/+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

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.2: Partial Derivatives
Problem 30E
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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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