Question: Let y = y(x) = x - x3 / 3! + x5 / 5! - x7 / 7! + .... Show that y satisfies that

Let y = y(x) = x - x3 / 3! + x5 / 5! - x7 / 7! + .... Show that y satisfies that differential equation y" + y = 0 with the conditions y(0) = 0 and y'(0) = 1. From this guess a simple formula for y?

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