Chapter 17.2, Problem 13E

### Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

Chapter
Section

### Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

# Write a trial solution for the method of undetermined coefficients. Do not determine the coefficients.13. y" – y' – 2y = xex cos x

To determine

To write: The trail solution for the method of undetermined coefficients.

Explanation

Given data:

The differential equation is,

yâ€³+yâ€²âˆ’2y=xexcosx (1)

Consider the auxiliary equation.

r2+râˆ’2=0(r+2)(râˆ’1)=0(r+2)=0,(râˆ’1)=0r=âˆ’2,1

Write the expression for the complementary solution for two distinct real roots.

yc(x)=c1er1x+c2er2x

Substitute âˆ’2 for r1 and 1 for r2 ,

yc(x)=c1eâˆ’2x+c2ex

If Right hand side (RHS) of a differential equation contains a product of an exponential function, a cosine function, and nth order polynomial, the trail solution of the differential equation also should be a product of these corresponding choices. So, the trail solution for this case can be expressed as follows

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Rationalize Numerator Rationalize the numerator. 91. 153

Precalculus: Mathematics for Calculus (Standalone Book)

#### Evaluate the integral. 04(4t)tdt

Single Variable Calculus: Early Transcendentals, Volume I

#### 84/3

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### Evaluate the integrals in Problems 1-11. 11.

Mathematical Applications for the Management, Life, and Social Sciences

#### Given the Taylor Series , a Taylor series for ex/2 is:

Study Guide for Stewart's Multivariable Calculus, 8th

#### The area of the shaded region is given by:

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