Find the Annihilator of the given function(s) f(x)=x + e*cos(2x) D²(D-1)(D²+4) a. b. D(D²+4)² C. D² (D²-2D+5) d. D² + (D²-2D+5)
Find the Annihilator of the given function(s) f(x)=x + e*cos(2x) D²(D-1)(D²+4) a. b. D(D²+4)² C. D² (D²-2D+5) d. D² + (D²-2D+5)
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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Question
![### Find the Annihilator of the Given Function(s)
Given Function:
\[ f(x) = x + e^x \cos(2x) \]
### Options:
a. \( D^2 (D - 1)(D^2 + 4) \)
b. \( D (D^2 + 4)^2 \)
c. \( D^2 (D^2 - 2D + 5) \)
d. \( D^2 + (D^2 - 2D + 5) \)
In the above expressions, \( D \) represents the differential operator \( \frac{d}{dx} \). The annihilator of the given function is determined by finding the differential operator that, when applied to the given function \( f(x) \), yields zero.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc59b3e01-f4fe-4ed0-a002-b05c91db4102%2Fd1c2b171-dfeb-4e05-b7e6-3ab86e40144d%2Fmn99h5f_processed.png&w=3840&q=75)
Transcribed Image Text:### Find the Annihilator of the Given Function(s)
Given Function:
\[ f(x) = x + e^x \cos(2x) \]
### Options:
a. \( D^2 (D - 1)(D^2 + 4) \)
b. \( D (D^2 + 4)^2 \)
c. \( D^2 (D^2 - 2D + 5) \)
d. \( D^2 + (D^2 - 2D + 5) \)
In the above expressions, \( D \) represents the differential operator \( \frac{d}{dx} \). The annihilator of the given function is determined by finding the differential operator that, when applied to the given function \( f(x) \), yields zero.
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