Example The time rate of change of a population P(t)with constant birth and death rates is proportional to the size of the population,i.e., dp (1) Note that P(t)=Cek is a solution of(1),because P'(t)=Cke=k(Ce)=kP(t),VIER 4日10y4至，1无2000 Ordinary Differential EquationsExample The time rate of change of a population P(t) with constant birth and death rates is proportional to the size of the population, i.e., dP dt = kP. (1) Note that P(t) = Ce kt is a solution of (1), because P 0 (t) = Ckekt = k(Cekt) = kP(t), ∀t ∈ R Ordinary Differential Equations