   Chapter 6.4, Problem 53E

Chapter
Section
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. ( 2 y − e x ) d x + x   d y = 0

To determine

To calculate: The expression for the general solution of the first-order differential equation given as, (2yex)dx+xdy=0.

Explanation

Given:

The differential equation as, (2yex)dx+xdy=0.

Formula used:

The formula of integration by parts is given as:

udvdxdx=uvvdudxdx

Calculation:

Rearrange the equation as follows:

(2yex)dx+xdy=0dydxx=ex2ydydx=exx2xydydx+2xy=exx

The general solution is of the form:

y(x)=eP(x)dxQ(x)+ceP(x)dx ..….

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