Exercise 26

Consider the differential equation $y' = y(2 - y)$.

1. Verify that $y(t) = 2/(1 + Ce^{-2t})$ is a solution to this equation.
2. Sketch solution curves for $C = 1, 2, \ldots, 5$.
3. Verify that $y = 0$ is a solution to the differential equation in part (a). Can you find a value for $C$ such that $$y(t) = \frac{2}{1 + Ce^{-2t}} = 0?$$