Introductory Mathematics for Engineering Applications

Differential Equations in Engineering

CHAPTER 10

The objective of this chapter is to familiarize engineering students with the solution of differential equations (DEQ) as needed for first- and second-year engineering courses such as physics, circuits, and dynamics. A differential equation relates an output variable and its derivatives to an input variable or forcing function. There are several different types of differential equations. This chapter discusses first- and second-order linear differential equations with constant coefficients. These are the most common type of differential equations found in undergraduate engineering classes.

10.1 INTRODUCTION: THE LEAKING BUCKET

Consider a bucket of cross-sectional area A being filled with water at a volume flow rate Q_in, as shown in Fig. 10.1. If h(t) is the height and V = Ah(t) is the volume of water in the bucket, the rate of change of the volume is given by

Figure 10.1 A leaking bucket with a small hole.

Suppose the bucket has a small hole on the side through which water is leaking at a rate

where K is a constant. In reality, Q_out is not a linear function of h(t), but it is assumed here for simplicity. The constant K is an ...