Chapter 17, Problem 1RE

### 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.1. 4y" – y =0

To determine

To solve: The differential equation of 4yy=0 .

Explanation

Given data:

The differential equation is,

4yâ€³âˆ’y=0 (1)

Formula used:

Write the expression for a second order differential equation.

ayâ€³+byâ€²+cy=0 (2)

Write the expression for a second order auxiliary equation.

ar2+br+c=0 (3)

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

y=c1er1x+c2er2x (4)

Here,

r1 and r2 are the roots of the auxiliary equation.

Compare equations (1) and (2).

a=4b=0c=âˆ’1

Substitute 4 for a, 0 for b, and â€“1 for c in equation (3),

(4)r2+(0)r+(âˆ’1)=0

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