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Let a > 0, b>0, c> 0 be constants. Show that the stationary path of the functional S[y] = √² Sºda with a natural boundary condition at x = 0 and subject to the constraint C[y] = is given by a dx (y2 +2by), y(a) = 0, dx y = C, 3c y(x) = 2a³ (a²-x²).

Let a > 0, b>0, c> 0 be constants. Show that the stationary path of the functional S[y] = √² Sºda with a natural boundary condition at x = 0 and subject to the constraint C[y] = is given by a dx (y2 +2by), y(a) = 0, dx y = C, 3c y(x) = 2a³ (a²-x²).

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.
Chapter14: Discrete Dynamical Systems
Section14.3: Determining Stability
Problem 13E: Repeat the instruction of Exercise 11 for the function. f(x)=x3+x For part d, use i. a1=0.1 ii...
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Let a > 0, b>0, c> 0 be constants. Show that the stationary path of the functional a S[y] = Ⓡ Sº dx (y¹² + 2by), y(a) = 0, with a natural boundary condition at x = 0 and subject to the constraint C[y] = f dry =c₁ dx is given by g(r) = 3c 2a³ 13 (a²-x²).
Transcribed Image Text:Let a > 0, b>0, c> 0 be constants. Show that the stationary path of the functional a S[y] = Ⓡ Sº dx (y¹² + 2by), y(a) = 0, with a natural boundary condition at x = 0 and subject to the constraint C[y] = f dry =c₁ dx is given by g(r) = 3c 2a³ 13 (a²-x²).
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