Chapter 17, Problem 2RE

### 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.2.  2y" – 2y' + 10y =0

To determine

To solve: The differential equation of y2y+10y=0 .

Explanation

Given data:

The differential equation is,

yâ€³âˆ’2yâ€²+10y=0 (1)

Formula used:

Write the expression of a second order differential equation.

ayâ€³+byâ€²+cy=0 (2)

Write the expression for a second order auxiliary equation.

ar2+br+c=0 (3)

Write the expression for the complex roots.

r=Î±Â±iÎ² (4)

Here,

Î± is the real part of the root, and

Î² is the imaginary part of the root.

Write the expression for general solution of ayâ€³+byâ€²+cy=0 with complex roots.

y=eÎ±x(c1cosÎ²x+c2sinÎ²x) (5)

Write the expression to find the roots of quadratic equation.

r=âˆ’bÂ±b2âˆ’4ac2a (6)

Compare equations (1) and (2).

a=1b=âˆ’2c=10

Substitute 1 for a, â€“2 for b, and 10 for c in equation (3),

(1)r2+(âˆ’2)r+(10)=0r2âˆ’2r+10=0

Find the roots of auxiliary equation using equation (6)

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