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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.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 69EQ: Let x=x(t) be a twice-differentiable function and consider the second order differential equation...
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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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