Consider the initial-value problem dy/dt = 2− y, y(0) = 1. Using Euler’s method, compute three different approximate solutions corresponding to = 1.0, 0.5, and 0.25 over the interval 0 ≤ t ≤ 4. Graph all three solutions. What predictions do you make about the actual solution to the initial-value problem? How do the graphs of these approximate solutions relate to the graph of the actual solution? Why?
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