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Laplace Transforms, Inverse Laplace Transforms, and Differential Equations: Analytical and MATLAB Verification

This assignment focuses on the application of Laplace transforms and differential equations, verified through analytical and MATLAB methods.

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    Laplace Transforms, Inverse Laplace Transforms, and Differential Equations: Analytical and MATLAB Verification Exercises: 1. Find the Laplace transforms of the following functions by hand and verify results using Matlab. 1. π‘₯ ( 𝑑 ) = 𝑑 Sol: Matlab code to verify results F=laplace(t) pretty(F)

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    2. 𝑓 ( 𝑑 ) = βˆ’ 1 . 25 + 3 . 5 𝑑 𝑒 βˆ’ 2 𝑑 + 1 . 25 𝑒 βˆ’ 2 𝑑 Sol Matlab code to verify results F=laplace( βˆ’ 1 . 25 + 3 . 5 βˆ— 𝑑 βˆ— 𝑒 βˆ’ 2 𝑑 + 1 . 25 βˆ— 𝑒 ^ ( βˆ’ 2 𝑑 ) ) pretty(F)

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