Advanced Engineering Mathematics
6th Edition
ISBN: 9781284105902
Author: Dennis G. Zill
Publisher: Jones & Bartlett Learning
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Chapter 6.3, Problem 7E
To determine
The approximated value of
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1. Find a general solution for y" + 4y = x2 by method of undetermined
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Problem 2
a. If y(t) = x₁(1) * x₂ (t)= e(+3)u(t+3), find z(t) = x₁(1+4)*x₂(t-5).
b. If x₁ (1) = 8e²¹u(-1) and x₂(t)=0.258(1-4), find y(t)=x (t)* x₂(t).
c. If x₁(t) = 4e-2¹u(t) and x₂ (1)= u(1), find y(t) = x₁(1) * x₂ (1)
Chapter 6 Solutions
Advanced Engineering Mathematics
Ch. 6.1 - Prob. 1ECh. 6.1 - Prob. 2ECh. 6.1 - Prob. 3ECh. 6.1 - Prob. 4ECh. 6.1 - Prob. 5ECh. 6.1 - Prob. 6ECh. 6.1 - Prob. 7ECh. 6.1 - Prob. 8ECh. 6.1 - Prob. 9ECh. 6.1 - Prob. 10E
Ch. 6.1 - Prob. 11ECh. 6.1 - Prob. 13ECh. 6.1 - Prob. 14ECh. 6.1 - Prob. 15ECh. 6.1 - Prob. 16ECh. 6.1 - Prob. 17ECh. 6.1 - Prob. 18ECh. 6.1 - Prob. 19ECh. 6.1 - Prob. 20ECh. 6.2 - Prob. 3ECh. 6.2 - Prob. 4ECh. 6.2 - Prob. 5ECh. 6.2 - Prob. 6ECh. 6.2 - Prob. 7ECh. 6.2 - Prob. 8ECh. 6.2 - Prob. 9ECh. 6.2 - Prob. 10ECh. 6.2 - Prob. 11ECh. 6.2 - Prob. 12ECh. 6.2 - Prob. 13ECh. 6.2 - Prob. 16ECh. 6.2 - Prob. 17ECh. 6.2 - Prob. 18ECh. 6.2 - Prob. 19ECh. 6.2 - Prob. 20ECh. 6.3 - Prob. 1ECh. 6.3 - Prob. 3ECh. 6.3 - Prob. 4ECh. 6.3 - Prob. 5ECh. 6.3 - Prob. 6ECh. 6.3 - Prob. 7ECh. 6.3 - Prob. 8ECh. 6.4 - Prob. 1ECh. 6.4 - Prob. 2ECh. 6.4 - Prob. 3ECh. 6.4 - Prob. 4ECh. 6.4 - Prob. 5ECh. 6.5 - Prob. 1ECh. 6.5 - Prob. 2ECh. 6.5 - Prob. 3ECh. 6.5 - Prob. 4ECh. 6.5 - Prob. 5ECh. 6.5 - Prob. 6ECh. 6.5 - Prob. 7ECh. 6.5 - Prob. 8ECh. 6.5 - Prob. 9ECh. 6.5 - Prob. 10ECh. 6.5 - Prob. 11ECh. 6.5 - Prob. 12ECh. 6.5 - Prob. 13ECh. 6 - Prob. 1CRCh. 6 - Prob. 2CRCh. 6 - Prob. 3CRCh. 6 - Prob. 4CRCh. 6 - Prob. 5CRCh. 6 - Prob. 6CRCh. 6 - Prob. 7CRCh. 6 - Prob. 8CR
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- 2. Assume that the population of a colony of Brazilian fire ants, P, is described by the function P(t)= \t+1·e-0.5t is measured in days (t=0 when one begins monitoring the population). (a) Find the initial population, P(0) (include units with your answer). +10t +200. The population here is measured in thousands of individuals, and time, t, %3D %3D (b) Find P (t). (c) Evaluate P (0) (include units with your answer).arrow_forward1. Consider the accidental death model illustrated below. Let μ Alive 0 Dead-Accident Dead-Other Causes 2 10-5 and μ 7.4 x 10-5 and c = 1.05. Let = max (5,7). Calculate: (i) TP 00 (ii) po (iii)+p 01 A+ Bc for all x where A = 5 x 10-4, B =arrow_forwardIn Problems 1 through 6, express the solution of the given ini- tial value problem as a sum of two oscillations as in Eq. (8). Throughout, primes denote derivatives with respect to time t. In Problems 1–4, graph the solution function x(t) in such a way that you can identify and label (as in Fig. 3.6.2) its pe- riod. 3. x" + 100x = 225 cos 5t + 300 sin 5t; x(0) = 375, x'(0) = 0arrow_forward
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- In Problems 1 through 6, express the solution of the given ini- tial value problem as a sum of two oscillations as in Eq. (8). Throughout, primes denote derivatives with respect to time t. In Problems 1–4, graph the solution function x(t) in such a way that you can identify and label (as in Fig. 3.6.2) its pe- riod. 1. x" + 9x = 10 cos 2t; x(0) = x'(0) = 0arrow_forward2. In problems 1-5 verify that the indicated function y = Ø(x) is an explicit solution of the given DEs: 4. y" – 2y' – 3y = 0; + 2xy = 4x3; dy 5. dx y = ce-* + c,e3x. y = 2(x2 – 1) + ce**.arrow_forwardProblem 4.2 (Textbook: Figure 2.5 on P84): Hypothetically, a patient is diagnosed to have P, coronavirus at time t = 0 and these viruses grow subsequently (nobody really knows the truth but we assume) according to = -aP(M – P) where P(t) is the number of the cells at time t while a and M are two given positive constants. The patient will die when the number of bugs approaches infinity. Consider the case Po > M, find the time the patient has left to live, timed from t = 0. Your result is a formula with the given parameters Pg, M, a. For a more concrete example, please set P, = 1984, M = 1000, a = 1. Compute the patient's survival time. Never mind if the number is small when you use , a = 1 as no unit is given. If you insist having a "reasonable" number, I set a = 10* for which the time unit is week. Either number you use is correct for your HW solution.arrow_forward
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