# Trouble solving a differential equation

1. Aug 31, 2011

### rmas

Hi,

How can I solve this equation (finding f(x,y)) ?

$\left (\frac{\partial f}{\partial x} \right )^2+ \left( \frac{\partial f}{\partial y} \right )^2=0$

Thanks a lot.

2. Sep 1, 2011

### jackmell

Can't you factor that with some i's? You know, like if I had:

$$(x^2+y^2)=0$$ and I wanted to factor it, then I'd write:

$$(x+iy)(x-iy)=0$$

Then that means:

$$(x+iy)=0$$

or:

$$x-iy=0$$

Ok, same dif then. Now do yours.

Nothing wrong with complex solutions. Try not to be intimidated by them.

3. Sep 3, 2011

### hunt_mat

Both term in the equation are greater than or equal to zero, so the equation says that they must both be zero and hence:
$$\frac{\partial f}{\partial x}=\frac{\partial f}{\partial y}=0$$
So what does this say about f?

4. Sep 5, 2011

### rmas

Thank you very much jackmell, that is very helpful.

The partial derivatives vanish, I suppose it means that f is constant ?

5. Sep 6, 2011

Yep.

6. Sep 6, 2011