Explanation Given: The given linear differential operator L is: L [ y ] ( x ) = x y ″ ( x ) + ( 2 − x 2 ) y ′ ( x ) + 3 y ( x ) Procedure used: Let L be the differential operator given by the L [ y ] = A 2 y ″ + A 1 y ′ + A 0 y . The formal adjoint of L is the differential operator L + define by L + [ y ] = ( A 2 y ) ′ ′ − ( A 1 y ) ′ + A 0 y Provided A 2 ′ ′ , A 1 ′ and A 0 are continuous on [ a , b ] . Calculation: Consider the given linear differential operator L: L [ y ] ( x ) = x y ″ ( x ) + ( 2 − x 2 ) y ′ ( x ) + 3 y ( x ) Here A 0 = 3 , A 1 = 2 − x 2 and A 2 = x

Fundamentals of Differential Equations and Boundary Value Problems

7th Edition

ISBN: 9780321977106

Author: Nagle, R. Kent

Publisher: Pearson Education, Limited

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Chapter 11.4, Problem 1E

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The formal adjoint for the given linear differential operator L L[y](x)=xy″(x)+(2−x2)y′(x)+3y(x).

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Chapter 11.3, Problem 26E

Chapter 11.4, Problem 2E

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u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (ū+v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅w) Support your answer mathematically or a with a written explanation. d) If possible, find u. (vxw) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

Chapter 11 Solutions

Fundamentals of Differential Equations and Boundary Value Problems

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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The formal adjoint for the given linear differential operator L L [ y ] ( x ) = x y ″ ( x ) + ( 2 − x 2 ) y ′ ( x ) + 3 y ( x ) .

Solution Summary: The author explains the formal adjoint for the given linear differential operator L.

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The formal adjoint for the given linear differential operator L L[y](x)=xy″(x)+(2−x2)y′(x)+3y(x).

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Chapter 11 Solutions