In the of Exercise, an autonomous differential equation is given in the form y' = ƒ(y). Perform the of the following tasks without the aid of technology.
(i) Sketch a graph of ƒ(y).
(ii) Use the graph of ƒ to develop a phase line for the autonomous equation. Classify the equilibrium point as either unstable or asymptotically stable.
(iii) Sketch the equilibrium solutions in the ty-plane. The see quilibrium solutions divide the ty-plane into regions. Sketch at least one solution trajectory in the of the seregions.
y' = 9y – y3
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