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ntial equations: (x+2y) 1. = y de

ntial equations: (x+2y) 1. = y de

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Find the bitwise OR, bitwise AND, and bitwise XOR of each of these pairs of bit strings:
a) 11 1111 1111, 00 0000 0000
b) 1111 0000, 1010 1010
c) 00 0111 0001, 10 0100 1000

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
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
à linear equation of the first order. 11.5 Review Questions Solve the following differential equations: (x+2y) 1. = y %3D dx d (dy 2y 2. de ( de x+ V1-x +(1-x²}-3/2) de y = (1-x}
Transcribed Image Text:à linear equation of the first order. 11.5 Review Questions Solve the following differential equations: (x+2y) 1. = y %3D dx d (dy 2y 2. de ( de x+ V1-x +(1-x²}-3/2) de y = (1-x}
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