Chapter 17.1, Problem 11E

### 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.11. 2   d 2 y d t 2 +   2 d y d t   −   y   =   0

To determine

To solve: The differential equation of 2d2ydt2+2dydty=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 auxiliary equation.

Consider the differential equation as follows.

2d2ydt2+2dydtâˆ’y=0 (4)

Compare equation (1) and (4).

a=2b=2c=âˆ’1

Find the auxiliary equation.

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

(2)r2+(2)r+(âˆ’1)=02r2+2râˆ’1=0

Find the value of r

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