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Mathematics

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TT Page 196 Problem 15. #2 Find the extremals of the functionals (a) J(y) = So (y2 + y + y2)dx such that y(0) = 0, y(1) = 1, (b) J(y) = Só (y2 + y2 + 2ye")dx such that y(a) = A, y(t) = B, #3 Find the extremals of the functional J(y) = SEC )dx such that y(1) = 1, y(e) = 3. #4 Find the general solution of the Euler equation corresponding to the functional J(y) = ["f(x)1+yada subject to y(a) = Q1, y(t) = 02, and then find extremal in the two special cases (a) f(x) = VT, (b) f(x) = x.
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