Can anyone help explain to me what the general solution is to this? As I understand it is not the same as dealing with PDE's as $f$ is a function of $z=x+iy$ so is probably not $f=g(z)+h(\bar{z})$
$\frac{\partial}{\partial \bar{z}}\left(\frac{\partial f}{\partial z}\right)=0$
Thanks very much in advance