Determine L '{F}. 4s +3 SF(s) – 5F(s) = 2 s+ 10s + 25
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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![**Determine** \( \mathcal{L}^{-1} \{ F \} \).
\[
sF(s) - 5F(s) = \frac{4s + 3}{s^2 + 10s + 25}
\]
[Click here to view the table of Laplace transforms.](#)
[Click here to view the table of properties of Laplace transforms.](#)
\[ \mathcal{L}^{-1} \{ F \} = \boxed{\phantom{\text{solution here}}} \]
**Explanation:**
The expression at the top is a Laplace transform equation, where \( F(s) \) is the Laplace transform of a function and \( s \) is the complex frequency variable. The task is to determine the inverse Laplace transform \( \mathcal{L}^{-1} \{ F \} \).
The right side of the equation shows a rational function, \( \frac{4s + 3}{s^2 + 10s + 25} \), which is typically decomposed to find the inverse transform using known Laplace transform pairs and properties. To fully solve this, one would typically perform partial fraction decomposition or identify a standard form from Laplace tables.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F502330eb-9fa1-41eb-8716-374edceb5782%2Fa2b7465f-9836-41c4-bd3b-96122fb3776c%2Fzyhz3bc_processed.png&w=3840&q=75)
Transcribed Image Text:**Determine** \( \mathcal{L}^{-1} \{ F \} \).
\[
sF(s) - 5F(s) = \frac{4s + 3}{s^2 + 10s + 25}
\]
[Click here to view the table of Laplace transforms.](#)
[Click here to view the table of properties of Laplace transforms.](#)
\[ \mathcal{L}^{-1} \{ F \} = \boxed{\phantom{\text{solution here}}} \]
**Explanation:**
The expression at the top is a Laplace transform equation, where \( F(s) \) is the Laplace transform of a function and \( s \) is the complex frequency variable. The task is to determine the inverse Laplace transform \( \mathcal{L}^{-1} \{ F \} \).
The right side of the equation shows a rational function, \( \frac{4s + 3}{s^2 + 10s + 25} \), which is typically decomposed to find the inverse transform using known Laplace transform pairs and properties. To fully solve this, one would typically perform partial fraction decomposition or identify a standard form from Laplace tables.
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