## 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.

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

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 ...

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