Let a, b and w be constants, with w‡0. (a) Show that the Euler-Lagrange equation for the functional S[y] = ² da (y² +w²y² + 2y(a sinwa + b sinh war)), dx y(1) = 0, y(2) = 1, is y" - w² y = a sin wx+bsinh wx, y(1) = 0, y(2) = 1.
Let a, b and w be constants, with w‡0. (a) Show that the Euler-Lagrange equation for the functional S[y] = ² da (y² +w²y² + 2y(a sinwa + b sinh war)), dx y(1) = 0, y(2) = 1, is y" - w² y = a sin wx+bsinh wx, y(1) = 0, y(2) = 1.
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 a,
(a)
b and w be constants, with w‡ 0.
Show that the Euler-Lagrange equation for the functional
+2
S[y] = da (y² + w²y² + 2y(a sinwa + b sinhwr)),
is
1
y(1) = 0, y(2) = 1,
y" - w²y = a sin cæ +bsinh x, y(1)=0, 3(2) = 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F59d44c96-efb1-4f3c-83b3-5a6a84cf94cb%2Fc04ae5e3-d135-4482-8a4e-274c6b9113a5%2F26k4p8q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let a,
(a)
b and w be constants, with w‡ 0.
Show that the Euler-Lagrange equation for the functional
+2
S[y] = da (y² + w²y² + 2y(a sinwa + b sinhwr)),
is
1
y(1) = 0, y(2) = 1,
y" - w²y = a sin cæ +bsinh x, y(1)=0, 3(2) = 1.
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