   Chapter 6.1, Problem 94E

Chapter
Section
Textbook Problem

Think About It It is known that y = e k t is a solution of the differential equation y ″ − 16 y = 0 . Find the value(s) of k.

To determine

To Calculate: The value(s) of k for the differential equation y16y=0.

Explanation

Given: y=ekt is a solution of the differential equation y16y=0.

Formula Used:

ddtekt=kekt

Calculation:

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

dydt=ddtekt

y=kekt..........(1)

Again, differentiating equation (1) with respect to t, we get

ddty=kddtekt

y=k2ekt

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