Our Archives

Call 09159097300, or 09067754232 for any enquiries.

Project Topic:

METHODS OF SOLUTION TO SECOND ORDER LINEAR DIFFERENTIAL EQUATION WITH VARIABLE COEFFICIENTS

Project Information:

 Format: MS WORD ::   Chapters: 1-5 ::   Pages: 40 ::   Attributes: SOLVED PROBLEMS ::   7,335 people found this useful

Project Body:

CHAPTER ONE

1.0 INTRODUCTION

1.1 BACKGROUND OF THE STUDY

The general second order homogeneous linear differential equation with constant coefficients is

Ay’’ + By’ + Cy = 0,

where y is an unknown function of the variable x, and A, B, and C are constants. If A = 0 this becomes a first order linear equation, which in this case is separable, and so we already know how to solve. So we will consider the case A  0. If we want, we can the divide through by A and obtain the equivalent equation

y″ + by′ + cy = 0,

where b = B/A and c = C/A (that is if we have nothing better to do, and like the first coefficient to be equal to 1)

Linear with constant coefficients means that each term in the Left Hand Side of the equation is a constant times y or a derivative of y. Homogeneous means that we exclude equations like

Ay″ + By′ + Cy = f(x)

which can be solved, in certain important cases, by an extension of the methods we will study here. Here we only will solve the case where the Right Hand Side f(x) is identically 0. Homogeneous also means that the constant function y = 0 is always a solution to the equation.

By now we know to expect 2 degrees of freedom in the solution of this second order equation, i.e., the general family of solutions should have two arbitrary constants. We call the general family of solutions for short the general solution. That means that to find our general solution we have to find two independent functions y = f1(x) and y = f2(x) which are solutions, and then the general solution will be

y = C1 · f1(x) + C2 · f2(x). Now If y = f1(x)

and y = f2(x) are indeed solutions, one can check by plugging in that y = C1 · f1(x) + C2 · f2(x) will be a solution. The fact that all solutions are of this form (i.e., we haven’t missed any solution) is harder to ascertain, but nevertheless true. Notice that of course we do need f1(x) and f2(x) to be independent. What does it mean for two functions to be independent? It means that one of them is not equal to a constant times the other. For example the functions f1(x) = e x

and f2(x) = 2e x are not independent, because f2(x) = 2 · f1(x). On the other hand, for example the functions g1(x) = e x and g2(x) = e 2x are independent (although we do not prove it, it seems intuitively clear that they are independent).

1.2 STATEMENT OF THE PROBLEM

The study will try to solve the problems below:

y″ -xy′ + 2y = 0

y″ + y′ = 0 and x2y″ + y′ + xy = 0 using power series and Frobenius method

1.3 AIM AND OBJECTIVES OF THE STUDY

The main aim of the research work is determine the methods of solution to second order linear differential equation with variable coefficients. Other specific objectives of the study are:

  1. to determine the solution around the origin for homogenous and non-homogenous second order differential equation with variable coefficients
  2. to determine the solution at other points
  3. to investigate on factors affecting methods of solution to second order linear differential equation with variable coefficients
  4. to determine the difference in efficiency of the methods of solution to second order linear differential equation with variable coefficients

1.4 SIGNIFICANCE OF THE STUDY

The study on the methods of solution to second order linear differential equation with variable coefficients will be of immense benefit to the mathematics department in the sense that the study will determine the solution around the origin for homogenous and non-homogenous second order differential equation with variable coefficients, the solution at other points and the difference in efficiency of the methods of solution to second order linear differential equation with variable coefficients. The study will serve as a repository of information to other researchers that desire to carry out similar research on the above topic. The study will contribute to the body of the existing literature on solution to second order linear differential equation with variable coefficients

1.5 SCOPE OF THE STUDY

The study on the methods of solution to second order linear differential equation with variable coefficients will focus on two methods (power series solution to DE and method of Frobenius.  

