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

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SUMMARY

The discussion focuses on converting the differential equation $y(x^3e^{xy}-y) \, dx+x(xy+x^3e^{xy}) \, dy=0$ into an exact form. Participants suggest multiplying the equation by a factor of the form $x^n y^m$ to achieve exactness. The goal is to determine the appropriate values for $n$ and $m$ that will satisfy the conditions for exactness in differential equations. This method is essential for solving the equation effectively.

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danny12345
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$y(x^3e^{xy}-y) \, dx+x(xy+x^3e^{xy}) \, dy=0$
change it into exact differential and help me in solving it
 
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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.
 

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