Elementary Differential Equations and Boundary Value Problems 9th Edition

Published by Wiley
ISBN 10: 0-47038-334-8
ISBN 13: 978-0-47038-334-6

Chapter 3 - Second Order Linear Equations - 3.3 Complex Roots of the Characteristic Equation - Problems - Page 163: 4



Work Step by Step

$e^{2-i(\frac{\pi}{2})} = e^2e^{-i\frac{\pi}{2}}$ Applying Euler's equation to $cos(-\frac{\pi}{2}) + isin(-\frac{\pi}{2}))$ $cos(-\frac{\pi}{2}) = 0, isin(-\frac{\pi}{2}) = - i$ $-ie^2$
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