Explanation The given differential equation is ( x 2 − 1 ) y ″ + 5 ( x + 1 ) y ′ + ( x 2 − x ) y = 0 . Rewrite the differential equation as follows. y ″ + 5 ( x + 1 ) ( x − 1 ) ( x + 1 ) y ′ + x ( x − 1 ) ( x − 1 ) ( x + 1 ) y = 0 On solving it becomes, y ″ + 5 x − 1 y ′ + x x + 1 y = 0 (1) Consider that if x = x 0 is a regular singular point of the differential equation then multiply the differential equation with ( x − x 0 ) 2 , which yields the differential equation of the form ( x − x 0 ) 2 y ″ + ( x − x 0 ) p ( x ) y ′ + q ( x ) y = 0 (2) So, the regular singular points of the given differential equation are x = 1 , − 1 . Now, for x o = 1 the required differential equation is obtained by multiplying ( x − 1 ) 2 to the differential equation (1), ( x − 1 ) 2 y ″ + 5 ( x − 1 ) 2 x − 1 y ′ + x ( x − 1 ) 2 x + 1 y = 0 ( x − 1 ) 2 y ″ + 5 ( x − 1 )

Student Solutions Manual For Zill's A First Course In Differential Equations With Modeling Applications, 11th

11th Edition

ISBN: 9781305965737

Author: Dennis G. Zill

Publisher: Brooks Cole

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Chapter 6.3, Problem 11E

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To perform: Transformation of the given differential equation to the required form and the identification of indicated functions.

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Chapter 6.3, Problem 10E

Chapter 6.3, Problem 12E

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Student Solutions Manual For Zill's A First Course In Differential Equations With Modeling Applications, 11th

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