Find the given inverse Laplace transform. 1 € - ¹3 s² +45+5 a. e²¹ sin(t) b. e-2¹ sin(t) C. e-2¹cos(2t) d. e-²'sin(2t)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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**Finding the Inverse Laplace Transform**

Find the given inverse Laplace transform:

\[ \mathcal{L}^{-1} \left\{ \frac{1}{s^2 + 4s + 5} \right\} \]

a. \( e^{2t} \sin(t) \)

b. \( e^{-2t} \sin(t) \)

c. \( e^{-2t} \cos(2t) \)

d. \( e^{-2t} \sin(2t) \)

**Answer Choices:**

- \( \circ \) a
- \( \circ \) b
- \( \circ \) c
- \( \circ \) d
Transcribed Image Text:**Finding the Inverse Laplace Transform** Find the given inverse Laplace transform: \[ \mathcal{L}^{-1} \left\{ \frac{1}{s^2 + 4s + 5} \right\} \] a. \( e^{2t} \sin(t) \) b. \( e^{-2t} \sin(t) \) c. \( e^{-2t} \cos(2t) \) d. \( e^{-2t} \sin(2t) \) **Answer Choices:** - \( \circ \) a - \( \circ \) b - \( \circ \) c - \( \circ \) d
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