   Chapter 17, Problem 3RE

Chapter
Section
Textbook Problem

Solve the differential equation.3.  y" + 3y =0

To determine

To solve: The differential equation y+3y=0 .

Explanation

Given data:

The given differential equation is,

y+3y=0 (1)

Formula used:

Write the expression of a 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 the complex roots.

r=α±iβ (4)

Here,

α is the real part of the root, and

β is the imaginary part of the root.

Write the expression for general solution of ay+by+cy=0 with complex roots.

y=eαx(c1cosβx+c2sinβx) (5)

Compare equations (1) and (2).

a=1b=0c=3

Substitute 1 for a, 0 for b, and 3 for c in equation (3),

(1)r2+(0)r+(3)=0r2+3=0r2=3

r=±i3 (6)

Compare equations (4) and (6)

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