   Chapter 17.2, Problem 17E

Chapter
Section
Textbook Problem

Write a trial solution for the method of undetermined coefficients. Do not determine the coefficients.17. y" + 2y' + 10y = x2e-x cos 3x

To determine

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

Explanation

Given data:

The differential equation is,

y+2y+10y=x2excos3x (1)

Consider the auxiliary equation is,

r2+2r+10=0 (2)

Roots of equation (2) are,

r=(2)±(2)24(1)(10)2(1){r=b±b24ac2afortheequationofar2+br+c=0}=2±i62=1±i3

Write the expression for the complementary solution for the complex roots,

yc(x)=eαx(c1cosβx+c2sinβx)

Substitute 1 for α and 3 for β ,

yc(x)=e1x(c1cos3x+c2sin3x)=ex(c1cos3x+c2sin3x)

Since G(x)=x2excos3x is a polynomial degree of 2.

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 yp(x) for this case can be expressed as follows.

y(x)=(Axn+Bxn1+Z)excos3x+(A1xn+B1xn1+Z1)exsin3x (3)

Here,

n is the order of a polynomial, and

A,B,Z,A1,B1,Z1, are the constants

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

Prove the identity. 56. tanx+tany=sin(x+y)cosxcosy

Single Variable Calculus: Early Transcendentals, Volume I

The difference between population variance and sample variance.

Statistics for The Behavioral Sciences (MindTap Course List)

Differentiate the function. B(y) = cy6

Single Variable Calculus: Early Transcendentals

True or False: If , then converge absolutely.

Study Guide for Stewart's Multivariable Calculus, 8th 