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11th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781337275378

Chapter 16, Problem 17PS

Textbook Problem

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**Bessel’s Equation: Order Zero** The differential equation

is known as Bessel’s equation of order zero.

Use a power series of the form

to find the solution.

Compare your result with that of the function

**(a)**

To determine

**To calculate:** The solution of the Bessel’s equation

**Given information:**

The given differential equation is

**Concept Used:**

Power series is defined as an infinite series of the form,

**Calculation:**

Assume

Let the general form of the Bessel’s equation of * n* order is,

On comparing the above equation, we get

Therefore, the order of the equation is zero.

Assume

Now, the given Bessel’s equation is,

Inserting the value of

The solution of the general equation

**(b)**

To determine

Compare the resultobtained from the function

Multivariable Calculus

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