2.9. Let Y = C [a, b] and F(y) = fa(x, y(x), y'(x), y(x)) dx =...

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· 2.9. Let Y = C² [a, b] and F(y) = faƒ(x, y(x), y'(x), y"(x)) dx = ſåƒ[y(x)] dx, where f = f(x, y, z, r) in C¹([a, b] × R³) is given. For v, y = Y, prove that a b 5F(y; 1) = f* {ſ,[y(x)]v(x) + ſz[y(x)]v'(x) + fr[y(x)]v"(x)) dx. a · 2.9. Let Y = C² [a, b] and F(y) = faƒ(x, y(x), y'(x), y"(x)) dx = ſåƒ[y(x)] dx, where f = f(x, y, z, r) in C¹([a, b] × R³) is given. For v, y = Y, prove that a b 5F(y; 1) = f* {ſ,[y(x)]v(x) + ſz[y(x)]v'(x) + fr[y(x)]v"(x)) dx. a

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To prove the given expression lets break it down step by step We have the functional Fy defined as F... View the full answer