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Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.3: Maxima And Minima
Problem 20E
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Let a ≤ b, A and B be constants. S[y] = [° da (y^² +w²y² + 2yxª¹), y(a)=A, _y(b)= B, a where w is a positive constant. the stationary path of S[y] satisfies the Euler-Lagrange equation, d'y dx² -w²y = x², y(a) = A, y(b) = B, For the case a = 0, b = 1, find a stationary path of S[y] for the boundary conditions y(0) = −24/w6, y(1) = 0.
Transcribed Image Text:Let a ≤ b, A and B be constants. S[y] = [° da (y^² +w²y² + 2yxª¹), y(a)=A, _y(b)= B, a where w is a positive constant. the stationary path of S[y] satisfies the Euler-Lagrange equation, d'y dx² -w²y = x², y(a) = A, y(b) = B, For the case a = 0, b = 1, find a stationary path of S[y] for the boundary conditions y(0) = −24/w6, y(1) = 0.
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