To convert the equation $y(x^3e^{xy}-y) \, dx+x(xy+x^3e^{xy}) \, dy=0$ into an exact differential, the discussion suggests multiplying by a factor of the form $x^n y^m$. Participants are encouraged to determine the appropriate values for $n$ and $m$ that will achieve this. The goal is to find a solution that makes the differential equation exact, facilitating further analysis and solutions. The conversation emphasizes the importance of identifying the correct multiplicative factor for achieving exactness. Overall, the focus is on transforming the given equation into a solvable exact form.