# (tricky) first order ODE

by mmh37
Tags: order, tricky
 P: 61 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 Attached Thumbnails
 Admin P: 21,399 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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