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

User Rmb
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1 Answer

4 votes

\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.
User Evilpenguin
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