Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 6 - Differential Equations - 6.1 Exercises - Page 403: 16


The function is a solution to the differential equation.

Work Step by Step

Begin by solving for the 4th derivative of y. $y=3sin(2x)$ $y'=6cos(2x)$ $y''=-12sin(2x)$ $y'''= -24cos(2x)$ $y^{(4)} = 48sin(2x)$ Now substitute back into the differential equation $48sin(2x) - 48sin(2x)=0$ $0=0$ Since both sides are equal, the function is a solution of the differential equation.
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