Question: Every autonomous first-order equation dy/dx = f (y) is separable. Find explicit solutions y1(x), y 2 (x), y 3 (x), and y 4 (x) of
Every autonomous first-order equation dy/dx = f (y) is separable. Find explicit solutions y1(x), y2(x), y3(x), and y4(x) of the differential equation dy/dx = y - y3 that satisfy, in turn, the initial conditions y1(0) = 2, y2(0) = ½, y3(0) = -1 and y4(0) = -2. Use a graphing utility to plot the graphs of each solution. Compare these graphs with those predicted in Problem 19 of Exercises‑2.1. Give the exact interval of definition for each solution.
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