I have a question about solving this differential equation.
So, the question is to solve it given that $P(0)=\frac23$
So this is what I've done so far
$$\frac{dP}{dt} = kP(1-P)$$ $$ k\,dt = \frac{dP}{P(1-P)}$$ $$ \int{k\,dt} = \int\frac{dP}{P(1-P)} $$ $$ kt + C = \ln(P) - \ln(1-P) $$ $$ \frac23k + C = \ln(0) - \ln(1) $$
This is where I'm lost in finding $C$ because $\ln(0)$ is $-\infty$ Am I doing something wrong?