Find the most general functions X(x) and Y(y), each of one variable, such that Z(x, y) = XY satisfies the partial differential equation Ə2z dz . дх2 - ду = Obtain a solution of the above equation which satisfies the boun- dary conditions : when x = 0 or π z = 0 z = sin 3x when y = 0 and 0 < x < π.

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