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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. y + y = 3 + 8(t – 2), y(0) = 0. a. Find the Laplace transform of the solution. Y(s) = L{y(t)} = = b. Obtain the solution y(t). y(t) = c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 2. y(t) = { if 0 ≤ t < 2, if 2 < t < 0.

Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. y + y = 3 + 8(t – 2), y(0) = 0. a. Find the Laplace transform of the solution. Y(s) = L{y(t)} = = b. Obtain the solution y(t). y(t) = c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 2. y(t) = { if 0 ≤ t < 2, if 2 < t < 0.

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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Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. y' +y = 3 + 8(t – 2), y(0) = 0. a. Find the Laplace transform of the solution. Y(s) = L{y(t)} = = b. Obtain the solution y(t). y(t) = c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 2. y(t) = { if 0 < t < 2, if 2 < t < 0.
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. y' +y = 3 + 8(t – 2), y(0) = 0. a. Find the Laplace transform of the solution. Y(s) = L{y(t)} = = b. Obtain the solution y(t). y(t) = c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 2. y(t) = { if 0 < t < 2, if 2 < t < 0.
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