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Unformatted text preview: t + y . (a) Sketch the slope eld using a scale of -3 to 3 on both axes, and showing the ve isocline for c =-2 ,-1 , , 1 , 2. (b) Sketch the two solution curves with initial conditions y (0) = 1 and y (0) =-1. 6. Consider the autonomous dierential equation y = y 3-y . (a) Compute the critical points, and the corresponding stationary solutions. (b) Sketch the phase line. (c) Sketch the graphs of some solutions. Make sure you include at least one solutions with values in each interval above, below, and between the critical points. (d) What is the long term behavior of the solution with the initial condition y (0) = 1 2 . ( Hint: You answer should be a number.)...
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- Spring '08