What am I doing wrong?
Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not exact, enter NOT.)
(tanx − sinxsiny)dx + cosxcosy dy = 0
My work:
pM/py= tan x-sinxsiny=-sinxcosy
pM/py=cosxcosy=-cosysinx
Therefore this is exact.
Solve.
f(x,y)=integral of (tanx-sinxsiny)dx+g(y)
f(x,y)=cosxsiny-ln(cosx)+c_1+g(y)
cosxsiny-ln(cosx)+c_1=c_2
Final Answer: cos(x)sin(y)-ln(cos(x))=C
But my answer is wrong and I don't know why.

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