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Consider the following initial value problem: x(0) = 2, x' (0) = -1. Using X for the Laplace transform of x(t), i.e., X = L{x(t)}, find the equation you get by taking the Laplace transform of the differential equation and solve for x" 5x' 14x = sin(8t),

Consider the following initial value problem: x(0) = 2, x' (0) = -1. Using X for the Laplace transform of x(t), i.e., X = L{x(t)}, find the equation you get by taking the Laplace transform of the differential equation and solve for x" 5x' 14x = sin(8t),

Calculus For The Life Sciences
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.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 5E
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Consider the following initial value problem: x" 5x' - 14x = sin(8t), x(0) = 2, x'(0) = -1. Using X for the Laplace transform of x(t), i.e., X = L{x(t)}, find the equation you get by taking the Laplace transform of the differential equation and solve for X(s) = (2s^(3)-11s^(2)+128s-632)/((s^(2)+64)(s^(2)-5s-14)) help (formulas)
Transcribed Image Text:Consider the following initial value problem: x" 5x' - 14x = sin(8t), x(0) = 2, x'(0) = -1. Using X for the Laplace transform of x(t), i.e., X = L{x(t)}, find the equation you get by taking the Laplace transform of the differential equation and solve for X(s) = (2s^(3)-11s^(2)+128s-632)/((s^(2)+64)(s^(2)-5s-14)) help (formulas)
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