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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. S[y] = [° da (y^² +w²y² + 2yxª¹), y(a)=A, _y(b)= B, a where w is a positive constant. the stationary path of S[y] satisfies the Euler-Lagrange equation, d'y dx² -w²y = x², y(a) = A, y(b) = B, For the case a = 0, b = 1, find a stationary path of S[y] for the boundary conditions y(0) = −24/w6, y(1) = 0.
Transcribed Image Text:Let a ≤ b, A and B be constants. S[y] = [° da (y^² +w²y² + 2yxª¹), y(a)=A, _y(b)= B, a where w is a positive constant. the stationary path of S[y] satisfies the Euler-Lagrange equation, d'y dx² -w²y = x², y(a) = A, y(b) = B, For the case a = 0, b = 1, find a stationary path of S[y] for the boundary conditions y(0) = −24/w6, y(1) = 0.
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