The simple population growth model, (because of limitation on resources, pollution, ...) is unsatisfactory over a 'long' period. We might look at
(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
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.