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- Find the Laplace transform of each given expression ( (1) 3 cos (2 t) e-2t + (t - 2)²

- Find the Laplace transform of each given expression ( (1) 3 cos (2 t) e-2t + (t - 2)²

Advanced Engineering Mathematics
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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**Problem A: Find the Laplace transform of each given expression.** (1) \( 3 \cos(2t) \, e^{-2t} + (t - 2)^2 \) (2) \( \ddot{x} + \dot{x} + t \sin(3t) + y \), where \( x = x(t) \), a function of time with initial conditions \( \dot{x}(0) = 1 \) and \( x(0) = 0 \). \( y = y(t) \), an unidentified function of time.
Transcribed Image Text:**Problem A: Find the Laplace transform of each given expression.** (1) \( 3 \cos(2t) \, e^{-2t} + (t - 2)^2 \) (2) \( \ddot{x} + \dot{x} + t \sin(3t) + y \), where \( x = x(t) \), a function of time with initial conditions \( \dot{x}(0) = 1 \) and \( x(0) = 0 \). \( y = y(t) \), an unidentified function of time.
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