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(a) Draw a direction field for the given differential equation. How do solutions appear to behave as t becomes large? Does the behavior depend on the choice of the initial value a ? Let a0 be the value of a for which the transition from one type of behavior to another occurs. Estimate the value of a0. (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. 3 y^'-2 y=e^-πt / 2, y(0)=a | Numerade