Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform e-s s(s+1) a. (1+e¹)u(t-1) b. (1-te¹)u(t-1) c. (1-e¹)u(t-1) d. (1-e¹)u(t-1)
Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform e-s s(s+1) a. (1+e¹)u(t-1) b. (1-te¹)u(t-1) c. (1-e¹)u(t-1) d. (1-e¹)u(t-1)
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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![**Inverse Laplace Transform Problem**
**Problem Statement:**
Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform.
\[ \mathcal{L}^{-1} \left( \frac{e^{-s}}{s(s+1)} \right) \]
**Options:**
a. \((1 + e^{1-t})u(t-1)\)
b. \((1 - te^{t})u(t-1)\)
c. \((1 - e^{1-t})u(t-1)\)
d. \((1 - e^{-1})u(t-1)\)
**Multiple Choice Answers:**
- ○ a
- ○ b
- ○ c
- ○ d](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8d2af6b8-35d3-4327-94c1-a05ff77beaf0%2F4d401f4c-ac8f-4b23-9629-38ea9bd04557%2Fi6qvey_processed.png&w=3840&q=75)
Transcribed Image Text:**Inverse Laplace Transform Problem**
**Problem Statement:**
Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform.
\[ \mathcal{L}^{-1} \left( \frac{e^{-s}}{s(s+1)} \right) \]
**Options:**
a. \((1 + e^{1-t})u(t-1)\)
b. \((1 - te^{t})u(t-1)\)
c. \((1 - e^{1-t})u(t-1)\)
d. \((1 - e^{-1})u(t-1)\)
**Multiple Choice Answers:**
- ○ a
- ○ b
- ○ c
- ○ d
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