Question

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

Answer 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.