a. Find the Laplace transform of the solution. Y(s) = L{y(t)} = 9/(s(s+1)) + e^-(4s)/(s+1) b. Obtain the solution y(t). y(t) = 9-9e^-t+ u(t-4)e^-(t-4) c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 4. y(t) = 9-9e^(-t) e^-(t-4) if 0 < t < 4, if 4 < t < ∞o.
a. Find the Laplace transform of the solution. Y(s) = L{y(t)} = 9/(s(s+1)) + e^-(4s)/(s+1) b. Obtain the solution y(t). y(t) = 9-9e^-t+ u(t-4)e^-(t-4) c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 4. y(t) = 9-9e^(-t) e^-(t-4) if 0 < t < 4, if 4 < t < ∞o.
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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Please help with the last part
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 = 9+8(t — 4), y(0) = 0.
a. Find the Laplace transform of the solution.
Y(s) = L{y(t)} = 9/(s(s+1)) + e^-(4s)/(s+1)
b. Obtain the solution y(t).
y(t)
=
9-9e^-t+ u(t-4)e^-(t-4)
c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 4.
y(t) =
{
9-9e^(-t)
e^-(t-4)
if 0 < t < 4,
if 4 < t < c.
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