Question

Determine if the given differential equation is exact (e^2y-y cos xy)dx+(2xe^2 y-cos xy+2y)dy=0

Answer 1

$\dfrac\partial{\partial y}\left[e^{2y}-y\cos xy\right]=2e^{2y}-\cos xy+xy\sin xy$

$\dfrac\partial{\partial x}\left[2xe^{2y}-y\cos xy+2y\right]=2e^{2y}+y\sin xy$

The partial derivatives are not equal, so the equation is not exact.