   Chapter 17.1, Problem 1E

Chapter
Section
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.

ay+by+cy=0 (1)

Write the expression for auxiliary equation.

ar2+br+c=0 (2)

Write the expression for general solution of ay+by+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=b+b24ac2a (4)

r2=bb24ac2a (5)

Consider the differential equation as follows.

yy6y=0 (6)

Compare equation (1) and (6).

a=1b=1c=6

Find the auxiliary equation.

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

(1)r2+(1)r+(6)=0r2r6=0

Find the value of r1 using equation (4)

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