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A Report ON: First Order Ordinary Differential Equation & It's Applications

This document is a report on first order ordinary differential equations and their applications. It contains an acknowledgment section thanking those who provided support and guidance. The contents section outlines four chapters that will cover ordinary differential equations, methods for solving different types of first order equations, and applications and examples of first order equations. The report aims to provide an overview of first order ordinary differential equations and demonstrate their real-world applications.

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Ehsan Abir
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122 views4 pages

A Report ON: First Order Ordinary Differential Equation & It's Applications

This document is a report on first order ordinary differential equations and their applications. It contains an acknowledgment section thanking those who provided support and guidance. The contents section outlines four chapters that will cover ordinary differential equations, methods for solving different types of first order equations, and applications and examples of first order equations. The report aims to provide an overview of first order ordinary differential equations and demonstrate their real-world applications.

Uploaded by

Ehsan Abir
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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A REPORT

ON
First Order Ordinary Differential Equation & it’s
Applications.

Submitted by:
Registration No: 41647
Exam Roll : 160102

Jahangirnagar University
Savar, Dhaka-1342
ACKNOWLEDGEMENT
All praise are for the almighty Allah . I would like to devote the effort to my
beloved parents who was brought me to this world.

I would like to thank my respective supervisor for her kind, gracious and
painstaking , guidance ,criticisms and valuable suggestions in preparation of this
report . I am indebted to him for giving his valuable times with fruitful
discussion ,continuous help and encouragement and assistance the preparation of
this report would never been possible.

At this moment I want to express my gratitude to my family the my friend for


their cordial support and inspiration.
CONTENTS

Chapter – 1: ORDINARY DIFFERENTIAL EQUATION

1.1 Differential equation………………………………………………………………………………………………………1


1.2 Classification of a Differential Equation………………………………………………………………………….1
1.3 Ordinary Differential Equation……………………………………………………………………………………….2
1.4 Partial Differential Equation……………………………………………………………………………………….….2
1.5 Order of a Differential Equation…………………………………………………..………………………………..3
1.6 Degree of a Differential Equation………………………………….…………….………………………………...3
1.7 Linear Differential Equation……………………………………………………………………………………………5
1.8 Non-linear Differential Equation………………………………..……………………………………………….…5
1.9 Identification of Differential Equation……………………………………………………………………….…..6
1.10 Solution of Differential Equation…………………………………………………………………………………….7
1.11 General Solution …………………………………………………………………………………………………………...7
1.12 Particular Solution……………………………………………………………………………………………………..…..7
1.13 Singular Solution…………………………………………………………………………………………………………....8
1.14 Formation of Differential Equation…………………………………………………………………………..…….8
1.15 Initial Value Problem(IVP)………………………………………………………………………………………..…….9
1.16 Boundary Value Problem(BVP)……………………………………………………………………………………..10
Chapter – 2: Working Rule For Solving Different Kinds Of First Order
Ordinary Differential Equation.
2.1 Introduction………………………………………………………………………………………………………………………11

2.2 Equation With Separable Variables……………………………………………………………………………….……12

2.3 Differential Homogeneous Equation……………………………………………………………………….…………13

2.4 Differential Homogeneous Equation……………………………………………………………………………….…16

2.5 Working Rule For Solving Differential Homogeneous Equation…………………………………….……17

2.6 Exact Differential Equation…………………………………………………………………………………………………20

2.7 Integrating Factor………………………………………………………………………………………………………………22

CHAPTER – 3 : Application And Examples Of First Order Ordinary


Differential Equation.
3.1 Exponential Growth And Decay …………………………………………………………………………………………24

3.2 Population Growth ……………………………………………………………………………………………………………25

3.3 Water Tanks ………………………………………………………………………………………………………................26

3.4 Mixing Problem…………………………………………………………………………………………………………………28

Conclusion………………………………………………………………………………………..….31

References……………………………………………………………………………………………32

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