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The first three positive values of λ for which the problem ( 1 − x 2 ) y ″ − 2 x y ′ + λ y = 0 , y ( 0 ) = 0 , y ( x ) , y ′ ( x ) bounded on [ − 1 , 1 ] has nontrivial solutions.

The first three positive values of λ for which the problem ( 1 − x 2 ) y ″ − 2 x y ′ + λ y = 0 , y ( 0 ) = 0 , y ( x ) , y ′ ( x ) bounded on [ − 1 , 1 ] has nontrivial solutions.

Solution Summary: The author explains the properties of Legendre polynomials: y(0)=0, where n is an odd number.

Advanced Engineering Mathematics

Advanced Engineering Mathematics

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Chapter 5.3, Problem 53E

To determine

The first three positive values of λ for which the problem (1−x2)y″−2xy′+λy=0, y(0)=0, y(x), y′(x) bounded on [−1,1] has nontrivial solutions.

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Chapter 5.3, Problem 52E

Chapter 5.3, Problem 54E

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Advanced Engineering Mathematics

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