ABSTRACT
A differential equation is any equation that contains the derivatives or differentials of one or more dependent variables with respect to one or more independent variables. Because many of the known physical laws are expressed as differential equations, a sound knowledge of how to solve them is essential. In the next two chapters we present the fundamental methods for solving ordinary differential equations - a differential equation that contains only ordinary derivatives of one or more dependent variables. Later, in Sections 11.6 and 12.8, we show how transform methods can be used to solve ordinary differential equations, while systems of linear ordinary differential equations are treated in Section 3.6. Solutions for partial differential equations—a differential equation involving partial derivatives of one or more dependent variables of two or more independent variables—are given in Chapters 7, 8, and 9.
