- #1

Pouyan

- 103

- 8

## Homework Statement

Show that xu_{x}+ yu

_{y}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))?

## Homework 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:

(∂

^{2}φ/∂x

^{2}) + (∂

^{2}φ/∂y

^{2}) =0

## The Attempt at a Solution

[/B]I say that there is a analytic function : f(z)=u(x,y)+iv(x,y)

(∂u/∂x)=u

_{x}+xu

_{xx}+yu

_{xy}=(∂v/∂y)

(∂u/∂y)=xu

_{xy}+u

_{y}+yu

_{yy}=-(∂v/∂x)

But further , should I integrate to find v(x,y) ?!

Am I in right path ?!