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In Problems 41 and 42 solve the given initial-value problem in which the input function g(x) is discontinuous. [Hint: Solve each problem on two intervals, and then find a solution so that y and y′ are continuous at x = π/2 (Problem 41) and at x = π (Problem 42).]
41. y″ + 4y = g(x), y(0) = 1, y′(0) = 2, where
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Differential Equations with Boundary-Value Problems (MindTap Course List)
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