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

2.9. Let Y = C [a, b] and F(y) = fa(x, y(x), y'(x), y"(x)) dx = [y(x)] dx, where f = f(x, y, z, r) in C([a, b] R) is given. For v, y = Y, prove that a b 5F(y; 1) = f* {,[y(x)]v(x) + z[y(x)]v'(x) + fr[y(x)]v"(x)) dx. a

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