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 the differential equation dy dx y y 3 that satisfy, in turn, the initial conditions y 1 (0) 2, y 2 (0) , y 3 (0) 1 and y 4 (0) 2 Use a graphing utility to plot the graphs o...

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Every autonomous first-order equation dy/dx = f (y) is separable. Find explicit solutions y1(x), y 2 (x),

Question:

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.