If a, b, and c are all positive constants and y(x) is a solution of the differential
Question:
If a, b, and c are all positive constants and y(x) is a solution of the differential equation ay'' + by' + cy = 0, show that limx→∞ y(x) = 0.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 70% (10 reviews)
The auxiliary equation is ar br c 0 If b 4ac 0 then any solution is of the form yx ce wher...View the full answer
Answered By
GERALD KAMAU
non-plagiarism work, timely work and A++ work
4.40+
6+ Reviews
11+ Question Solved
Related Book For
Question Posted:
Students also viewed these Mathematics questions
-
Consider the boundary-value problem y'' - 2y' + 2y = 0, y(a) = c, y(b) = d. (a) If this problem has a unique solution, how are a and b related? (b) If this problem has no solution, how are a, b, c,...
-
Solve the differential equation or initial-value problem using the method of undetermined coefficients. y'' - 4y' + 5y = e -x
-
Graph the particular solution and several other solutions. What characteristics do these solutions have in common? y'' + 4y = e -x
-
A puck on a horizontal, frictionless surface is attached to a string that passes through a hole in the surface, as shown in FIGURE 11-52. As the puck rotates about the hole, the string is pulled...
-
Convert the following names into the corresponding molecular structures. After doing so, check to see if the name of each molecule as given here is in accord with the IUPAC system of nomenclature. If...
-
A picnic basket contains five jars: one of marmalade, two of peanut butter and two of jam. A boy removes one jar at random from the basket and then his sister takes two jars, both selected at random....
-
True or False: If \(E R R>M A R R\), then MIRR \(>\) MARR.
-
Lopez Corporation incurred the following costs while manufacturing its product. Work in process inventory was $12,000 at January 1 and $15,500 at December 31. Finished goods inventory was $60,000 at...
-
4. Consider a quantum system Q described by a Hilbert space H. (a) Suppose we are given a subspace Ho of H and a linear map from kets in Ho to others in h. That is, Vo)), in a linear way. This map...
-
A group of Northeastern University researchers developed a new method for ranking the total driving performance of golfers on the Professional Golf Association (PGA) tour (The Sport Journal Winter...
-
Let L be a nonzero real number. (a) Show that the boundary-value problem y'' + y = 0, y(0) = 0, y(L) = 0 has only the trivial solution y = 0 for the cases = 0 and < 0. (b) For the case > 0, find...
-
Solve the differential equation or initial-value problem using the method of undetermined coefficients. y'' + 2y' - 8y = 1 - 2x 2
-
Patty Bayan is a single taxpayer living at 543 Space Drive, Houston, TX 77099. Her Social Security number is 466-33-1234. For 2014, Patty has no dependents, and her W-2 from her job at a local...
-
Claytor Lake dam has a length of 348m and a maximum water depth of 35m (a) What is the pressure at the water surface? (b) Calculate the pressure at the maximum depth. (c) Calcuate the maximum force...
-
VI. Accounting Principles and Assumptions. Answer the following questions. Identify the accounting principles or assumptions that are applied, and briefly explain. (6%) 1) On December 1, Spring, a...
-
(a) A company plans to sell 1,08,000 units of a certain product line in the first quarter, 1,20,000 units in second quarter, 1,32,000 units in third quarter, 1,56,000 units in fourth quarter and...
-
At 25 C, 1.00 L of liquid mercury contains 4.05 x 10 22 atoms. Find the number of moles of mercury atoms.
-
(a) A car has an initial speed of 25m/s and a constant deceleration of 3m/s. Determine the velocity of the car when t-4s. What is the displacement of the car during the 4s time interval? How much...
-
How can St. Joseph ensure that it uses physical ability test in a nondiscriminatory manner?
-
If a force of F = 50 Ib is applied to the pads at A and C, determine the smallest dimension d required for equilibrium if the spring has an unstretched length of 1 ft. B 1 ft 1 ft F k = 15016/fr 1ft...
-
Cosmic rays hit an organism at a rate of 1.2/day and are monitored for one week. Find , the expectation, the variance, the standard deviation, the coefficient of variation, and the mode of Poisson...
-
Dandelion seeds fall into a garden with area 4.0 m2 with an average density of 0.9/m2. Find , the expectation, the variance, the standard deviation, the coefficient of variation, and the mode of...
-
Find the probabilities of the following events. 1. Molecules leave a cell at rate = 0.3/s. What is the probability that exactly two have left by the end of the third second? 2. Phone calls arrive at...
-
Write the feature of Super's Career Development Assessment and Counseling (C-DAC) system?
-
Describe one type of role-play technique you could use in a specific group setting. Explain who would benefit from this technique and why. Toseland, R. W., & Rivas, R. F. (2017). An introduction to...
-
Suppose that a manager is following a base stock policy where the optimal inventory position is 10. Assume the component lead time is 2 days. At the end of day 1, there is no ordered units yet to be...
Study smarter with the SolutionInn App