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1. Determine the stationary functions associated with the integral I = where a and 8 are constants, in each of the following situations: (a) The end conditions y(0) = 0 and y(1) = 1 are preassigned. (b) Only the end condition y(0) = 0 is preassigned. (c) Only the end condition y(1) = 1 is preassigned. (d) No end conditions are preassigned. Note any exceptional cases. 2. Let = for 1 for I < 1 1 Find the external of J(y) when (a) y(0) = 0. y(1) = 1. (b) y(0) = 0 and y(1) is unassigned. (c) y(0) is unassigned and y(1) = 1. (d) both y(0) and y(1) are unassigned.

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