(Solution) - A direction field for the differential equation y y 1 -(2025 Original AI-Free Solution)

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A direction field for the differential equation y? = y(1 ? 1/4y2) is shown.
(a) Sketch the graphs of the solutions that satisfy the given initial conditions.
(i) y(0) = 1 (ii) y(0) = ? 1
(iii) y(0) = ? 3 (iv) y(0) = 3
(b) Find all the equilibrium solutions.