   Chapter 6.4, Problem 51E

Chapter
Section
Textbook Problem

Solving s First-Order Differential Equation In Exercises 49-56, find the general solution of the find-order differential equation for x > 0 by any appropriate method. y cos x − cos x = d y d x = 0

To determine

To calculate: The general solution of the first-order differential equation ycosxcosx+dydx=0.

Explanation

Given:

The differential equation,

ycosxcosx+dydx=0 …… (1)

Calculation:

Rearrange the equation as follows:

dydx+ycosx=cosx

The general solution is of the form:

y(x)=eP(x)dxQ(x)+ceP(x)dx ..….. (2)

From the rearranged equation above,

P(x)=cosx, Q(x)=cosx

Therefore,

eP(x)dx=e(cosx)dx=esinx<

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