(a) Draw a direction field for the given differential equation. How do solutions appear to behave as t → 0? Does the behavior depend on the choice of the initial value a? Let ao be the value of a for which the transition from one type of behavior to another occurs. Estimate the value of ao. (b) Solve the initial value problem and find the critical value ao exactly. (c) Describe the behavior of the solution corresponding to the initial value ao.

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