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CalculusMultivariable Calculus11th Edition
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True or False? In exercises 67-70, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. It is possible to choose a and b such that y = x 2 e x is a solution of y ' ' + a y ' + b y = 0 .

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Multivariable Calculus

11th Edition
Ron Larson + 1 other
Publisher: Cengage Learning
ISBN: 9781337275378

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Multivariable Calculus

11th Edition
Ron Larson + 1 other
Publisher: Cengage Learning
ISBN: 9781337275378
Chapter 16.2, Problem 70E
Textbook Problem
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True or False? In exercises 67-70, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

It is possible to choose a and b such that y = x 2 e x is a solution of y ' ' + a y ' + b y = 0 .

To determine

Whether the giving statement “It is possible to choose a and b such that y=x2ex is a solution of y''+ay'+by=0”. If false, explain why or given an example that shows it is false.

Explanation of Solution

Given information:

The given statement is “It is possible to choose a and b such that y=x2ex is a solution of y''+ay'+by=0”.

Differentiate y with respect to x, we get

y'=2xex+x2ex

Again, Differentiate y' with respect to x, we get

y''=2ex+2xex+2xex+x2ex

Now, substitute the value of y and y', we get

2ex+2xex+2xex+x2ex+a(2xex

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