I am trying to refresh my diffy and am having trouble recalling the handling of coefficents >1 in the solution. For example, given the exact differential equation:

dr/dΘ=(r^2 sin Θ)/(2r cos Θ -1)

Since it is exact I get the form Mdr + NdΘ = 0:

(2r cos Θ -1)dr-(r^2 sin Θ)dΘ = 0

Solving, I get:

2r^2 cos Θ -r = c

My book says the answer is:

r^2 cos Θ -r = c

I understand the concept of incorporating coefficients on the left into the constant on the right. However, in this case I don't see how the coefficient '2' can be incorporated from just the one term. How can a constant 'c' be obtained that does not change the relationship between the two terms? Can someone please explain? TIA.

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