Fundamentals of Differential Equations and Boundary Value Problems
Fundamentals of Differential Equations and Boundary Value Problems
7th Edition
ISBN: 9780321977106
Author: Nagle, R. Kent
Publisher: Pearson Education, Limited
bartleby

Concept explainers

bartleby

Videos

Question
Book Icon
Chapter 13.4, Problem 14E
To determine

To show:

The following result remains valid if L is replaced by a positive continuous function l(x) and the inequality |ϕ(x,y0)ϕ(x,y˜0)||y0y˜0|eLh is replaced by the inequality |ϕ(x,y0)ϕ(x,y˜0)||y0y˜0|exp{|x0xl(x)dx|}.

Let f and f/y be continuous functions on an open rectangle

R={(x,y):a<x<b,c<y<d}

containing the point (x0,y0). Assume that for all y˜0 sufficiently close to y0, the solution ϕ(x,y˜0) to (7) exists on the interval [x0h,x0+h] and its graph lies within a fixed closed rectangle R0R. Then, for |xx0|h,

|ϕ(x,y0)ϕ(x,y˜0)||y0y˜0|eLh

Here, L is any positive constant such that |(f/y)(x,y)|L for all (x,y) in R0.

Blurred answer
Students have asked these similar questions
For each of the following series, determine whether the absolute convergence series test determines absolute convergence or fails. For the ¿th series, if the test is inconclusive then let Mi = 4, while if the test determines absolute convergence let Mi 1 : 2: ∞ Σ(−1)"+¹ sin(2n); n=1 Σ n=1 Σ ((−1)”. COS n² 3+2n4 3: (+ 4: 5 : n=1 ∞ n 2+5n3 ПП n² 2 5+2n3 пп n² Σ(+)+ n=1 ∞ n=1 COS 4 2 3+8n3 П ηπ n- (−1)+1 sin (+727) 5 + 2m³ 4 = 8. Then the value of cos(M₁) + cos(2M2) + cos(3M3) + sin(2M) + sin(M5) is -0.027 -0.621 -1.794 -1.132 -1.498 -4.355 -2.000 2.716
i need help with this question i tried by myself and so i am uploadding the question to be quided with step by step solution and please do not use chat gpt i am trying to learn thank you.
i need help with this question i tried by myself and so i am uploadding the question to be quided with step by step solution and please do not use chat gpt i am trying to learn thank you.

Chapter 13 Solutions

Fundamentals of Differential Equations and Boundary Value Problems

Knowledge Booster
Background pattern image
Math
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
College Algebra
Algebra
ISBN:9781938168383
Author:Jay Abramson
Publisher:OpenStax
Text book image
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Text book image
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Text book image
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Text book image
Elements Of Modern Algebra
Algebra
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Cengage Learning,
Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY