### Introduction

Sections 19.2 and 19.3 have introduced several techniques for solving commonly occurring first-order and second-order ordinary differential equations. In this Section we solve a number of these equations which model engineering systems.

#### Prerequisites

• understand what is meant by a differential equation
• be familiar with the terminology associated with differential equations: order, dependent variable and independent variable
• be able to integrate standard functions

#### Learning Outcomes

• recognise and solve first-order ordinary differential equations, modelling simple electrical circuits, projectile motion and Newton’s law of cooling
• recognise and solve second-order ordinary differential equations with constant coefficients modelling free electrical and mechanical oscillations
• recognise and solve second-order ordinary differential equations with constant coefficients modelling forced electrical and mechanical oscillations