Chapter 8.1, Problem 27ES

(a) Suppose that a quantity $y=y\left(t\right)$ increases at a rate that is proportional to the square of the amount present, and suppose that at time $t=0,$ the amount present is $y_0$ . Find an initial-value problem whose solution is $y\left(t\right).$

(b) Suppose that a quantity $y=y\left(t\right)$ decreases at a rate that is proportional to the square of the amount present, and suppose that at a time $t=0,$ the amount present is $y_0.$ Find an initial-value problem whose solution is $y\left(t\right).$