Let n I be a positive integer. Show that the functional •1 S[y] = √² dx (y')"e", y(0) = 1, y(1) = A > 1, has a stationary path given by y = = eA/n - e¹/n. C= n ln(cx + e¹/n), where

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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Let n 1 be a positive integer.
Show that the functional
•1
Sly] = f dx (y')"ey, y(0) = 1, y(1) = A > 1,
has a stationary path given by y = n ln(cx + e¹/n), where
c = eA/n _e¹/n
Transcribed Image Text:Let n 1 be a positive integer. Show that the functional •1 Sly] = f dx (y')"ey, y(0) = 1, y(1) = A > 1, has a stationary path given by y = n ln(cx + e¹/n), where c = eA/n _e¹/n
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