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8th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781285741550

Chapter 9.1, Problem 3E

Textbook Problem

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(a) For what values of *r* does the function *y* = *e ^{rx}* satisfy the differential equation 2

(b) If *r*_{1} and *r*_{2} are the values of *r* that you found in part (a), show that every member of the family of functions

(a)

To determine

**To find:** The values of *r* when the function

**Given:**

The function is

The differential equation is

**Calculation:**

Obtain the values of *r* when the function

Differentiate the function *y* with respect to *x*,

Thus,

Differentiate the function
*x*,

Thus,

Since the function

Substitute the values of
*r* as follows,

(b)

To determine

**To show:** Every member of the family of functions

Calculus: Early Transcendentals

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