   Chapter 17.2, Problem 15E

Chapter
Section
Textbook Problem

Write a trial solution for the method of undetermined coefficients. Do not determine the coefficients.15. y" – 3y' + 2y = ex + sin x

To determine

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

Explanation

Given data:

The differential equation is,

y3y+2y=ex+sinx (1)

Consider the auxiliary equation is,

r23r+2=0 (2)

Roots of equation (2) are,

r=(3)±(3)24(1)(2)2(1){r=b±b24ac2afortheequationofar2+br+c=0}=3±12=2and1

Write the expression for the complementary solution for two real roots,

yc(x)=c1er1x+c2er2x

Substitute 2 for r1 and 1 for r2 ,

yc(x)=c

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