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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.

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.2: Introduction To Conics: parabolas
Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.
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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.
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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