Answer
The differential equation is not exact.
Work Step by Step
We are given $ye^{xy}dx+(2y-xe^{xy})dy=0$
In this case,we have $M =ye^{xy}$ and $N =2y-xe^{xy}$
so that $M_y =e^{xy}$,whereas $N_x =-e^{xy}$.
Since $M_y \ne N_x$, the differential equation is not exact.
