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Function plz help!!!

If a function u(x,y)=arctan(y/x)
deduce the laplace equation of the function.
plz show working i don't no where to start from...plz
thanks

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Collins

  1. How about starting with the definition of the equation?

    ∇^2(u) = 0
    ∂u/∂x = 1/(1+y^2/x^2) (-y/x^2)
    = x^2/(x^2+y^2) (-y/x^2)
    = -y/(x^2+y^2)
    ∂^u/∂x^2 = 2xy/(x^2+y^2)^2

    Now do ∂u/∂y and then form the equation.

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    Steve

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