   Chapter 17.2, Problem 16E

Chapter
Section
Textbook Problem

Write a trial solution for the method of undetermined coefficients. Do not determine the coefficients.16. y" + 3y' – 4y = (x3 + x)ex

To determine

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

Explanation

Given data:

The differential equation is,

y+3y4y=(x3+x)ex (1)

Consider the auxiliary equation is,

r2+3r4=0 (2)

Roots of equation (2) are,

r=(3)±(3)24(1)(4)2(1){r=b±b24ac2afortheequationofar2+br+c=0}=3±52=1and4

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

yc(x)<

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