Given a generic 2-dimensional metric $$ ds^2=E(x,y)dx^2+2F(x,y)dxdy+G(x,y)dy^2 $$ what is the change of coordinates that move it into the conformal form $$ ds^2=e^{\phi(\xi,\zeta)}(d\xi^2+d\zeta^2) $$ being $\xi=\xi(x,y)$ and $\zeta=\zeta(x,y)$? Is it generally known? Also a good reference will fit the bill.
Thanks beforehand.