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 dt =kP, (1) where k is an unknown constant.Note that P(t)=Ce,C0 is a solution of(1),because P'(t)=Cke=k(Ce)=kP(t);VIER 4口14①y至元2000 Peipei Shang School of Mathematical Sciences shang@tongji.edu.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) where k is an unknown constant. Note that P(t) = Ce kt , C > 0 is a solution of (1), because P 0 (t) = Ckekt = k(Cekt) = kP(t), ∀t ∈ R Q: What can we do with the solution? Peipei Shang School of Mathematical Sciences shang@tongji.edu.cn Ordinary Differential Equations