Question: 1. Partial Differential Equations (40%) Consider the PDE (a) Xfyy - fx = f2: Let g(u, v) be such that f(x, y) = g(x2, 4).

1. Partial Differential Equations (40%) Consider the PDE (a) Xfyy - fx = f2: Let g(u, v) be such that f(x, y) = g(x2, 4). Find the PDE satisfied by g ( u, v). (b) Xfyy - fx = 0: Find the separable solutions to this PDE

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