MHB How to Make $y(x^3e^{xy}-y) \, dx+x(xy+x^3e^{xy}) \, dy=0$ Exact?

[danny12345]

$y(x^3e^{xy}-y) \, dx+x(xy+x^3e^{xy}) \, dy=0$
change it into exact differential and help me in solving it

 

[Ackbach]

I've improved your typesetting by including dollar signs, as well as introducing a right parenthesis that seemed implied.

So, we need to convert this into an exact equation. I would recommend multiplying by something of the form $x^n y^m$, and see if you can figure out the $n$ and $m$ that make it exact.