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11th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781337275378

Chapter 16.4, Problem 7E

Textbook Problem

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Finding Terms of a Power Series SolutionIn Exercises 7 and 8, the solution of the differential equation is a sum of two power series. Find the first three terms of each power series. (See Example 2.)

To determine

**To calculate:** The solution of the differential equation

**Given information:**

The given differential equation is

**Concept Used:**

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

**Calculation:**

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*+2 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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