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Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. "+ 4n'y 2n5(t - 1), y(0) = 0, v (0) - 0. a Find the Laplace transform of the solution. Y(s) L{(t)} b. Obtain the solution y(t). v(t) C. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t= 1 if 0st<1, y(t) if 1

Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. "+ 4n'y 2n5(t - 1), y(0) = 0, v (0) - 0. a Find the Laplace transform of the solution. Y(s) L{(t)} b. Obtain the solution y(t). v(t) C. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t= 1 if 0st<1, y(t) if 1

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. /"+ 4x'y = 2x5(t – 1), y(0) = 0, y (0) - 0. a. Find the Laplace transform of the solution. Y(s) = L{u(t}} b. Obtain the solution y(t). C. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t= 1. if 0<t<1, y(t) if 1<t<00.
Transcribed Image Text:Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. /"+ 4x'y = 2x5(t – 1), y(0) = 0, y (0) - 0. a. Find the Laplace transform of the solution. Y(s) = L{u(t}} b. Obtain the solution y(t). C. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t= 1. if 0<t<1, y(t) if 1<t<00.
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