(a) Use a CAS and the concept of level curves to plot representative graphs of membe...

(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 Experiment with different numbers of level curves as well as various rectangular regions in the xy-plane until your result resembles Figure 2.2.6.

(b) On separate coordinate axes, plot the graph of the implicit solution corresponding to the initial condition Use a colored pencil to mark off that segment of the graph that corresponds to the solution curve of a solution 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 [Hint: First find the points on the curve in part (a) where the tangent is vertical.]

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