1. The problem statement, all variables and given/known data Show that xux + yuy is the real part of an analytic function if u(x,y) is. To which analytic function is the real part of u = Re (f(z))? 2. Relevant equations What I know about analytic functions is Cauchy-Riemann condition (∂u/∂x) =(∂v/∂y) and (∂y/∂y)=-(∂v/∂x) I know actually Harmonic functions and Laplace equation (2-dim) but I don't know if I need it here: (∂2φ/∂x2) + (∂2φ/∂y2) =0 3. The attempt at a solution I say that there is a analytic function : f(z)=u(x,y)+iv(x,y) (∂u/∂x)=ux+xuxx+yuxy =(∂v/∂y) (∂u/∂y)=xuxy+uy+yuyy=-(∂v/∂x) But further , should I integrate to find v(x,y) ?! Am I in right path ?!