(Solution) - Autonomous Analysis For the first order autonomous equations in Problems complete -(2025 Original AI-Free Solution)

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Autonomous Analysis For the first-order autonomous equations in Problems, complete the following.
(a) Sketch qualitative solution graphs.
(b) Highlight the equilibrium points of the equation and draw phase-line arrows along the y-axis indicating the increasing or decreasing behavior of the solution y = y (t). Classify their stability behavior.
1. y' = y2
2. y' = -y(1-y)