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Richa Nandra, Lovely Professional University Unit 5: Differential Equations

Unit 5: Differential Equations Notes

CONTENTS
Objectives
Introduction

5.1 Classifications of Differential Equations
5.2 Examples of Differential Equations
5.3 Linear Ordinary Differential Equations of First Order

5.4 Summary
5.5 Keywords
5.6 Review Questions
5.7 Further Readings

Objectives

After studying this unit, you should be able to:

 Know that before dealing with any equation we classify various differential equation.
 Notice that the order of a differential equation is the highest differential coefficient.

 Show how to develop a differential from a certain relation between independent variable
x and dependent variable y.
 See that this unit on differential equations is helpful for the next few units.

Introduction

This chapter gives an introduction to the various types of differential equations. Some methods
of solving a linear ordinary first order differential equations are given. In the next unit we will
discuss the existence of the solution of a first order differential equation.

5.1 Classifications of Differential Equations

Quite often we come across a function f(x) of a variable x. Whenever the value of x, known as
independent variable changes, it brings about a change in the value of f(x), known as dependent
variable (say y). This dependence of y on x can be translated in mathematical terms by means of
2
dy d y
a differential equation. This differential equation involves y, x, and the derivatives , 2 ,
dx dx
2
3
3
d y dy d y d y , ,, ,,,
3 ..... Sometimes , 2 , 3 ..... are denoted by y , y , y ..... respectively. Sometimes we
dx dx dx dx
may be concerned by more than one dependent variables. Some examples of differential
equations are:
dy
sin y x 0 ...(i)
dx

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