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: 18

Answer

The function is not a solution of the differential equation.

Work Step by Step

Begin by solving for the 4th derivative of y. $y= 5\ln{x}$ $y'= \frac{5}{x}$ $y''=- \frac{5}{x^2}$ $y'''= \frac{10}{x^3}$ $y^{(4)}= -\frac{30}{x^4}$ Substitute back into the differential eqution. $y^{(4)} -16y=0$ $-\frac{30}{x^4} -80\ln{x} \ne 0$ Since both sides are not equal, the function is not a solution of the differential equation.
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