Determine the value of r for which the given differential equation has a solution of the form y(t) =e^(rt) a) y^ ' + 2y = 0 b) y^ '' - y = 0 c) y^ ''+ y^ ' - y = 0 d) y^ ''' - 3y^ '' + 2y^ ' = 0

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A: Given:

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A: This is a problem of differential equation.

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