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?