differential equation: Determine whether a member of the family can be found that satisfies the initial conditions

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Dutsky Kamdon
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differential equation: Determine whether a member of the family can be found that satisfies the initial conditions

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
initial conditions.
y = c1e^x cos x + c2e^x sin x; y" − 2y' + 2y = 0,
i. y(0) = 1, y'(π) = 0
ii. y(0) = 1, y(π) = −1

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