Page 117 - DMTH202_BASIC_MATHEMATICS_II

Basic Mathematics-II Sachin Kaushal, Lovely Professional University

Notes Unit 9: Solution of Differential Equation

CONTENTS
Objectives
Introduction

9.1 Order & Degree of Differential Equation
9.2 Solution of a Differential Equation
9.2.1 General Solution

9.2.2 Particular Solution
9.3 Solution and Constant of Integration
9.4 Differential Equations of the First Order and First Degree
9.4.1 Geometric Meaning of a Differential Equation of the First
Order and First Degree
9.4.2 Equations in which the Variables are Separable
9.4.3 Exact Differential Equations
9.5 Summary

9.6 Keywords
9.7 Review Questions
9.8 Further Readings

Objectives

After studying this unit, you will be able to:
 Understand the order & degree of differential equation
 Illustrate the concept of solution of differential equation
 Understand the geometric meaning of a differential equation of the first order and first
degree
 Discuss the equations in which the variables are separable

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

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