Need help with partial differential equation

  • #1

Homework Statement


Given that z = √3x/y show that:


Homework Equations


2z/∂x∂y = ∂2z/∂y∂x

The Attempt at a Solution

 
Last edited:

Answers and Replies

  • #2
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Both sides of that equation are the same, did you mistype something?
 
  • #3
Yes I did, thats it sorted now.
 
  • #4
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Ahh, as I suspected. Have you made an attempt yet?
 
  • #5
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
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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?
 
  • #7
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The equation under "Relevant Equations" is what you're trying to show, correct?
 
  • #8
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
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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:

[itex]\frac{\partial}{\partial y}(\frac{\partial z}{\partial x}) = \frac{\partial}{\partial x}(\frac{\partial z}{\partial y}) [/itex]

Does that make any more sense now?
 
  • #10
I am just trying to work out how to read the latex way of writing equations. Ill get it. Thanks for that.
 
  • #11
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:

[itex]\frac{\partial}{\partial y}(\frac{\partial z}{\partial x}) = \frac{\partial}{\partial x}(\frac{\partial z}{\partial y}) [/itex]

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.
 
  • #12
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You can't read that equation? It should read: ∂/∂y(∂z/∂x) = ∂/∂x(∂z/y)
 
  • #13
You can't read that equation? It should read: ∂/∂y(∂z/∂x) = ∂/∂x(∂z/y)

Thanks again.Is the next step now to bring the ∂z over to the other side and that is it complete?
 
  • #14
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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.
 

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