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Let a < b, A and B be constants. Gâteaux differential of the functional ·b [* dx (y² +w²y² + 2yx¹), y(a)=A, y(b) = B, a S[y] = d. where w is a positive constant. Using the Gateaux differential show that the stationary path of S[y] satisfies the Euler-Lagrange equation,

Let a < b, A and B be constants. Gâteaux differential of the functional ·b [* dx (y² +w²y² + 2yx¹), y(a)=A, y(b) = B, a S[y] = d. where w is a positive constant. Using the Gateaux differential show that the stationary path of S[y] satisfies the Euler-Lagrange equation,

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let a < b, A and B be constants. Gâteaux differential of the functional S[y] = d dx (y² +w²y² + 2yxª), y(a)= A, y(a) = d'y dx² where is a positive constant. Using the Gateaux differential show that the stationary path of S[y] satisfies the Euler-Lagrange equation, A, _y(b) = B, - w²y = x¹, y(a) = A, y(b) = B, -
Transcribed Image Text:Let a < b, A and B be constants. Gâteaux differential of the functional S[y] = d dx (y² +w²y² + 2yxª), y(a)= A, y(a) = d'y dx² where is a positive constant. Using the Gateaux differential show that the stationary path of S[y] satisfies the Euler-Lagrange equation, A, _y(b) = B, - w²y = x¹, y(a) = A, y(b) = B, -
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