Q.NO.1: Show that the function z=ln(x^2 + y^2)+2tan^-1(y/x) satisfies Laplace’s equation.

Question

(∂^2z/∂x^2)+(∂^2z/∂y^2)=0

Answer 1

I've done a couple of these for you now. Where do you get stuck? What do you have so far? Doing the partials can be tedious, but not difficult.

You can get some help here, for example, to verify your work:

http://www.wolframalpha.com/input/?i=d%5E2%2Fdx%5E2+ln(x%5E2+%2B+y%5E2)%2B2tan%5E-1(y%2Fx)