Chapter 6.4, Problem 51E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
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,

ycosxâˆ’cosx+dydx=0 â€¦â€¦ (1)

Calculation:

Rearrange the equation as follows:

dydx+ycosx=cosx

The general solution is of the form:

y(x)=âˆ«eâˆ«P(x)dxQ(x)+ceâˆ«P(x)dx ..â€¦.. (2)

From the rearranged equation above,

P(x)=cosx,Â Q(x)=cosx

Therefore,

eâˆ«P(x)dx=eâˆ«(cosx)dx=esinx<

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