Laplace Transforms, Inverse Laplace Transforms, and Differential Equations: Using MATLAB - Document preview page 1

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Laplace Transforms, Inverse Laplace Transforms, and Differential Equations: Using MATLAB

This assignment provides a comprehensive analysis of Laplace transforms, inverse Laplace transforms, and differential equations, using MATLAB for verification.

Ava Martinez

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Laplace Transforms, Inverse Laplace Transforms, and Differential Equations: Using MATLAB - Page 1 preview image

Laplace Transforms, Inverse Laplace Transforms, and DifferentialEquations: A Comprehensive Analysis and Solution Verification UsingMATLABExercises:1.Find the Laplace transforms of the following functions by hand and verify results usingMatlab.General Laplace transform tableF(t)f(t)11𝑠𝑡𝑛𝑛!𝑠𝑛+1𝑒𝑎𝑡/𝑒−𝑎𝑡1𝑠−𝑎/1𝑠+𝑎sin𝑎𝑥𝑎𝑠2+𝑎2cos𝑎𝑥𝑠𝑠2+𝑎2y𝑦̃𝑦̕ ̕s𝑦̕−𝑦(0)y̋𝑠2𝑦̄−𝑠𝑦(0)−𝑦̕(0)

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1.𝑥(𝑡)=𝑡Handcalculationɭ[x (t)] =∫𝑥(𝑡)𝑒−𝑠𝑡𝑑𝑡∞0=∫𝑡𝑒−𝑠𝑡𝑑𝑡∞0Using differentiation by partsLet u=t and dv=𝑒−𝑠𝑡du=1 and also v will be v=−𝑒−𝑠𝑡𝑠x(t)=∫𝑡𝑒−𝑠𝑡𝑑𝑡∞0=−𝑡𝑒−𝑠𝑡𝑠ǀ0∞+1𝑠∫𝑒−𝑠𝑡𝑑𝑡∞0=1𝑠2𝑒−𝑠𝑥ǀ0∞=0--1𝑠2=1𝑠2Matlab codesymst% Declare a symbolic variable tF=laplace(t) %Calculate Laplace transform, store in F

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