Homework Help is Here – Start Your Trial Now!
Math
Calculus
The differential equation y" + (sgn x)y = 0 (25) has the discontinuous coefficient function S+1 ifx > 0, |-1 ifx < 0. sgnx = Show that Eq. (25) nevertheless has two linearly indepen- dent solutions y1(x) and y2(x) defined for all x such that • Each satisfies Eq. (25) at each point x # 0; • Each has a continuous derivative at x = 0; • yı (0) = y (0) = 1 and y2(0) = y (0) = 0. (Suggestion: Each y¡(x) will be defined by one formula for x < 0 and by another for x 2 0.) The graphs of these two solutions are shown in Fig. 3.3.2. у (к) 21 х удх) уда) FIGURE 3.3.2. Graphs of y1 (x) and y2(x)

The differential equation y" + (sgn x)y = 0 (25) has the discontinuous coefficient function S+1 ifx > 0, |-1 ifx < 0. sgnx = Show that Eq. (25) nevertheless has two linearly indepen- dent solutions y1(x) and y2(x) defined for all x such that • Each satisfies Eq. (25) at each point x # 0; • Each has a continuous derivative at x = 0; • yı (0) = y (0) = 1 and y2(0) = y (0) = 0. (Suggestion: Each y¡(x) will be defined by one formula for x < 0 and by another for x 2 0.) The graphs of these two solutions are shown in Fig. 3.3.2. у (к) 21 х удх) уда) FIGURE 3.3.2. Graphs of y1 (x) and y2(x)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
See similar textbooks
icon
Related questions
Question
The differential equation y" + (sgn x)y = 0 (25) has the discontinuous coefficient function S+1 ifx > 0, |-1 ifx < 0. sgnx = Show that Eq. (25) nevertheless has two linearly indepen- dent solutions y1(x) and y2(x) defined for all x such that • Each satisfies Eq. (25) at each point x # 0; • Each has a continuous derivative at x = 0; • yı (0) = y (0) = 1 and y2(0) = y (0) = 0. (Suggestion: Each y¡(x) will be defined by one formula for x < 0 and by another for x 2 0.) The graphs of these two solutions are shown in Fig. 3.3.2. у (к) 21 х удх) уда) FIGURE 3.3.2. Graphs of y1 (x) and y2(x)
Transcribed Image Text:The differential equation y" + (sgn x)y = 0 (25) has the discontinuous coefficient function S+1 ifx > 0, |-1 ifx < 0. sgnx = Show that Eq. (25) nevertheless has two linearly indepen- dent solutions y1(x) and y2(x) defined for all x such that • Each satisfies Eq. (25) at each point x # 0; • Each has a continuous derivative at x = 0; • yı (0) = y (0) = 1 and y2(0) = y (0) = 0. (Suggestion: Each y¡(x) will be defined by one formula for x < 0 and by another for x 2 0.) The graphs of these two solutions are shown in Fig. 3.3.2. у (к) 21 х удх) уда) FIGURE 3.3.2. Graphs of y1 (x) and y2(x)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 10 steps with 15 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS