let:

Is there a function

that is analytic in the complex plane.

If so determine all the functions f.

........................................

So i know that if u(x,y) and v(x,y) are harmonic and satisfy the cauchy riemann equations f are analytic.

My standard method for this kind of problems is:

Find

then with CR(1):

i integrate so i get v(x,y) = something + g(x).

Then with CR(2):

i get g(x).

But with my method it gets really messy! i cant solve the integration, so i wonder if theres another way to do this?

regards