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 For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 5CR
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 For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
SEE MORE TEXTBOOKS