Prove-that-if-u-f-x-3-y-3-where-f-is-arbitry-function-then-x-2-u-y-y-2-u-x-

Question Number 191867 by Spillover last updated on 02/May/23

P r o v e t h a t i f u = f (x^{3} + y^{3}), w h e r e f i s a r b i t r y

f u n c t i o n t h e n x^{2} \frac{\partial u}{\partial y} = y^{2} \frac{\partial u}{\partial x}

Answered by qaz last updated on 02/May/23

\partial u = f^{'} (3 x^{2} d x + 3 y^{2} d y)

\Rightarrow \frac{\partial u}{\partial x} = 3 x^{2} f^{'} \frac{\partial u}{\partial y} = 3 y^{2} f^{'}

\Rightarrow x^{2} \frac{\partial u}{\partial y} = y^{2} \frac{\partial u}{\partial x}

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