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Consider the following initial value problem, in which an input of large amplitude an short duration has been idealized as a delta function. y' + y = 1 + 8(t – 5), a. Find the Laplace transform of the solution. Y(s) = L{y(t)} 1/(s(s+1))+e^(-5s)/(s+1) b. Obtain the solution y(t). 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 = = 5. 1-e^(-t) y(0) = 0. 1-e^(-t)+e^(-(t-5)) if 0 < t < 5, if 5 < t < c.

Consider the following initial value problem, in which an input of large amplitude an short duration has been idealized as a delta function. y' + y = 1 + 8(t – 5), a. Find the Laplace transform of the solution. Y(s) = L{y(t)} 1/(s(s+1))+e^(-5s)/(s+1) b. Obtain the solution y(t). 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 = = 5. 1-e^(-t) y(0) = 0. 1-e^(-t)+e^(-(t-5)) if 0 < t < 5, if 5 < t < c.

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 = 1 + 8(t – 5), a. Find the Laplace transform of the solution. Y(s) = L{y(t)} 1/(s(s+1))+e^(-5s)/(s+1) b. Obtain the solution y(t). 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 - = 1-e^(-t) y(0) = 0. 1-e^(-t)+e^(-(t-5)) 5. if 0 ≤ t < 5, if 5 < t <∞.
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 = 1 + 8(t – 5), a. Find the Laplace transform of the solution. Y(s) = L{y(t)} 1/(s(s+1))+e^(-5s)/(s+1) b. Obtain the solution y(t). 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 - = 1-e^(-t) y(0) = 0. 1-e^(-t)+e^(-(t-5)) 5. if 0 ≤ t < 5, if 5 < t <∞.
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