   Chapter 6.1, Problem 93E

Chapter
Section
Textbook Problem

Think About It It is known that y = A sin ω t is a solution of the differential equation y ″ + 16 y = 0 . Find the value(s) of ω .

To determine

To Calculate: The value(s) of ω for the differential equation y+16y=0.

Explanation

Given: y=Asinωt is a solution of the differential equation y+16y=0.

Formula Used:

ddtsinωt=ωcosωt

ddtcosωt=ωsinωt

Calculation:

Differentiating the solution y=Asinωt with respect to t, we get

y=Aωcosωt.........

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