(a) Use a CAS and the concept of level curves to plot

Chapter 2, Problem 2.1.102

(choose chapter or problem)

(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 y(0) 3 2 dy dx x(1 x) y(2 y) 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 fin the points on the curve in part (a) where the tangent is vertical.] (c) Repeat part (b) for the initial condition y(0) 2. x y