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  3. suppose we know that the function f t y is...

Question: suppose we know that the function f t y is...

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Suppose we know that the function f (t, y) is continuous and that f (t, 3) - -1 for all tER 1. What does this information tell us about the slope field for the differential equation ly = f(t,y) dt 2. What can we conclude about solutions ylt) of -f(t, y)? For example, if y(0) 3, dt can y(t) -+oo as t-+00? The spiking of a neuron can be modeled by the differential equation d1- cos(o)ro where I (t) is the input. Often the input function l(t) is a constant I. When θ is an odd multiple of π , the neuron spikes 1. Sketch the direction field (you may use technology, one for each values of I: I- -0.1, I2-0 and I3 0.1 2. Compute the equilibrium solutions for each one of the values of I 3. Use the direction field to describe the long term behavior of the solutions in each cases

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