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11th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781337275378

Chapter 16.4, Problem 15E

Textbook Problem

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EXPLORING CONCEPTS

Using Different MethodsIn Exercises 15-18, verify that the power series solution of the differential equation is equivalent to the solution found using previously learned solution techniques.

To determine

**To verify:** That the solution of the differential equation

**Given information:**

The given differential equation is

**Formula used:**

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

**Proof:**

Assume

Now, the given differential equation is,

Inserting the value of

To obtain equal power of *x*, adjust the summation indices by replacing *n* by *n*+1 in the left hand side sum to obtain,

Equating the coefficients of like terms, one can obtain the recursion formula

Multivariable Calculus

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