Among relationships between variables reflecting movement process in natural, there are many mathematical models that satisfy ordinary differential equation (ODE). Generally, as an important tool for solving many problems in practice, ODE is used to understand property of an unknown function. This paper describes four practical cases that apply ODE, i.e. identification of death time in criminal investigation; Malthusian population model; archaeology of Mawangdui Han Dynasty Tomb in Changsha (Hunan Province); and authentication of oil painting, etc.