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Arctan(2/(x^2y^2-1)) satisfies Laplace's equation?

  1. Oct 10, 2012 #1
    1. The problem statement, all variables and given/known data
    Verify that [tex]\arctan(2/(x^2y^2-1))[/tex] satisfies Laplace's equation when [tex]x^2+y^2\ne 1[/tex].

    You can also see at: (Problem 38)
    http://books.google.ca/books?id=qh1...nepage&q=arctan(2/(x2y2-1)) laplacian&f=false

    2. Relevant equations

    3. The attempt at a solution

    I really have no clue. I keep getting [tex]\frac{12x^4y^6-8x^2y^4-20y^2+12x^6y^4-8x^4y^2-20x^2}{(x^4y^4 - 2x^2y^2 + 5)^2}=\frac{4(x^2+y^2)(3x^2y^2-5)(x^2y^2+1)}{(x^4y^4 - 2x^2y^2 + 5)^2}[/tex], which is obviously not zero.
  2. jcsd
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