Chapter 17.2, Problem 15E

### 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.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,

yâ€³âˆ’3yâ€²+2y=ex+sinx (1)

Consider the auxiliary equation is,

r2âˆ’3r+2=0 (2)

Roots of equation (2) are,

r=âˆ’(âˆ’3)Â±(âˆ’3)2âˆ’4(1)(2)2(1)â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰{âˆµr=âˆ’bÂ±b2âˆ’4ac2aforâ€‰theâ€‰equationâ€‰ofar2+br+c=0â€‰â€‰}=3Â±12=2â€‰andâ€‰1

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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