In each of Problems 1 through 26:(a) Find the general solution in terms of real functions.(b) From the roots of the characteristic equation, determinewhether each critical point of the corresponding dynamicalsystem is asymptotically stable, stable, or unstable, and clas-sify it as to type.(c) Use the general solution obtained in part (a) to find a two-parameter family of trajectories x = x₁i + x₂j = yi+y'j ofthe corresponding dynamical system. Then sketch by hand,or use a computer, to draw a phase portrait, including anystraight-line orbits, from this family of trajectories.1. y" + 2y' - 3y = 0

Given Information:The differential equation is .Objective:a) Find the general solution.b) Analyze…

Answered: In each of Problems 1 through 26: (a)…

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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Harry Wilson, a mechanical engineer at Lehigh manufacturing, has found that the anticipated profitability of a newly developed motion detector for its popu- lar home security device product line can be estimated as follows: PW = 40.28W (2X - 11) – 77,860 where W is the number of units produced and sold and X is the sales price per unit. Harry also found that W parameter value could occur anywhere over a range of 1,000 to 6,000 units and the X parameter value anywhere between $20 and $40 per unit. Suppose both W and X are statistically independent continuous random variables with the following means and variances: E[W} = 3,500, V[W] = 2,083,333 %3D E[X] 30, V[X] = 33. What is the variance of PW? (a) 2.2309× 10" (c) 2.769 x 10° (b) 4.4618 × 10" (d) 1.118549 x 1013
1. Solve for the orthogonal trajectories. y2 =x2 - cx3 2. A body at unknown temperature is placed in a room which is held at a constant temperature of 30 °F. If after 10 minutes the temperature of the body is 0°F and after 20 minutes, the temperature of the body is 15°F, find the unknown initial temperature
(3) The approximate enrollment, in millions between the years 2009 and 2018 is provided by a linear model Y3D0.2309x+18.35 Where x-0 corresponds to 2009, x=1 to 2010, and so on, and y is in millions of students. Use the model determine projected enrollment for the year 2014. 近
The weekly demand for the Pulsar 40-in. high-definition television is given by the demand equation p = −0.05x + 600 (0 ≤ x ≤ 12, 000) where p denotes the wholesale unit price in dollars and x denotes the quantity demanded. The weekly total cost function associated with manufacturing these sets is given by C(x) = 0.000002x 3 − 0.03x 2 + 250x + 80, 000 where C(x) denotes the total cost incurred in producing x sets. 4. Give the profit that corresponds to your production level from part (3). If necessary, round profit to the nearest cent.
The weekly demand for the Pulsar 40-in. high-definition television is given by the demand equation p = −0.05x + 600 (0 ≤ x ≤ 12, 000) where p denotes the wholesale unit price in dollars and x denotes the quantity demanded. The weekly total cost function associated with manufacturing these sets is given by C(x) = 0.000002x 3 − 0.03x 2 + 250x + 80, 000 where C(x) denotes the total cost incurred in producing x sets. 2. Find a profit function P(x) that gives Pulsar’s weekly revenue in dollars when x sets are sold. Write that function out explicitly.
The weekly demand for the Pulsar 40-in. high-definition television is given by the demand equation p = −0.05x + 600 (0 ≤ x ≤ 12, 000) where p denotes the wholesale unit price in dollars and x denotes the quantity demanded. The weekly total cost function associated with manufacturing these sets is given by C(x) = 0.000002x 3 − 0.03x 2 + 250x + 80, 000 where C(x) denotes the total cost incurred in producing x sets. 1. Find a revenue function R(x) that gives Pulsar’s weekly revenue in dollars when x sets are sold. Write that function out explicitly. 2. Find a profit function P(x) that gives Pulsar’s weekly revenue in dollars when x sets are sold. Write that function out explicitly. 3. Determine the level of production x (with 0 ≤ x ≤ 12, 000) that will yield the maximum profit for the manufacturer. Make sure to show that this x corresponds to an absolute maximum of profit using a strategy we have discussed. You may find it useful to use the quadratic formula. If necessary, round units to…
The weekly demand for the Pulsar 40-in. high-definition television is given by the demand equation p = −0.05x + 600 (0 ≤ x ≤ 12, 000) where p denotes the wholesale unit price in dollars and x denotes the quantity demanded. The weekly total cost function associated with manufacturing these sets is given by C(x) = 0.000002x 3 − 0.03x 2 + 250x + 80, 000 where C(x) denotes the total cost incurred in producing x sets. 3. Determine the level of production x (with 0 ≤ x ≤ 12, 000) that will yield the maximum profit for the manufacturer. Make sure to show that this x corresponds to an absolute maximum of profit using a strategy we have discussed. You may find it useful to use the quadratic formula. If necessary, round units to the nearest whole television set at the end of your calculations.
I. We need to enclose a rectangular field with a fence. We have 500 ft. of fencing material and a building is on one side of the field and so won't need any fencing. Determine the dimensions of the field that will enclose the largest area. 2. Find two positive numbers whose product is 750 and for which the sum of one and 10 times the other is a minimum. (Apply the 2d derivative of the formulated equation to check if the point x is minimized) 3. We want to construct a box with a square base and we only have 10 m² of material to use in construction of the box. If all the material is used in the construction process determine the maximum volume that the box can have. 4. We have a piece of cardboard that is 14 inches by 10 inches and we're going to cut out the corners as shown below and fold up the sides to form a box, also shown below. Determine the height of the box that will give a maximum volume.
This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise 600,000 The cost C for ordering and storing x units is C = 3x + What order size will produce a minimum cost? Step 1 To find the size of order that will produce a minimum cost, begin by finding the derivative of 600,000 С 3D Зх + dC C' = dx Therefore, we can find the second derivative as follows. dC' C" dx
This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise 800,000 The cost C for ordering and storing x units is C = 9x + What order size will produce a minimum cost? Step 1 To find the size of order that will produce a minimum cost, begin by finding the derivative of C = 9x + 800,000 C' = dx Therefore, we can find the second derivative as follows. dC" C" = dx Submit Skip (you cannot come back)
IT Find the orthogonal trajectories to the given curve -3x Y= 3x-1 + Ce C
8. (a) For (x) = Vx, give the linearization at a= 25. (b) Use your answer from part a to approxi- mate v27. Show your work; no credit for simply punching v27 into your calculator! %3D 8a.

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