   Chapter 17, Problem 4RE

Chapter
Section
Textbook Problem

Solve the differential equation.4.  y" + 8y' + 16y =0

To determine

To solve: The differential equation of y+8y+16y=0 .

Explanation

Given data:

The differential equation is,

y+8y+16y=0 (1)

Formula used:

Write the general expression for second order differential equation.

ay+by+cy=0 (2)

Write the expression for a second order auxiliary equation.

ar2+br+c=0 (3)

Write the expression for general solution of ay+by+cy=0 with two same real roots r .

y=c1erx+c2xerx (4)

Here,

r is the root of auxiliary equation.

Compare equations (1) and (2).

a=1b=8c=16

Substitute 1 for a, 8 for b, and 16 for c in equation (3),

(1)r2+(8)r+(16)=0r2+8r+16=0(r+4)2=0

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