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Consider the autonomous differential equation dy/dt = f(y) where the graph of f(y) is given below. J ) (a) Sketch the phase line for this
Consider the autonomous differential equation dy/dt = f(y) where the graph of f(y) is given below. J ) (a) Sketch the phase line for this equation and identify the equilibrium points as sinks, sources, or nodes. (b) Give a rough sketch of the slope field that corresponds to this equation. (c) Give rough sketches of the graphs of the solutions that satisfy the initial condi- tions y(0) = -3, y(0) =0, y(0) = 1, and y(0) = 2
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