The given two-parameter family is a solution of the indicated differential equation on the interval (, ).
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Question:
The given two-parameter family is a solution of the indicated differential equation on the interval (−∞, ∞). Determine whether a member of the family can be found that satisfies the boundary conditions. (If yes, enter the solution. If an answer does not exist, enter DNE.)
y = c 1 ex cos x + c 2 ex sin x; y '' − 2y ' + 2y = 0 (a) y(0) = 1, y '(π) = 0 y = (b) y(0) = 1, y(π) = −1 y = (c) y(0) = 1, y(π/2) = 1 y = (d) y(0) = 0, y(π) = 0
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