Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 10 - Introduction to Differential Equations - 10.1 Solving Differential Equations - Exercises - Page 504: 8

Answer

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Work Step by Step

Since $ y=e^x \sin 2x $, then $$ y'=e^x\sin 2x+2e^x\cos 2x=e^x(\sin 2x+2\cos 2x), \\ y'' =e^x(\sin 2x+2\cos 2x)+e^x(2\cos 2x-4\sin 2x).$$ Now, by substitution of $ y $, $ y'$ and $ y''$ into the equation, we verify that $ y $ is a solution of the given differential equation.
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