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Show that the functionals Si[y] = ["da (1+ry) y_and_S2[y] = ["dary'², dx a where b> a > 0, y(b) = B and y(a) = A, are both stationary on the same curve, namely y(x) = A + (B − A) In(x/a) In(b/a) Explain why the same function makes both functionals stationary.

Show that the functionals Si[y] = ["da (1+ry) y_and_S2[y] = ["dary'², dx a where b> a > 0, y(b) = B and y(a) = A, are both stationary on the same curve, namely y(x) = A + (B − A) In(x/a) In(b/a) Explain why the same function makes both functionals stationary.

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.CR: Chapter 9 Review
Problem 4CR
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Show that the functionals cb rb Si[y] = fª dæ dx (1+ry) y' and S₂[y] = = [² de xy², a a where b> a > 0, y(b) = B and y(a) = A, are both stationary on the same curve, namely y(x) = A + (B − A) In(x/a) In(b/a) Explain why the same function makes both functionals stationary.
Transcribed Image Text:Show that the functionals cb rb Si[y] = fª dæ dx (1+ry) y' and S₂[y] = = [² de xy², a a where b> a > 0, y(b) = B and y(a) = A, are both stationary on the same curve, namely y(x) = A + (B − A) In(x/a) In(b/a) Explain why the same function makes both functionals stationary.
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