Prove that if u=f(x^3 +y^3 ),where f is arbitry function then x^2 (∂u/∂y) = y^2 (∂u/∂x)


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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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