Chapter 1.7, Problem 22E

(a)

To determine

To calculate:To describe the different types of phase lines that occur for the differential equation $\frac{dy}{dt}=ay-y^{2}where\alpha isaparameter.$

(b)

To determine

To calculate: To determine the bifurcation values for the one parameter family $\frac{dy}{dt}=ay-y^2$ .

(c)

To determine

To calculate: To analyze the bifurcation diagram for the differential equation, $\frac{dy}{dt}=r+\alpha y-y^2$

(d)

To determine

To calculate: To analyze the bifurcation diagram for the differential equation, $\frac{dy}{dt}=r+\alpha y-y^2$ where r is negative.