A necessary condition for the functional defined by X2 = dx f(x, Y(x),Y'(x)) to have a local minimum for ôf of dx Y(x) = y(x) is h(x) + h'(x) | = 0 for all ду lifferentiable functions h with h(x) h(x,) = 0. ) Show how to obtain the Euler-Lagrange condition ôf d of 0 from this. ду dx ôy'
A necessary condition for the functional defined by X2 = dx f(x, Y(x),Y'(x)) to have a local minimum for ôf of dx Y(x) = y(x) is h(x) + h'(x) | = 0 for all ду lifferentiable functions h with h(x) h(x,) = 0. ) Show how to obtain the Euler-Lagrange condition ôf d of 0 from this. ду dx ôy'
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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