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Question Number 197317 by universe last updated on 13/Sep/23

if x = \frac{\cos θ}{u}, y = \frac{\sin θ}{u} a n d z = f (x, y)

then show that

\frac{\partial^{2} z}{\partial x^{2}} + \frac{\partial^{2} z}{\partial y^{2}} = u^{4} \frac{\partial^{2} z}{\partial u^{2}} + u^{3} \frac{\partial z}{\partial u} + u^{4} \frac{\partial^{2} z}{\partial θ^{2}}