dY/dt = y(c - yb)
C and B are constants.
Im supposed to find and explicit solution for y, but im having trouble.
The Attempt at a Solution
dY/y(c - yb) = dt
∫(1/c)dy/y + ∫(b/c)dY/c - yb = ∫dt (i used partial fraction decompositions)
(1/c)ln|y| - (b/c)ln|c - yb| = t + K (K stands for an arbitrary constant)
ln|[(c-yb)^b]/y| = -ct + K (Multiplied by negative c and then combine the natural logs on the left)
What im having trouble with is the last expression on the LHS. I have (c-yb)^b so how am I supposed to solve for y, if i dont know b?