Explanation Given that the differential equation is x 2 y ″ − 2 y = 0 . It can be written as x 2 d 2 y d x 2 − 2 y = 0 . Assume y = x m and differentiate it twice as follows. d y d x = m x m − 1 , d 2 y d x 2 = m ( m − 1 ) x m − 2 Substitute y and d 2 y d x 2 into the differential equation yields, x 2 d 2 y d x 2 − 2 y = 0 x 2 [ m ( m − 1 ) x m − 2 ] − 2 x m = 0 On further simplification gives, m x m ( m − 1 ) <

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Differential Equations

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Chapter 3.6, Problem 1E

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To solve: The differential equation x2y″−2y=0.

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Chapter 3.5, Problem 36E

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Chapter 3 Solutions

Advanced Engineering Mathematics

Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E

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The differential equation x 2 y ″ − 2 y = 0 .

Solution Summary: The author explains how to solve the differential equation x2y′′-2y=0.

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Chapter 3 Solutions