   Chapter 6.4, Problem 7E

Chapter
Section
Textbook Problem

Solving a First-Order Linear Differential Equation In Exercises 7-14, find the general solution of the first-order linear differential equation for x > 0 d y d x + ( 1 x ) y = 6 x + 2

To determine

To calculate: The general solution of the provided first order linear differential equation dydx+(1x)y=6x+2.

Explanation

Given:

The first order linear differential equation is;

dydx+(1x)y=6x+2

Formula used:

The general solution is of first order linear differential equation is y(x)eP(x)dx=eP(x)dxQ(x)+c where P(x),Q(x) are functions and c is a constant value.

Calculation:

The first order linear differential equation is;

dydx+(1x)y=6x+2

From the above differential equation,

P(x)=1xQ(x)=6x+2

The general solution is of first order linear differential equation is y(x)eP(x)dx=eP(x)dxQ(x)+c where P(x),Q(x) are functions and c is a constant value

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