Question: Consider the partial differential equation uxx - 3uxy - 4uyy = 0. 1. (a) What is its type? (elliptic, parabolic, hyperbolic) 2. (b) Factor

Consider the partial differential equation uxx - 3uxy - 4uyy = 0.

Consider the partial differential equation uxx - 3uxy - 4uyy = 0. 1. (a) What is its type? (elliptic, parabolic, hyperbolic) 2. (b) Factor the equation using ax and dy. 3. (c) Choose coordinates x = ax' + by' and y = cx' + dy' so that the original equation can be rewritten asux'y' =0. 4. (d) Find the general solution u(x, y) and use it to solve the equation subject to the auxiliary conditions u(x,0) = x2 and uy(x,0) = ex.

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