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
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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
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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