Solving a differential equation involving $y$ and its exponential

Hi all I have a question Ive been asked to solve. But I have no idea where to begin.

The equation is $y'=\dfrac{y+e^x}{x+e^y}$.

I think this is homogeneous but I have no idea as to how to manipulate this to get it into the required form.

Maple 16 does not find a closed-form solution, or any symmetries. This strongly suggests that there is no closed-form solution. Almost certainly there are no closed-form solutions that can be found by elementary techniques.

We can write the ode in the form $\omega=Mdx+Ndy=0,$ where $M=-(y+e^x)$ and $N=x+e^y.$
This means that we replace the search for solutions of the ode with the search for curves $\gamma(t)=(x(t),y(t))$ such that $\gamma^\ast\omega=0.$

As showed in Peter Tamaroff's answer $\omega$ is not closed $d\omega\neq 0.$ However it can be showed (invoking Frobenius'theorem) that there exists a function $\mu$ not vanishing s.t. $\mu\omega$ is exact, i.e. $d(\mu\omega)=0.$

To find $\mu$ we need a solution for the $1^{\textrm{st}}$-order linear pde $$0=\frac{\partial \mu N}{\partial x}-\frac{\partial\mu M}{\partial y}\equiv(x+e^y)\partial_x\mu+(y+e^x)\partial_y\mu+2\mu.$$