A particular solution of y" +9y=2cos(3x) + 3sin(3x) 1 xsin(3x)-xcos(3x) 2xcos (3x) -—-xsin (3x) xsin (3x)-3xcos(3x) a. b. C. d. e. -xcos(3x)-xsin (3x) 3× -xcos(3x)
A particular solution of y" +9y=2cos(3x) + 3sin(3x) 1 xsin(3x)-xcos(3x) 2xcos (3x) -—-xsin (3x) xsin (3x)-3xcos(3x) a. b. C. d. e. -xcos(3x)-xsin (3x) 3× -xcos(3x)
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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![**Differential Equation Problem and Solution Choices**
Given a differential equation:
\[ y'' + 9y = 2\cos(3x) + 3\sin(3x) \]
Determine which of the following options is a particular solution:
a. \( \frac{1}{3}x\sin(3x) - \frac{1}{2} x\cos(3x) \)
b. \( 2x\cos(3x) - \frac{1}{2} x\sin(3x) \)
c. \( \frac{1}{3} x\sin(3x) - 3x\cos(3x) \)
d. \( \frac{4}{3} x\cos(3x) - x\sin(3x) \)
e. \( \frac{2}{3} x\cos(3x) \)
**Select the correct answer:**
- \( \bigcirc \) a
- \( \bigcirc \) b
- \( \bigcirc \) c
- \( \bigcirc \) d
- \( \bigcirc \) e](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa72e8965-bd79-4464-a740-a72095a0be2c%2F88ca8766-09b7-416d-abed-3db4c2826fac%2F1zle19_processed.png&w=3840&q=75)
Transcribed Image Text:**Differential Equation Problem and Solution Choices**
Given a differential equation:
\[ y'' + 9y = 2\cos(3x) + 3\sin(3x) \]
Determine which of the following options is a particular solution:
a. \( \frac{1}{3}x\sin(3x) - \frac{1}{2} x\cos(3x) \)
b. \( 2x\cos(3x) - \frac{1}{2} x\sin(3x) \)
c. \( \frac{1}{3} x\sin(3x) - 3x\cos(3x) \)
d. \( \frac{4}{3} x\cos(3x) - x\sin(3x) \)
e. \( \frac{2}{3} x\cos(3x) \)
**Select the correct answer:**
- \( \bigcirc \) a
- \( \bigcirc \) b
- \( \bigcirc \) c
- \( \bigcirc \) d
- \( \bigcirc \) e
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