Consider the functional S[y] = ay(1)² + 1 dx ẞy², y(0) = 0, with a natural boundary condition at x = 1 and subject to the constraint 1 C[v] = vy(1)² + [* dx w(x) y² = 1, where a, ẞ and y are nonzero constants. Euler-Lagrange equation β d²y dx² +\w(x)y=0, y(0) = 0, (a — yλ) y(1) + ß y′(1) = 0, where is a Lagrange multiplier.

Consider the functional S[y] = ay(1)² + 1 dx ẞy², y(0) = 0, with a natural boundary condition at x = 1 and subject to the constraint 1 C[v] = vy(1)² + [* dx w(x) y² = 1, where a, ẞ and y are nonzero constants. Euler-Lagrange equation β d²y dx² +\w(x)y=0, y(0) = 0, (a — yλ) y(1) + ß y′(1) = 0, where is a Lagrange multiplier.

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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