Solving ((y^2)+xy+1)dx+((x^2)+xy+1)dy=0 Using Exact Equations

[TheFirstOrder]

Homework Statement

Solve

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

using the method of exact equations.

Homework Equations

I must use:

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

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

Please help. It's my first time here.

And sorry, the superscripts are meant to be subscripts!

 

[ideasrule]

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

 

[TheFirstOrder]

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

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.