## 12

## Applications of Ordinary Differential Equations

##### 12.0 Introduction

This chapter deals with some of the important applications of differential equations. The growth and decay population model of Malthus is represented by the first order differential equation.

where *x*(*t*) is the population at any time *t* and the constant of propotionality *K* is the growth constant. This equation is used for finding the bacteria in a culture, life of radio active substance and Newton’s law of cooling.

Some of the other applications dealt with are the mixing of solutions, simple L-C-R circuits, orthogonal trajectories, simple harmonic motion and bending of beams. ...