Explanation Given: The differential equation is ( 1 − 2 sin x ) y ″ + x y = 0 . Concept used: The linear differential equation is represented as follows: y ″ + P ( x ) y ' + Q ( x ) y = 0 At point x = x 0 is an ordinary point if both P ( x ) and Q ( x ) are both analytic at x 0 . If a point in not ordinary it is a singular point. A singular point x = x 0 is said to be regular singular point of the above differential equation if the function p ( x ) = ( x − x 0 ) P ( x ) and q ( x ) = ( x − x 0 ) 2 Q ( x ) are both analytic at x 0 . A singular point that is not regular is said to be an irregular singular point of the equation. Calculation: Consider the differential equation ( 1 − 2 sin x ) y ″ + x y = 0

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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The lower bound for the radius of convergence of power series solutions about the ordinary point x=0 for the differential equation.

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The lower bound for the radius of convergence of power series solutions about the ordinary point x = 0 for the differential equation.

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