Every autonomous first-order equation dy/dx = f (y) is separable. Find explicit solution...

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, 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.

(reference problem 19 of exercise 2.1)

Consider the autonomous first-order differential equation dy/dx = y - y³ and the initial condition y(0) = y₀. By hand, sketch the graph of a typical solution y(x) when y0 has the given values.