ABSTRACT
It is well known that differential equations (DEs) are the backbone of physical systems. It may be noted that most of the fundamental laws of nature can be formulated as DEs, namely, the growth of a population, motion of a satellite, flow of current in an electric circuit, change in prices of commodities, conduction of heat in a rod, vibration of structures, etc. The order of a differential equation is defined as the order of the highest derivative involved in the given DE. The degree of a differential equation is the highest power (positive integral index) of the highest-order derivative of the differential equation. Many problems in science and engineering can be modeled by ordinary differential equations or partial differential equations, along with one or more supplementary conditions. If these conditions are given at one point of independent variable, the problem is called initial value problem and these conditions are known as initial conditions.
