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

1. Oct 10, 2012

### car202

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

You can also see at: (Problem 38)

2. Relevant equations

3. The attempt at a solution

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