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Chapter 7 Solutions
Numerical Analysis
- Solve the following IVP 4y′′ + 24y′ + 37y = 0; y(π) = 1; y′(π) = 0arrow_forwardFigure attached below. 1. A bin of 5 transistors is known to contain 2 that are defective. The transistors are to be tested, one at atime, until the defective ones are identified. Denote by X the number of tests made until the first defectis identified and by Y the number of additional tests until the second defect is identified.(a) Find g(x|y) and draw a figure like Figure 4.3-1(b), depicting the conditional pmfs fory = 1,2,3,and 4.(b) Find h(y|x) and draw a figure like Figure 4.3-1(c), depicting the conditional pmfs forx = 1,2,3,and 4.(c) Find E [X|Y = 2] and Var (X|Y = 2)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
- . Solve the following initial value problem. -2 -2 6 -2 & y = ( ²2 √ ) Y, Y(0) = ( ² ) -Y dt -2 -1 -1arrow_forward2. Find the general solution of the first-order equation dy_ y? – 2ry drarrow_forward12.1: Problem 18 Previous Problem Problem List Next Problem Calculate ye dA, where R = [0,7] × [0, 4]. Answer:arrow_forward
- Problem 2 Show whether the two equations y₁ = 12e and y2 = 1.2e are independent or dependent using the Wronskian.arrow_forwardProblem 4.14. Suppose that a, b e Z, and that a, b + 0. Show that f(r, y) = ax + by is a Latin square.arrow_forwardThis is the fourth part of a four-part problem. If the given solutions ÿ₁ (t) = - [²2²], 2(0)-[¹7¹]. form a fundamental set (i.e., linearly independent set) of solutions for the initial value problem 21-² -21-2 y' = - [22 12t¹+2t 27 2t ¹-2t 2 [²], 2t | Ü‚ ÿ(5) — [34], t = t> 0, impose the given initial condition and find the unique solution to the initial value problem for t> 0. If the given solutions do not form a fundamental set, enter NONE in all of the answer blanks y(t) = (arrow_forward
- A Moving to another question will save this response. Question 11 Find the general solution of Xy" + xy -4y 0 where y(1) =0 and y (1) = 4arrow_forwardConsider the two tanks shown in the figure below. Assume that tank A contains 50 gallons of water in which 25 pounds of salt is dissolved. Suppose tank B contains 50 gallons of pure water. Liquid is pumped into and out of the tanks as indicated in the figure; the mixture exchanged between the two tanks and the liquid pumped out of tank B are assumed to be well stirred. We wish to construct a mathematical model that describes the number of pounds x₁(t) and x₂(t) of salt in tanks A and B, respectively, at time t. dx₁ dt dx₂ dt mixture 4 gal/min This system is described by the system of equations 1 50 2 2 25 2 dx₁ dt dx2 dt = = pure water 3 gal/min = 2 25 2 110 25 A + 1 1 mixture 1 gal/min B with initial conditions x₁(0) = 25, x₂(0) = 0 (see (3) and the surrounding discussion on mixtures on page 107). What is the system of differential equations if, instead of pure water, a brine solution containing 4 pounds of salt per gallon is pumped into tank A? mixture 3 gal/minarrow_forwardIf it is known that L {y′′(t)} = - 19s + 24 with y (0) = - 2 and y′ (0) = 4, then it can be ensured that: the answers are in the first attached imagearrow_forward
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage