# (tricky) first order ODE

1. ### mmh37

59
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

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Last edited: Apr 15, 2006

### Staff: Mentor

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

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