Chapter 17.1, Problem 10E

### 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.10. 3y" + 4y' – 3y = 0

To determine

To solve: The differential equation of 3y+4y3y=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 different 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€²âˆ’3y=0 (4)

Compare equation (1) and (4).

a=3b=4c=âˆ’3

Find the auxiliary equation.

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

(3)r2+(4)r+(âˆ’3)=03r2+4râˆ’3=0

Find the value of r

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