Chapter 17.1, Problem 1E

### 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. y" – y' – 6y = 0

To determine

To solve: The differential equation of yy6y=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 distinct real roots.

y=c1er1x+c2er2x (3)

Here,

r1 and r2 are the roots of the auxiliary equation.

Write the expression to find the roots of quadratic equation.

r1=âˆ’b+b2âˆ’4ac2a (4)

r2=âˆ’bâˆ’b2âˆ’4ac2a (5)

Consider the differential equation as follows.

yâ€³âˆ’yâ€²âˆ’6y=0 (6)

Compare equation (1) and (6).

a=1b=âˆ’1c=âˆ’6

Find the auxiliary equation.

Substitute 1 for a , âˆ’1 for b and âˆ’6 for c in equation (2),

(1)r2+(âˆ’1)r+(âˆ’6)=0r2âˆ’râˆ’6=0

Find the value of r1 using equation (4)

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Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th