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Homework Help: Need help with partial differential equation

  1. Feb 18, 2013 #1
    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. jcsd
  3. Feb 18, 2013 #2
    Both sides of that equation are the same, did you mistype something?
  4. Feb 18, 2013 #3
    Yes I did, thats it sorted now.
  5. Feb 18, 2013 #4
    Ahh, as I suspected. Have you made an attempt yet?
  6. Feb 18, 2013 #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
  7. Feb 18, 2013 #6
    I think you're thinking too hard, you know how to take a partial derivative I assume?
  8. Feb 18, 2013 #7
    The equation under "Relevant Equations" is what you're trying to show, correct?
  9. Feb 18, 2013 #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.
  10. Feb 18, 2013 #9
    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?
  11. Feb 18, 2013 #10
    I am just trying to work out how to read the latex way of writing equations. Ill get it. Thanks for that.
  12. Feb 18, 2013 #11
    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.
  13. Feb 18, 2013 #12
    You can't read that equation? It should read: ∂/∂y(∂z/∂x) = ∂/∂x(∂z/y)
  14. Feb 18, 2013 #13
    Thanks again.Is the next step now to bring the ∂z over to the other side and that is it complete?
  15. Feb 18, 2013 #14
    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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