In this exercise we derive superposition principles for nonhomogeneous problems.
(a) Consider L(u) = f. If up is a particular solution, L(up) = f, and if u1 and u2 are homogeneous solutions, L(ui) = 0, show that u = up + c1u1 + c2u2 is another particular solution.
(b) If L(u) = f1 + f2, where upi is a particular solution corresponding to fi, what is a particular solution for f1 + f2?
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