1. Find the general solution of the PDE f xy + f y + 2x 2 y(f x + f) = 0 2. Find the general solution of the PDE e -2x f xx – e -2y fyy – e -2x fx + e -2y fy + 8e y = 0 3. Solve the PDE f xx – 2 sin(x)f xy – (3 + cos 2 (x))fyy + fx + (2 – sin(x) – cos(x))f y = 0 subject to the conditions f(x, cos(x)) = 0, f y (x, cos(x)) = e – cos(x)
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