1.6 DEFINITION OF TERMS

 ODE: differential equation

Differential equation: A differential equation is a mathematical equation that relates some function with its derivatives


Get The Complete Project »

Project Department:

MORE MATHEMATICS FREE UNDERGRADUATE PROJECT TOPICS AND RESEARCH MATERIALS

Instantly Share this Project On Social Media:

CLOSELY RELATED MATHEMATICS FREE UNDERGRADUATE PROJECT TOPICS AND RESEARCH MATERIALS

THE RELEVANCE OF THE USE OF THE METHOD OF UNDETERMINED COEFFICIENT FOR SOLVING DIFFERENTIAL EQUATIONS

 Format: MS WORD ::   Chapters: 1-5 ::   Pages: 51 ::   Attributes: N/A  ::   18968 engagements

1.0 CHAPTER ONE 1.1 BACKGROUND OF STUDY The method of undetermined coefficient has been used as a tool for solving a particular non homogeneous differential equation. One of the main advantages of t...Continue reading »

DIFFERENTIATION AND ITS APPLICATION

 Format: MS WORD ::   Chapters: 1-5 ::   Pages: 78 ::   Attributes: PROBLEMS AND SOLUTIONS  ::   29719 engagements

CHAPTER ONE INTRODUCTION From the beginning of time man has been interested in the rate at which physical and non physical things change. Astronomers, physicists, chemists, engineers, business enterp...Continue reading »

THE APPLICATION OF LINEAR PROGRAMMING IN PROFIT MAXIMIZATION (A CASE STUDY OF CRUNCHES FRIED CHICKEN AKA ROAD)

 Format: MS WORD ::   Chapters: 1-5 ::   Pages: 60 ::   Attributes: Linear programming

CHAPTER ONE INTRODUCTION BACKGROUND OF THE STUDY Linear programming (LP) can be defined as a mathematical technique for determining the best allocation of a firm’s limited resources to achi...Continue reading »

MODELING THE EFFECTS OF CARRIERS ON TRANSMISSION DYNAMICS OF INFECTIOUS DISEASES

 Format: MS WORD ::   Chapters: 1-5 ::   Pages: 60 ::   Attributes: Questionnaire, Data Analysis  ::   15774 engagements

CHAPTER ONE 1.0 INTRODUCTION 1.1 BACKGROUND OF STUDY For certain infectious diseases, there are individuals who are able to transmit their illness but do not exhibit any symptoms. These individuals...Continue reading »

MODELLING AND SIMULATION OF THE SPREAD OF HBV DISEASE WITH INFECTIOUS LATENT

 Format: MS WORD ::   Chapters: 1-5 ::   Pages: 50 ::   Attributes: maths simulation  ::   14078 engagements

CHAPTER ONE 1.0 INTRODUCTION 1.1 BACKGROUND OF STUDY The spread of the HBV in Nigeria has posed a lot of threat to health and well being citizens in Nigeria. It is evident that about a third of the ...Continue reading »

SOLUTION OF FIRST ORDER DIFFERENTIAL EQUATION USING NUMERICAL NEWTONS INTERPOLATION AND LAGRANGE

 Format: MS WORD ::   Chapters: 1-5 ::   Pages: 40 ::   Attributes: numerical method  ::   17141 engagements

CHAPTER ONE 1.0 INTRODUCTION 1.1 BACKGROUND OF STUDY Differential equation is one of the major areas in mathematics with series of method and solutions. A differential equation as for example u(x) ...Continue reading »

What are you looking for today?

TESTIMONIALS:

  • 1. Jayone from FPA said " I had a wonderful experience using UniProjectMaterials,though they did not deliver the material on time, but the content had good quality. I recommend UniProjectMaterials for any project research work.".
    Rating: Very Good
  • 2. Mugisha R from B.U, UGANDA said "Wow, this is great, your materials has helped me alot. Many blessings. I will inform my friends. Thanks. ".
    Rating: Very Good
  • 3. Nwachukwu Ruth Chinyerr from Michael okpara university of Agriculture,umudike said "I really appreciate this. Materials like this are good guides to writing a researchable project.".
    Rating: Good
  • 4. Ibrahim Salama from Kaduna said "Thanks You So Much Sir We Appreciate ".
    Rating: Excellent
  • 5. Ibrahim Salama from Kaduna said "Thanks You So Much Sir We Appreciate ".
    Rating: Excellent
  • 6. Mohammed A.B from Veterinary Laboratory, Zanzibar ,Tanzania said "You are doing good job to assists in research. God bless you.".
    Rating: Very Good

Paper Information

Format:ms word
Chapter:1-5
Pages:40
Attribute:SOLVED PROBLEMS
Price:₦3,000
Get The Complete Project »

Best Selling Projects

Our Archives