How Can This Non-Separable First Order ODE Be Solved?

[mmh37]

Does anyone see how one can tackle the following ODE?

$$[2y*exp^{y/x} + x}] \frac {dy} {dx} -2x - 2y = 0$$

that is my attempt:

rearrange to get

$$dy/dx = \frac {2x + 2y} {2y*exp^{y/x}-x}$$

I do not see how to go on from here. Surely, the ODE is not seperabale and I don't find a way to get the integrating factor here.

thanks for any hints!

[edit:] for a more clearly written version of the ODE see attached file

 

[Astronuc]

First thought would be to try a change of variable, u = y/x, so

du/dx = (1/x) dy/dx - y/x² = (1/x) dy/dx - u/x