Given [tex]V=xf(u)[/tex] and [tex] u = \frac{y}{x}[/tex] How do you show that:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] x^2 \frac{\partial^2V}{\partial x^2} + 2xy\frac{\partial^2V}{\partial x\partial y} + y^2 \frac{\partial^2V}{\partial y^2}= 0 [/tex]

My main problem is that I am not sure how to expressVin terms of a total differential, because it is a function ofxandf(u). So it depends on a variable and a function, and doesn'txalso depend onuandy?

[tex]dV = \frac{\partial V}{\partial x} * dx + \frac{\partial V}{\partial f(u)} * f(u) [/tex]

This total differential doesn't really help much, there must be some other way of writing it down and simplifying it?

So how should you go about solving this?

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# Partial derivatives, change of variable

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