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Introductory Mathematics for Engineering Applications by Nathan W. Klingbeil, Kuldip S. Rattan

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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 Qin, 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, Qout is not a linear function of h(t), but it is assumed here for simplicity. The constant K is an ...

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