The differential equation y"+ y = 0 has the general solution y(x) = c1 cos x + c2 sin x.
(a) Show that the boundary-value problem y" +y = 0, y(0) = 0, y(π) = 1 has no solutions.
(b) Show that the boundary-value problem y" +y = 0, y(0) = 0, y(π) = 0, has an infinite number of solutions.
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