(a) Use a CAS and the concept of level curves to plot representative graphs of members of the family of solutions of the differential equation

dy/dx = x(1 - x)/y(-2 + y).

Experiment with different numbers of level curves as well as various rectangular regions in the xy-plane until your result resembles from the following figure.

(b) On separate coordinate axes, plot the graph of the implicit solution corresponding to the initial condition y(0) = 3/2.

Use a colored pencil to mark off that segment of the graph that corresponds to the solution curve of a solution φ that satisfi­es the initial condition. With the aid of a root fi­nding application of a CAS, determine the approximate largest interval I of defi­nition of the solution φ. 

(c) Repeat part (b) for the initial condition y(0) = -2.

Transcribed Image Text:

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