Given $K(0) = 0,2P$. I'm supposed to solve the ODE
$ \frac{dK}{dt} = \lambda K(P-K)$
I have tried to seperate and integrate both sides
$ \int \frac{1}{K(P-K)} dK = \int \lambda \space dt$
to get
$ \ln|K(P-K)| = \lambda t + C$
and then solve for $K$
$ e^{\ln|K(P-K)|} = K(P-K)=e^{\lambda t + C}$
But there I'm stuck as to getting any further to finding the general solution. Does the $K(P-K)$ term require integrating using partial fractions?