Chapter 6.4, Problem 54E

### 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 a First-Order Differential Equation In Exercises 49-56, find the general solution of the first-order differentialequation for x > 0 by any appropriate method. ( x + y ) d x − x   d y = 0

To determine

To calculate: The general solution of the first-order differential equation (x+y)dxxdy=0.

Explanation

Given:

The differential equation,

(x+y)dxâˆ’xdy=0 â€¦â€¦ (1)

Calculation:

Rearrange the equation as follows:

(x+y)dxâˆ’xdy=0dydxx=x+ydydxâˆ’yx=1

The general solution is of the form:

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

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