# Need help with partial differential equation

1. Feb 18, 2013

### Needhelp2013

1. The problem statement, all variables and given/known data
Given that z = √3x/y show that:

2. Relevant equations
2z/∂x∂y = ∂2z/∂y∂x

3. The attempt at a solution

Last edited: Feb 18, 2013
2. Feb 18, 2013

### bossman27

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

3. Feb 18, 2013

### Needhelp2013

Yes I did, thats it sorted now.

4. Feb 18, 2013

### bossman27

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

5. Feb 18, 2013

### Needhelp2013

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

6. Feb 18, 2013

### bossman27

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

7. Feb 18, 2013

### bossman27

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

8. Feb 18, 2013

### Needhelp2013

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.

9. Feb 18, 2013

### bossman27

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?

10. Feb 18, 2013

### Needhelp2013

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

11. Feb 18, 2013

### Needhelp2013

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.

12. Feb 18, 2013

### bossman27

13. Feb 18, 2013

### Needhelp2013

Thanks again.Is the next step now to bring the ∂z over to the other side and that is it complete?

14. Feb 18, 2013

### bossman27

No, figure out the parts in the parentheses first. That is, find ∂z/∂x and ∂z/∂y.

You don't seem to be familiar with taking partial derivatives, so heres a quick explanation:

∂z/∂x = the derivative of z with respect to x; treat y as if it were a constant (i.e. just a number). Simply take the x derivative like you would for dz/dx, if y was just some number.

∂z/∂y is exactly the same, just switch x and y in my instructions.