Assignment:
Q1. (a) Use PhaseLines to investigate the bifurcation diagram for the differential equation
dy / dt = ay - y2
where a is a parameter. Describe the different types of phase lines that occur.
(b) What are the bifurcation values for the one-parameter family in part (a)?
(c) Use PhaseLines to investigate the bifurcation diagram for the differential equation
dy / dt = r + ay - y2
where r is a positive parameter. How does the bifurcation diagram change from the r = 0 case (see part (a))?
(d) Suppose r is negative in the equation in part (c). How does the bifurcation diagram change?
Provide complete and step by step solution for the question and show calculations and use formulas.