Chapter 17.1, Problem 5E

### Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

Chapter
Section

### Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

# Solve the differential equation.5. 4y" + 4y' + y = 0

To determine

To solve: The differential equation of 4y+4y+y=0 .

Explanation

Formula used:

Write the expression for differential equation.

ayâ€³+byâ€²+cy=0 (1)

Write the expression for auxiliary equation.

ar2+br+c=0 (2)

Write the expression for general solution of ayâ€³+byâ€²+cy=0 with two same real roots r .

y=c1erx+c2xerx (3)

Here,

r is the root of auxiliary equation.

Consider the differential equation as follows.

4yâ€³+4yâ€²+y=0 (4)

Compare equation (1) and equation (4).

a=4b=4c=1

Find the auxiliary equation.

Substitute 4 for a , 4 for b and 1 for c in equation (2),

(4)r2+(4)r+(1)=04r2+4r+1=0

Re-write equation as follows

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