Explanation Given: Given differential equation is ( x 2 + x ) y ″ + 3 y ′ − 6 x y = 0 . Approach: A point x 0 is said to be a singular point of an equation if x 0 is not an ordinary point. An equation has ordinary point x 0 if p ( x ) and q ( x ) of the equation y ″ + p ( x ) y ′ + q ( x ) y = 0 are analytic at x 0 . Calculation: Consider the given problem. ( x 2 + x ) y ″ + 3 y ′ − 6 x y = 0 …… (1) Divide the equation (1) by ( x 2 + x ) . y ″ + 3 ( x 2 + x ) y ′ − 6 ( x 2 + x ) x y = 0 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 8.3, Problem 4E

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All the singular points of the given differential equation.

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Fundamentals of Differential Equations and Boundary Value Problems

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All the singular points of the given differential equation.

Solution Summary: The author explains that the singular point of the given differential equation is at x=0,-1.

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