7 & 8 PLEASE SHOW S
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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7 & 8 PLEASE SHOW STEPS
![Sure, here is the transcription of the provided text:
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**7.** The order of the linear, constant coefficient, homogeneous equation of least order that has
\[ y = 4e^{2x} - 5xe^{3x} + 4e^{-2x} \cos 4x + 5 \]
as a solution is:
- (a) 7
- (b) 6
- (c) 5
- (d) 4
- (e) None of the above.
**8.** The linear, constant coefficient, homogeneous equation of least order that has
\[ y = 2 \cos 3x + 5xe^{-x} \]
as a solution is:
- (a) \( y^{(5)} + 2y^{(4)} + 10y''' - 8y'' + 9y = 0 \)
- (b) \( y^{(4)} + 2y''' + 10y'' + 10y' + 9y = 0 \)
- (c) \( y^{(4)} + 2y''' + 10y'' + 18y' + 9y = 0 \)
- (d) \( y^{(4)} - 2y''' + 10y'' - 18y' + 9y = 0 \)
- (e) None of the above.
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Transcribed Image Text:Sure, here is the transcription of the provided text:
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**7.** The order of the linear, constant coefficient, homogeneous equation of least order that has
\[ y = 4e^{2x} - 5xe^{3x} + 4e^{-2x} \cos 4x + 5 \]
as a solution is:
- (a) 7
- (b) 6
- (c) 5
- (d) 4
- (e) None of the above.
**8.** The linear, constant coefficient, homogeneous equation of least order that has
\[ y = 2 \cos 3x + 5xe^{-x} \]
as a solution is:
- (a) \( y^{(5)} + 2y^{(4)} + 10y''' - 8y'' + 9y = 0 \)
- (b) \( y^{(4)} + 2y''' + 10y'' + 10y' + 9y = 0 \)
- (c) \( y^{(4)} + 2y''' + 10y'' + 18y' + 9y = 0 \)
- (d) \( y^{(4)} - 2y''' + 10y'' - 18y' + 9y = 0 \)
- (e) None of the above.
---
No graphs or diagrams are present on this page.
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