Part 4/9:
Equilibrium Solutions: The analysis includes points where the population stabilizes, reflected in the equilibria at populations of 250 and 750. Using these equilibrium solutions in conjunction with specified initial populations allows for discerning the impact of varying initial conditions on eventual population trajectories.
Integration and Partial Fractions: To navigate the complexities of the fractions within the equation, partial fractions serve as a helpful tool. By breaking the fractional equation down, integrals can be derived, leading towards an explicit function that describes the relationships among populations at various time intervals.