Explanation Given: The given linear differential operator is, L ( y ) = ( 1 + x 2 ) y ″ + 2 x y ′ + λ r y y ′ ( 0 ) = 0 , y ( π ) − ( 1 + π 2 ) y ′ ( π ) = 0 Calculation: The given linear differential operator is, L ( y ) = ( 1 + x 2 ) y ″ + 2 x y ′ + λ r y y ′ ( 0 ) = 0 , y ( π ) − ( 1 + π 2 ) y ′ ( π ) = 0 The given linear differential operator can be written as, L ( v ) = ( 1 + x 2 ) v ″ + 2 x v ′ + λ r v L ( u ) = ( 1 + x 2 ) u ″ + 2 x u ′ + λ r u By Green’s formula, ∫ a b u [ v ] − v [ u ] ( x ) d x = ∫ 0 π u [ ( 1 + x 2 ) v ″ + 2 x v ′ + λ r v ] − v [ ( 1 + x 2 ) u ″ + 2 x u ′ + λ r u ] ( x ) d x = ∫ 0 π [ ( 1 + x 2 ) u v ″ + 2 x u v ′ + λ r u v − ( 1 + x 2 ) v u ″ − 2 x v u

Fundamentals Of Differential Equations And Boundary Value Problems, Books A La Carte Edition (7th Edition)

7th Edition

ISBN: 9780321977182

Author: Nagle, R. Kent, Saff, Edward B., Snider, Arthur David

Publisher: PEARSON

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Chapter 11.3, Problem 11E

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Whether the given linear differential operator L(y) is self adjoint or not.

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Chapter 11.3, Problem 10E

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Fundamentals Of Differential Equations And Boundary Value Problems, Books A La Carte Edition (7th Edition)

Ch. 11.2 - In Problems 1-12, determine the solutions, if any,...Ch. 11.2 - In Problems 1-12, determine the solutions, if any,...Ch. 11.2 - Prob. 3E Ch. 11.2 - In Problems 1-12, determine the solutions, if any,...Ch. 11.2 - In Problems 1-12, determine the solutions, if any,...Ch. 11.2 - In Problems 1-12, determine the solutions, if any,...Ch. 11.2 - Prob. 7E Ch. 11.2 - In Problems 1-12, determine the solutions, if any,...Ch. 11.2 - Prob. 9E Ch. 11.2 - In Problems 1-12, determine the solutions, if any,...

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Whether the given linear differential operator L ( y ) is self adjoint or not.

Solution Summary: The author explains that the given linear differential operator L(y) is self adjoint.

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Whether the given linear differential operator L(y) is self adjoint or not.

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