Consider the inhomogeneous differential equation du/dt = au + b, where a, b are constants. (a) Show
Question:
du/dt = au + b,
where a, b are constants.
(a) Show that u* = - b/a is a constant equilibrium solution.
(b) Solve the differential equation.
(c) Discuss the stability of the equilibrium solution u*.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 71% (14 reviews)
a If ut u ba then du dt 0 au b hence it is a ...View the full answer
Answered By
Bhartendu Goyal
Professional, Experienced, and Expert tutor who will provide speedy and to-the-point solutions. I have been teaching students for 5 years now in different subjects and it's truly been one of the most rewarding experiences of my life. I have also done one-to-one tutoring with 100+ students and help them achieve great subject knowledge. I have expertise in computer subjects like C++, C, Java, and Python programming and other computer Science related fields. Many of my student's parents message me that your lessons improved their children's grades and this is the best only thing you want as a tea...
3.00+
2+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Linear Algebra questions
-
Solve the differential equation. du/dt = 1 + t 4 /ut 2 + u 4 t 2
-
Consider again the differential equation dC/dt = 3( C) + 1 where is a constant. a. Solve the equation when C(0) = 0. b. Check your answer. c. Find C(0.4). d. After what time will the solution be...
-
Consider the differential equation dC/dt = 3( - C) + 1 where C is the concentration of some chemical in a cell, measured in moles per liter, and is a constant. a. What kind of differential equation...
-
Determine the degrees of freedom under the following conditions: (a) Tl-20 wt% Pb at 325 C and 400 C; (b) Tl-40 wt% Pb at 325 C and 400 C; (c) Tl-90 wt% Pb at 325 C and 400 C. Refer to the phase...
-
In 2002, Michael Sabol, doing business in the recording industry as Sound Farm Productions, applied to Morton Community Bank in Bloomington, Illinois, for a $58,000 loan to expand his business....
-
Complete the table: Type of electrolyte (strong, weak or Substance Name nonelectrolyte) NaCl HNO3 Mg(NO3)2 HF NaF NH4Cl Type of acid/base (strong or weak) - Reaction (s) in water (1) e e d e
-
The heat equation problem is solved using the explicit scheme (6.2). Find the maximum grid steps \(\Delta x\) and \(\Delta t\) at which the expected error of the solution is less than \(\sim...
-
The Road King Tire Company in Birmingham wants to monitor the quality of the tires it manufactures. Each day the company quality-control manager takes a sample of 100 tires, tests them, and...
-
Discuss the use of a balance sheet hedge and give examples of when such a hedge could be justified and how the desired results of such a hedge can alter the financial outcome for a business.
-
Consider the following two mutually exclusive projects. Whichever project you choose, if any, you require a 15 percent return on your investment. a. If you apply the payback criterion, which...
-
A bacteria colony grows according to the equation du/dt = 1.3 m. How long until the colony doubles? quadruples? If the initial population is 2, how long until the population reaches 2 million?
-
Use the method of Exercise 8.1.7 to solve the following initial value problems: (a) du/dt = 2u - 1, u(0) = 1, (b) du/dt = 5u + 15, u(1) = -3. (c) du/dt = -3u + 6. u(2) = -1.
-
Given that the argument of (z 1)/(z + 1) is 1/4, show that the locus of z in the Argand diagram is part of a circle of centre (0, 1) and radius 2.
-
Explain how attitudes vary across cultures.
-
Define personality and explain how personality differences affect individual behavior.
-
True or False. Some periodic functions cannot be replaced by a sum of harmonic functions.
-
Give conditions under which FFO may be negative during a period.
-
What must be determined before using correlation? Why is it essential?
-
Exercise 11 Garbage Data From Exercise 11 The weights (pounds) of discarded yard waste, as listed in Data Set 31 Garbage Weight in Appendix B. In use the Excel, or StatCrunch) or a TI-83 , 84 Plus...
-
During the month, services performed for customers on account amounted to $7,500 and collections from customers in payment of their accounts totaled $6,000. At the end of the month, the Accounts...
-
A manufacturer of precision measuring instruments claims that the standard deviation in the use of the instruments is at most 0.00002 millimeter. An analyst, who is unaware of the claim, uses the...
-
A biotechnology company produces a therapeutic drug whose concentration has a standard deviation of 4 grams per liter. A new method of producing this drug has been proposed, although some additional...
-
Consider the 40 observations collected on the number of nonconforming coil springs in production batches of size 50 given in Exercise 6-79. (a) Based on the description of the random variable and...
-
An employee received an option to purchase shares of a public company at $8 per share when the price of the stock was $10 per share. Ihe ($)/(_()) difterence creates a taxable benefit that is taxed...
-
The cost of goods sold for Frye Manufacturing in the year was $233,000. The January 1 Finished Goods Inventory balance was $31,700, and the December 31 Finished Goods Inventory balance was $25,200....
-
S Fill in the missing amounts in each of the eight case situations below. Each case is independent of the others. (Hint: One way to find the missing amounts would be to prepare a contribution format...
Study smarter with the SolutionInn App