Suppose that we are given a second order operator where A, B, C are constant coefficients. By factorizing L in terms of first order entities ?1 and ?2 asgiven by show that a general solution to Lf = 0 can be written as the superposition f = f 1 + f 2 , where f 1 and f 2 are solutions of ? 1 f 1 = 0 and ? 2 f 2 = 0.Hence establish that for the PDE its general solution is expressible as f(x, y) = f(2x – y) + e y g(x) for arbitrary functions f and g.
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