1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook