Show that the stationary path of the functional V S[y] = ["™ dx (y² +y²), _y(0) = 1, y(v) = v, v > 0, is given by Y coshæ + B sinh , 0 ≤ x ≤v, where B and v are given by the solutions of the equations v = cosh v+ B sinh v and B² – 1 = 2 sinh v + 2B cosh v.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Show that the stationary path of the functional
S[y] = ["da (y² + y²), _y(0) = 1, y(v) = v, v > 0,
dx
is given by
y = coshx + Bsinhæ, 0 ≤ x ≤v,
where B and v are given by the solutions of the equations
v = cosh v + B sinh v and B² 12 sinh v + 2B cosh v.
Transcribed Image Text:Show that the stationary path of the functional S[y] = ["da (y² + y²), _y(0) = 1, y(v) = v, v > 0, dx is given by y = coshx + Bsinhæ, 0 ≤ x ≤v, where B and v are given by the solutions of the equations v = cosh v + B sinh v and B² 12 sinh v + 2B cosh v.
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