Determine whether the pairs of functions in Problems 20 through 26 are linearly independent or linearly dependent on the real line. 20. f(x) = 1, g(x) = cos' x + sin x 21. f(x) = x'. g (x) = x²|x| 22. f(x) = 1+x, g(x) = 1+ |x| %3D

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
please send handwritten solution for Q 22 only handwritten solution accepted
Determine whether the pairs of functions in Problems 20
through 26 are linearly independent or linearly dependent on
the real line.
20. f(x) = 7, g(x) = cos' x + sin x
21. f(x) = x', g(x) = x2x|
22. f(x) = 1+x, g(x) 1+ x|
23. f(x) = xe", g(x) xle
24. f(x) = sin x, g(x) 1- cos 2x
25. f(x) = e sin x, g(x) e cos x
26. f(x) = 2 cos x + 3 sin x, g(x) = 3 cos x - 2 sin x
27. Let y, be a particular solution of the nonhomogeneous
equation y" + py' + qy f(x) and let y, be a solu-
tion of its associated homogeneous equation. Show that
y ye + Yp is a solution of the given nonhomogeneous
equation.
%3D
%3D
%3D
%3D
%3D
Transcribed Image Text:Determine whether the pairs of functions in Problems 20 through 26 are linearly independent or linearly dependent on the real line. 20. f(x) = 7, g(x) = cos' x + sin x 21. f(x) = x', g(x) = x2x| 22. f(x) = 1+x, g(x) 1+ x| 23. f(x) = xe", g(x) xle 24. f(x) = sin x, g(x) 1- cos 2x 25. f(x) = e sin x, g(x) e cos x 26. f(x) = 2 cos x + 3 sin x, g(x) = 3 cos x - 2 sin x 27. Let y, be a particular solution of the nonhomogeneous equation y" + py' + qy f(x) and let y, be a solu- tion of its associated homogeneous equation. Show that y ye + Yp is a solution of the given nonhomogeneous equation. %3D %3D %3D %3D %3D
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,