   Chapter 17.2, Problem 13E

Chapter
Section
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,

y+y2y=xexcosx (1)

Consider the auxiliary equation.

r2+r2=0(r+2)(r1)=0(r+2)=0,(r1)=0r=2,1

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

yc(x)=c1er1x+c2er2x

Substitute 2 for r1 and 1 for r2 ,

yc(x)=c1e2x+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

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