7 1 t) = L-1 2 %3D %3D 4 - 2)

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

Objective: Find the inverse Laplace transform \( f(t) \) of the given function \( F(s) \).

Given:
\[ f(t) = \mathcal{L}^{-1} \{ F(s) \} \]
Where:
\[ F(s) = \frac{2}{s^2} - \frac{7}{s-4} \]

Approach:
- Identify each term in the function \( F(s) \).
- Use inverse Laplace transform properties to find \( f(t) \).

Components:
1. For \( \frac{2}{s^2} \)
2. For \( \frac{7}{s-4} \)

You will need to apply the inverse Laplace transform rules, such as basic transforms for standard forms and shifting theorems, if applicable, to find \( f(t) \).
Transcribed Image Text:**Problem: Finding the Inverse Laplace Transform** Objective: Find the inverse Laplace transform \( f(t) \) of the given function \( F(s) \). Given: \[ f(t) = \mathcal{L}^{-1} \{ F(s) \} \] Where: \[ F(s) = \frac{2}{s^2} - \frac{7}{s-4} \] Approach: - Identify each term in the function \( F(s) \). - Use inverse Laplace transform properties to find \( f(t) \). Components: 1. For \( \frac{2}{s^2} \) 2. For \( \frac{7}{s-4} \) You will need to apply the inverse Laplace transform rules, such as basic transforms for standard forms and shifting theorems, if applicable, to find \( f(t) \).
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