Let L be a second order linear differential operator. Show that the solution y = (x) of

Chapter 11, Problem 15

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Let L be a second order linear differential operator. Show that the solution y = (x) of the problem L[y] = f(x), 1y(0) + 2y (0) = a, 1y(1) + 2y (1) = b can be written as y = u + v, where u = 1(x) and v = 2(x) are solutions of the problems L[u] = 0, 1u(0) + 2u (0) = a, 1u(1) + 2u (1) = b and L[v] = f(x), 1v(0) + 2v (0) = 0, 1v(1) + 2v (1) = 0, respectively

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