Question: Consider the autonomous first-order differential equation dy/dx = y - y 3 and the initial condition y(0) = y 0 . By hand, sketch the

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.

(a) y₀ > 1

(b) 0 < y₀ < 1

(d) y₀ < -1

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