dy 2 -4ysin x = 4y secx 10 cosx dx
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
I attched formula for your refference. Please solve these sums according to this method. If you know this method then solve otherwize forward to others don't give wrong answer.
Transcribed Image Text:9.
2xy y 2x where y(1)-2
dy
-4ysin x = 4y secx
10
cosx
dx
sec x
dy
+ tan x=cosy cos x
de
11. tan y
Transcribed Image Text:Basic Mathematics-IL
Richa Nandra Lovely Professional University
Unit 11: Linear Differential Equations of First Order
Notes
Notes
Le.
CONTENTS
Integrating, we have
Objectives
Introduction
which is the required general solution
11.1 Linear Equations
112 Equations Reducible to the Lincar (Bernoulli's Equation)
113 Summary
11.4 Keywords
1.
Jra is known as Integrating factor, in short, LF
11.5 Review Questions
2.
Linear differential equation is commonly known as nitz's lineaquat
11.6 Further Readings
Objectives
Example
After studying this unit, you will be able to:
e COs
Understand the concept of linear equations
Solution:
Discuss the equations reducible to linear form
n equation d
be written as
Introduction
ylanr a secs
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
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
a the con of linear equations and equations reducible to linear form.
Here P tan X
Q-sec r.
LF. g secr.
Solution of (1) is
y. secr-fsecx. sec xdse
11.1 Linear Equations
or
y sectan a+c Ans
An equation of the form
Example
dy- Py = Q
dx
(1)
Solve (1+) 2xy-4-0.
dy.
Solution
in which P & Q are functions of x alone or constant is called a linear equation of the first order
Given equation is
d 1+ 1+r
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
Here
P.
Multiplying both sides of (1) by ra, we have
LE ra "-ii - (1+).
dy
Pye- OelrA
ds
LOVELY PROFESSIONAL UNIVERSITY
143
144
IONAL UNIVERSITY
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