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Appendix B

W. Bolton

B.1 Differential Equations

As will be evident from the models discussed earlier, 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:

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 not additionally dx/dt or dx2/dt2. The order of a differential equation is equal to the order of the highest derivative that appears in the equation. ...

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