Introduction

Many models of engineering systems involve the rate of change of a quantity. There is thus a need to incorporate derivatives into the mathematical model. These mathematical models are examples of differential equations .

Accompanying the differential equation will be one or more conditions that let us obtain a unique solution to a particular problem. Often we solve the differential equation first to obtain a general solution; then we apply the conditions to obtain the unique solution. It is important to know which conditions must be specified in order to obtain a unique solution.

Prerequisites

• be able to differentiate; ( HELM booklet  11)
• be able to integrate; ( HELM booklet  13)

Learning Outcomes

• understand the use of differential equations in modelling engineering systems
• identify the order and type of a differential equation
• recognise the nature of a general solution
• determine the nature of the appropriate additional conditions which will give a unique solution to the equation