Question

] Consider the autonomous differential equation y 0 = 10 + 3y − y 2 ....

] Consider the autonomous differential equation y 0 = 10 + 3y − y 2 . Sketch a graph of f(y) by hand and use it to draw a phase line. Classify each equilibrium point as either unstable or asymptotically stable. The equilibrium solutions divide the ty plane into regions. Sketch at least one solution trajectory in each region.

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The vertical axis is y and horizontal axis is t.

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