Chapter 17.1, Problem 7E

### 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.7. 3y" = 4y'

To determine

To solve: The differential equation of 3y=4y .

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 distinct real roots.

y=c1er1x+c2er2x (3)

Here,

r1 and r2 are the roots of auxiliary equation.

Consider the differential equation as follows.

3yâ€³=4yâ€²

3yâ€³âˆ’4yâ€²=0 (4)

Compare equation (1) and equation (4).

a=3b=âˆ’4c=0

Find the auxiliary equation.

Substitute 3 for a , âˆ’4 for b and 0 for c in equation (2),

(3)r2+(âˆ’4)r+(0)=03r2âˆ’4r=0r(3râˆ’4)=0

Re-write equation as follows

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