> 
> A certain person starts a rumour in a small town. The number of people who have heard the
>  rumour, $R(t)$, is given by
>  $$
> \frac{\text d R}{\text d t} = KR \left(1300 - R\right)
> $$
>  where $K$ is a positive constant, and 1300 is the number of residents in that small town.
> 
> 
> By regarding this equation as a Bernoulli equation, find $R(t)$.
> 
> 
> 

This is my current working, I have no idea how the answer got $\frac1R=\frac1{1300}+Ce^{-1300Kt}$

Where did my t go to?

Followed by solving the equation to get $\frac1R=\frac1{1300}+\frac{1299}{1300}e^{-1300Kt}$