. Applications of First Order Ordinary Differential Equations The subject of differential equations has vast applications in solving real world problems. The solutions of the differential equations are used to predict the behaviors of the system at a future time, or at an unknown location. In several problems, the rate at which a quantity changes is a given function of the quantity and /or the time.
The objective is to find the quantity itself. If x denotes the amount of the quantity present at time t , then the instantaneous rate at which the quantity changes at time t is dx dt . This leads to a differential equation of the form dx dt f x t ( , ) . In this section we shall consider this type of problems only.
Further, by rate, we mean the instantaneous rate only.