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

$$\mathrm{if}\mathrm{x}=\frac{\cos \theta }{\mathrm{u}},\mathrm{y}=\frac{\sin \theta }{\mathrm{u}}and\mathrm{z}=\mathrm{f}(\mathrm{x},\mathrm{y})$$$$\mathrm{then}\mathrm{show}\mathrm{that}$$$$\frac{{\partial }^2\mathrm{z}}{\partial {\mathrm{x}}^2}+\frac{{\partial }^2\mathrm{z}}{\partial {\mathrm{y}}^2}={\mathrm{u}}^4\frac{{\partial }^2\mathrm{z}}{\partial {\mathrm{u}}^2}+{\mathrm{u}}^3\frac{\partial \mathrm{z}}{\partial \mathrm{u}}+{\mathrm{u}}^4\frac{{\partial }^2\mathrm{z}}{\partial {\theta }^2}$$

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