Instrumentation and Control Systems, 3rd Edition

Appendix B

Differential Equations

Abstract

This appendix looks at the mathematics behind the solution of differential equations.

Keywords

Differential equations

B.1 Differential Equations

As will be evident from the models discussed in Chapter 8, many systems have input–output relationships which have to be described by differential equations. A differential equation is an equation involving derivatives of a function, i.e. terms such as dy/dt and d²y/dt². Thus:

$\tau \frac{\mathrm{d}y}{\mathrm{d}t}+y=0$

is a differential equation. The term ordinary differential equation is used when there are only derivatives of one variable, e.g. we only have terms such as dy/dt and d²y/dt² and ...