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/+y=2+6(t-4), 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 = 4. if 0

/+y=2+6(t-4), 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 = 4. if 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=2+8(t- 4), y(0)%3D0. 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 = 4. if 0 <t < 4, y(t) = if 4 <t < oo.
Transcribed Image Text:y+y=2+8(t- 4), y(0)%3D0. 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 = 4. if 0 <t < 4, y(t) = if 4 <t < oo.
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