# Exact equations

1. Mar 14, 2010

### TheFirstOrder

1. The problem statement, all variables and given/known data

Solve

((y^2)+xy+1)dx+((x^2)+xy+1)dy=0

using the method of exact equations.

2. Relevant equations

I must use:

(N$$_{x}$$-M$$_{y}$$)/(xM-yN)=F(xy)

3. The attempt at a solution

The problem that I'm having is that I can't get the required partial derivatives to be equal to each other. How do can I change it so that N$$_{x}$$=M$$_{y}$$?

When I started this problem initially, I got F(xy)=1, which is not right as 1 is not a function of xy (and I had forgotten to check that the partial derivatives were equal to each other) :P

And sorry, the superscripts are meant to be subscripts!

2. Mar 14, 2010

### ideasrule

Since Nx is not equal to My, the equation isn't exact. Are you sure you copied the question correctly?

3. Mar 14, 2010

### TheFirstOrder

Yes, that is the precise equation. And that's how I'm stuck.

Mx=2y+x
Ny=2x+y

I read things in my textbook that says I could times the original equation by a factor that would result in the two partial equations being equal, but that doesn't seem to work in this case. I'm completely clueless.