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

`\frac\partial{\partial y}\left[e^(2y)-y\cos xy\right]=2e^(2y)-\cos xy+xy\sin xy`


`\frac\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.