   Chapter 6.4, Problem 39E

Chapter
Section
Textbook Problem

Using an Integrating Factor The expression u(x) is an integrating factor for y ' + P ( x ) y = Q ( x ) . Which of the following is equal to u ' ( x ) ? Verify your answer.(a) P ( x ) u ( x ) (b) P ' ( x ) u ( x ) (c) Q ( x ) u ( x ) (d) Q ' ( x ) u ( x )

To determine

To calculate: The expression equivalent to u(x), where u(x) is the integrating factor for the differential equation y+P(x)y=Q(x). The expressions in the options are:

(a)P(x)u(x)

(b)P(x)u(x)

(c)Q(x)u(x)

(d)Q(x)u(x)

Explanation

Given:

The granted differential equation is,

y+P(x)y=Q(x) …… (1)

The expressions in the options are:

(a)P(x)u(x)

(b)P(x)u(x)

(c)Q(x)u(x)

(d)Q(x)u(x)

Formula used:

The integrating factor is:

u(x)=P(x)eP(x)dx

The differentiation of

(p

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