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Have I answered these questions on Laplace's equation correctly?

  1. Oct 16, 2008 #1
    1. The problem statement, all variables and given/known data
    I missed the lecture on this so I just wanted to check if I am doing this correctly?

    Which of the following functions obey Laplace’s equation?
    a) Ψ(x, y) = 2xy
    b) Ψ(x, y) = x^3 - 3y^2
    c) Ψ(x, y) = x^4 - 6x^2.y^2
    d) Ψ(x, y) = e^x.siny
    e) Ψ(x, y) = sinxsinhy

    2. Relevant equations

    [tex]\nabla[/tex][tex]^{2}[/tex] = [tex]\partial^2/\partial x^2 + \partial^2/\partial y^2 + \partial^2/\partial z^2[/tex]

    3. The attempt at a solution

    I am not showing me working out the partial derivatives of each question so I'm just showing the final line of my working.

    a) 0 - 0 = 0 so yes

    b) 6x - 6x = 0 so yes

    c)12x^2 - 12y^2 - 12x^2 so no it doesn't

    d) e^x.sin(y) - e^x.sin(y) = 0 so yes

    e) -sin(x)sinh(y) + sin(x)sinh(y) = 0 so yes
  2. jcsd
  3. Oct 16, 2008 #2


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    Hi lozzyjay! :smile:

    ok except for:
  4. Oct 16, 2008 #3
    Ah yes! Thank you! :)
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