Draw a direction field for the given differential equation. Based on the direction field, determine the behavior of y as t → ∞. If this behavior depends on the initial value of y at t = 0, describe this dependency. y' = y(y - 6)² VIV a Where a = 6. Equilibrium solutions: //// 7 y(t) = 0 and y(t) = 6. !!!!!! !!!!!!! Behavior of y(t) as to depends on initial value y(to): / / / / / / / / / / / / 1 !!!!!!!!!!!!! 117111111111 / / / / / / / / / / 1 ******* y(to) > 0: y(t)→ 6. 11111111 1 y(to) < 0: y(t) diverges from y = 0. ////// Where a = 6. Equilibrium solutions: y(t) = 0 and y(t) = 6. ******* Behavior of y(t) as t→∞ depends on initial value y(to): 11 201 y(to) > 6: y(t) diverges from y = 6. 0 < y(to) < 6:y(t) → 6. y(to) < 0: y(t) diverges from y = 0. O a

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