(a) Draw a direction field for the given differential equation. How do solutions behave as t becomes large? Does the behavior depend on the choice of the initial value a? Let b be the value of a at which the transition from one type of behavior to another occurs. Estimate the value of b. (b) Solve the initial value problem and find the critical value a0 exactly. (c) Describe the behavior of the solution corresponding to the initial value a0.
