pde satisfy with conditions

Hello everybody.

I am new and I have one new question :)

i am trying these question, i must to show:

$\displaystyle y=log((x-a)^2+(z-b)^2))$

satisfies

$\displaystyle \frac{\partial^2y}{\partial{x^2}}+\frac{\partial^2 {y}}{\partial{z^2}}=0$

except at (a,b)

I differentiated twice for z and for x (chain rule and quotient) and put in equation to get:$\displaystyle \frac{2x+2y+4(x-a)^2+4(z-b)^2}{((x-a)^2 +(z-b)^2)^2}$

I think it is ok and it does not work for a, b (as it goes to infinity) but is it enough to do this and say equation is satisfied? sorry if is obvious question! or have i done calculation wrong?

Thank you