - Section 17.1 - Second-Order Linear Equations - 17.1 Exercise: 3

Answer

y = $C_1cos(\sqrt 2x)$ + $C_2sin(\sqrt 2x)$

Work Step by Step

Question: y"+2y=0 We know: y = $e^{rx}$ y' = $re^{rx}$ y" = $r^{2}e^{rx}$ This results in $(r^{2}+2)e^{rx}$=0 The corresponding characteristic equation is: $r^{2}+2=0$ Solving the equation with complex numbers gives: $r^{2}=-2$ $r=\frac{+}{-}\sqrt 2 i$ Adding the constants gives the following general solution: y = $C_1cos(\sqrt 2x)$ + $C_2sin(\sqrt 2x)$
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