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Richa Nandra, Lovely Professional University Unit 11: Linear Differential Equations of First Order

Unit 11: Linear Differential Equations of First Order Notes

CONTENTS
Objectives
Introduction

11.1 Linear Equations
11.2 Equations Reducible to the Linear (Bernoulli’s Equation)
11.3 Summary

11.4 Keywords
11.5 Review Questions
11.6 Further Readings

Objectives

After studying this unit, you will be able to:

 Understand the concept of linear equations
 Discuss the equations reducible to linear form

Introduction

An equation is basically the mathematical manner to portray a relationship among two variables.
The variables may be physical quantities, possibly temperature and position for instance, in
which case the equation informs us how one quantity relies on the other, so how the temperature
differs with position. The easiest type of relationship that two such variables can comprise is
a linear relationship. This shows that to locate one quantity from the other you multiply the
first by some number, then add a different number to the outcome. In this unit, you will
understand the concept of linear equations and equations reducible to linear form.

11.1 Linear Equations

An equation of the form

dy
 Py  Q ….(1)
dx
in which P & Q are functions of x alone or constant is called a linear equation of the first order.

Did u know? If you are provided a value of x, you can simply discover the value of y.
The general solution of the above equation can be found as follows:

Multiplying both sides of (1) by e Pdx , we have

dy  Pdx  Pdx  Pdx
e  Pye  Qe
dx

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