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Solve this equation to show that the stationary path is x(1+2A) (3 + 2A) 1 + 2 y(x) = = X

Solve this equation to show that the stationary path is x(1+2A) (3 + 2A) 1 + 2 y(x) = = X

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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Consider the functional 2 S[(y)] = [₁² dx ln(1 + x²y'), y(1) = 0, y(2) = A, where A is a constant and y is a continuously differentiable function for 1 ≤ x ≤ 2. Let h be a continuously differentiable function for 1 ≤ x ≤ 2, and let e be a constant. Let A = S[y+ ch] — S[y]. 2 = cf ₁² A = E dx y(x) x²h' €² = x4h2 (1+x²y')² 1 & ff d 2 +0(€³). if h(1) = h(2) = 0, then the term O(e) in this expansion vanishes if y'(x) satisfies the equation 1 + x²y' dx dy 1 1 dx с x² where c is a nonzero constant. Solve this equation to show that the stationary path is x(1+2A) − (3+2A) 1 + 2 X
Transcribed Image Text:Consider the functional 2 S[(y)] = [₁² dx ln(1 + x²y'), y(1) = 0, y(2) = A, where A is a constant and y is a continuously differentiable function for 1 ≤ x ≤ 2. Let h be a continuously differentiable function for 1 ≤ x ≤ 2, and let e be a constant. Let A = S[y+ ch] — S[y]. 2 = cf ₁² A = E dx y(x) x²h' €² = x4h2 (1+x²y')² 1 & ff d 2 +0(€³). if h(1) = h(2) = 0, then the term O(e) in this expansion vanishes if y'(x) satisfies the equation 1 + x²y' dx dy 1 1 dx с x² where c is a nonzero constant. Solve this equation to show that the stationary path is x(1+2A) − (3+2A) 1 + 2 X
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