# Need help with partial differential equation

## Homework Statement

Given that z = √3x/y show that:

## Homework Equations

2z/∂x∂y = ∂2z/∂y∂x

## The Attempt at a Solution

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Both sides of that equation are the same, did you mistype something?

Yes I did, thats it sorted now.

Ahh, as I suspected. Have you made an attempt yet?

Thanks for spotting that.No I am pretty lost to be honest. I am fairly new to this. I believe I am working with the Laplace equation though

Thanks for spotting that.No I am pretty lost to be honest. I am fairly new to this. I believe I am working with the Laplace equation though

I think you're thinking too hard, you know how to take a partial derivative I assume?

The equation under "Relevant Equations" is what you're trying to show, correct?

Yes the equation under "Relevant Equations" is what I'm trying to show. There could be a simple solution but I'm missing it. I tried substituting what 'z=' into the laplace equation but that didnt get me anywhere.

I tried substituting what 'z=' into the laplace equation but that didnt get me anywhere.

Exactly what I meant by thinking too hard. All that it's asking you to do is show that if you take the derivative of z with respect to x and then y, it's the same as taking the derivative of z with respect to y and then x. In other words, show:

$\frac{\partial}{\partial y}(\frac{\partial z}{\partial x}) = \frac{\partial}{\partial x}(\frac{\partial z}{\partial y})$

Does that make any more sense now?

I am just trying to work out how to read the latex way of writing equations. Ill get it. Thanks for that.

Exactly what I meant by thinking too hard. All that it's asking you to do is show that if you take the derivative of z with respect to x and then y, it's the same as taking the derivative of z with respect to y and then x. In other words, show:

$\frac{\partial}{\partial y}(\frac{\partial z}{\partial x}) = \frac{\partial}{\partial x}(\frac{\partial z}{\partial y})$

Does that make any more sense now?

Is your equation meaning this ∂y/zx = ∂x/zy

any other help would be great becuase I am struggling to realise where to go next.