# 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

And sorry, the superscripts are meant to be subscripts!