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Sachin Kaushal, Lovely Professional University Unit 8: Formation of Differential Equation

Unit 8: Formation of Differential Equation Notes

CONTENTS
Objectives
Introduction

8.1 Definition
8.2 Classification of Differential Equation
8.3 Formation of a Differential Equation

8.4 Summary
8.5 Keywords
8.6 Review Questions
8.7 Further Readings

Objectives

After studying this unit, you will be able to:

 Define differentiation equation
 Understand the classification of differential equation

 Discuss the formation of differential equation
Introduction

From times immemorial, man has made progress through observing the nature, questioning
and improvising himself. Scientists observe the positions of various celestial bodies, noting
their movements and finally discovering the paths traversed by these bodies and later on
representing them in the form of equations known as laws. This process of mathematical
formulations of natural phenomena lead to a differential equation -which is a natural choice as
phenomena change in time or change in other constants. Thus, in the fields of physics, engineering,
economics, finance, management, etc., differential equations play a very important role. They
arise in many practical problems where variation of distance of a moving particle, variation of
current in an electric circuit, in mechanical systems, agriculture, etc. A differential equation
involves independent variables, dependent variables, their derivatives and constants.

8.1 Definition

A differential equation is an equation, which involves differentials or differential coefficient.

Ordinary differential equations are those, which involve only one independent variable. Thus
dy
y
(i)  cosx sin x
dx
2
d y 2
(ii) 2  a y  tan ax
dx

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