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In an integro-differential equation, the unknown dependent variable x appears within an integral, and its derivative dx/dt also appears. Consider the following initial value problem, defined for t > 0: dx dt +4 [*x(t - w) e -4w dw = 9, x(0) = 0. 0 Use convolution and Laplace transforms to find the Laplace transform of the solution. X(s) = L {x(t)} = help (formulas) Obtain the solution x(t). x(t) = help (formulas) Book: Section 6.3 of Notes on Diffy Qs

In an integro-differential equation, the unknown dependent variable x appears within an integral, and its derivative dx/dt also appears. Consider the following initial value problem, defined for t > 0: dx dt +4 [*x(t - w) e -4w dw = 9, x(0) = 0. 0 Use convolution and Laplace transforms to find the Laplace transform of the solution. X(s) = L {x(t)} = help (formulas) Obtain the solution x(t). x(t) = help (formulas) Book: Section 6.3 of Notes on Diffy Qs

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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In an integro-differential equation, the unknown dependent variable x appears within an integral, and its derivative dx/dt also appears. Consider the following initial value problem, defined for t > 0: dx dt +4 [*x(t - w) e -4w dw = 9, x(0) = 0. 0 Use convolution and Laplace transforms to find the Laplace transform of the solution. X(s) = L {x(t)} = help (formulas) Obtain the solution x(t). x(t) = help (formulas) Book: Section 6.3 of Notes on Diffy Qs
Transcribed Image Text:In an integro-differential equation, the unknown dependent variable x appears within an integral, and its derivative dx/dt also appears. Consider the following initial value problem, defined for t > 0: dx dt +4 [*x(t - w) e -4w dw = 9, x(0) = 0. 0 Use convolution and Laplace transforms to find the Laplace transform of the solution. X(s) = L {x(t)} = help (formulas) Obtain the solution x(t). x(t) = help (formulas) Book: Section 6.3 of Notes on Diffy Qs
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