Problem 1. Let a € R and u solve the 2nd order linear partial differential equation Uzz – 2auzy – 3a°uyy + uz + au, = 0. (A) Classify the type of equation for (1.1) according to the value of a. (1.1) (B) Transform (1.1) into the canonical form and solve the equation. | (Hint: the type of equation may depend on the value of a, and you may need to divide the discussion into several cases.)

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