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
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
Problem 1RQ
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F59d44c96-efb1-4f3c-83b3-5a6a84cf94cb%2F285b8848-b2f0-4446-a161-13541a4ea6a1%2F0pmyjef_processed.jpeg&w=3840&q=75)
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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