Explanation Given: Given differential equation is y ″ − ( tan x ) y ′ + y = 0 ; x 0 = 0 . Approach: The radius of convergence of any power series solution is the minimum distance from a point x 0 to the nearest singular point of a differential equation y ″ ( x ) + p ( x ) y ′ ( x ) + q ( x ) y ( x ) = 0 . It is given by formula y ( x ) = ∑ n = 0 ∞ a n ( x − x 0 ) n . Calculation: Consider the given problem. y ″ − ( tan x ) y ′ + y = 0 ; x 0 = 0 ... ( 1 ) Separate p ( x ) and q ( x ) from above equation

Fundamentals of Differential Equations and Boundary Value Problems

7th Edition

ISBN: 9780321977106

Author: Nagle, R. Kent

Publisher: Pearson Education, Limited

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Chapter 8.4, Problem 5E

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The minimum value for the radius of convergence of the power series solution of a differential equation about x0.

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Chapter 8.4, Problem 4E

Chapter 8.4, Problem 6E

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The minimum value for the radius of convergence of the power series solution of a differential equation about x 0 .

Solution Summary: The author explains the minimum value of the radius of convergence of a power series solution about x_0.

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To find:

The minimum value for the radius of convergence of the power series solution of a differential equation about x0.

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Chapter 8 Solutions

The minimum value for the radius of convergence of the power series solution of a differential equation about x 0 .

Solution Summary: The author explains the minimum value of the radius of convergence of a power series solution about x_0.

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To find: The minimum value for the radius of convergence of the power series solution of a differential equation about x0.

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Chapter 8 Solutions

To find:

The minimum value for the radius of convergence of the power series solution of a differential equation about x0.