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sec 6.4: Problem 5 Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. x” – 6x′ = d(t − 1), x(0) = 7, x'(0) = 0. Find the Laplace transform of the solution. X(s) = L {x(t)} = ☐ help (formulas) Obtain the solution x(t). x(t) = help (formulas) Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 1. if 0

sec 6.4: Problem 5 Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. x” – 6x′ = d(t − 1), x(0) = 7, x'(0) = 0. Find the Laplace transform of the solution. X(s) = L {x(t)} = ☐ help (formulas) Obtain the solution x(t). x(t) = help (formulas) Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 1. 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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sec 6.4: Problem 5 Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. x” – 6x′ = d(t − 1), x(0) = 7, x'(0) = 0. Find the Laplace transform of the solution. X(s) = L {x(t)} = ☐ help (formulas) Obtain the solution x(t). x(t) = help (formulas) Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 1. if 0<t<1, x(t) help (formulas) if 1<t<∞. Book: Section 6.4 of Notes on Diffy Qs
Transcribed Image Text:sec 6.4: Problem 5 Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. x” – 6x′ = d(t − 1), x(0) = 7, x'(0) = 0. Find the Laplace transform of the solution. X(s) = L {x(t)} = ☐ help (formulas) Obtain the solution x(t). x(t) = help (formulas) Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 1. if 0<t<1, x(t) help (formulas) if 1<t<∞. Book: Section 6.4 of Notes on Diffy Qs
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