The question

The simple population growth model, $\displaystyle \frac{dy}{dt} = ky$ (because of limitation on resources, pollution, ...) is unsatisfactory over a 'long' period. We might look at

$\displaystyle \frac{dy}{dt} = k(y)y$ ...........(1)

(which of course ignores seasonal and other variations with time). Mathematically one of the simplest assumptions we can make is that k(y) decreases linearly as y increases. In this case (1) may be written in the form

$\displaystyle \frac{dy}{dt} = k(1 - \frac{y}{K})y$, ...........(2)

where k and K are constants.

a) i) Equation (2) has two constant (stationary) solutions. What are they?

I'm not sure how to calculate this. Do I have to solve the ODE? Or is there an obvious method? Thanks.