Question: Consider the differential equation y' = y 2 + 4. (a) Explain why there exist no constant solutions of the DE. (b) Describe the graph

Consider the differential equation y' = y2 + 4.

(a) Explain why there exist no constant solutions of the DE.

(b) Describe the graph of a solution y = ϕ(x). For example, can a solution curve have any relative extrema?

(c) Explain why y = 0 is the y-coordinate of a point of inflection of a solution curve

(d) Sketch the graph of a solution y = ϕ(x) of the differential equation whose shape is suggested by parts (a) –(c).

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