Explanation Given: The given differential equation is, ( x 2 − x ) y ″ + x y ′ + 7 y = 0 . Approach: A singular point x 0 of y ″ ( x ) + p ( x ) y ′ ( x ) + q ( x ) y ( x ) = 0 is a regular singular point if both ( x − x 0 ) p ( x ) and ( x − x 0 ) 2 q ( x ) are analytic at x 0 .otherwise the point is irregular singular point. If a function is defined at a point x 0 , then it is analytic at the point x 0 . Calculation: Compare the given equation with the standard form to get, p ( x ) = x x 2 − x q ( x ) = 7 x 2 − x The singular points are 1 and 0 . At x 0 = 1 ( x − x 0 ) p ( x ) = ( x − 1 ) p ( x ) = ( x − 1 ) x x ( x − 1 ) = 1

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 8.6, Problem 8E

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Whether the given differential equation has a regular singular point or an irregular singular point.

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Chapter 8.6, Problem 7E

Chapter 8.6, Problem 9E

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To state: Whether the given differential equation has a regular singular point or an irregular singular point.

Solution Summary: The author analyzes whether the given differential equation has a regular or irregular singular point.