Consider the following integral equation, so called because the unknown dependent variable, y, appears within an integral: t ['sir sin(6(t – w)) y(w) dw = 8t². This equation is defined for t ≥ 0.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 77E
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Consider the following integral equation, so called because
the unknown dependent variable, y, appears within an
integral:
t
l' sin
sin(6(t – w)) y(w) dw = 8t².
This equation is defined for t≥ 0.
a. Use convolution and Laplace transforms to find the
Laplace transform of the solution.
Y(s) = L{y(t)} =
b. Obtain the solution y(t).
y(t) =
Transcribed Image Text:Consider the following integral equation, so called because the unknown dependent variable, y, appears within an integral: t l' sin sin(6(t – w)) y(w) dw = 8t². This equation is defined for t≥ 0. a. Use convolution and Laplace transforms to find the Laplace transform of the solution. Y(s) = L{y(t)} = b. Obtain the solution y(t). y(t) =
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