Question: Consider the inhomogeneous differential equation du/dt = au + b, where a, b are constants. (a) Show that u* = - b/a is a constant

Consider the inhomogeneous differential equation
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*.

Step by Step Solution

★★★★★

3.34 Rating (163 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a If ut u ba then du dt 0 au b hence it is a ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

952-M-L-A-E (2592).docx

120 KBs Word File

Students Have Also Explored These Related 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...

Please answer both question (a) (b) (c) in this problem 6. (20 points) Consider the stochastic differential equation dx, = 0(u-X,)dt+odw, Xo = xo, (0.1) where e > 0, xo, u R and o >0 are constants....

Math232 : answer with process and detail plz, due on Tuesday 3/9 'F'F9258 8H31EI Elf: '6' 89%EJ' n ilearn.mq.edu.au MATH232: Assignment 1. (Due by 11:55 pm on Tuesday, September 3, week 6) Part A...

- Consider the partial differential equation and boundary conditions provided below: au k at dx2 Assuming the initial and boundary conditions are: -(0,t) = B. u(L, 1) = 1(x,0) = f(x) derive the...

SOLVE Questions 1-5: PLEASE AND THANK YOU 1: What is the difference between homogenous and non-homogenous differential equation? Write an example for each and solve it. 2: What is the main formula to...

1 A mathematical model for the forces on a car suspension system The goal of this project is to describe one of the ways in which resonance phenomena. appear in the "real world\" and to use second...

10 Green's functions for PDEs In this final chapter we will apply the idea of Green's functions to PDEs, enabling us to solve the wave equation, diffusion equation and Laplace equation in unbounded...

Fraction of hosts infected Case Study 2 Hosts, Parasites, and Time-Travel 0.8 0.6 0.4 0.2 0 Past Contemporary Future Time Figure \u00031 Horizontal axis is the time from which the parasite was taken,...

In a 100 mL volumetric flask, accurately prepare an approximately 0.02 M aqueous benzoic acid by dissolving the 0.01606g of benzoic acid in about 20 mL and diluting In a separatory funnel place 25 mL...

a. Explain how a cut in corporate income taxes would create jobs and have little impact on budget revenue. Draw a graph to illustrate the effect. b. Explain why the effect of corporate tax cuts would...

What is the slop of the security market line ( SML )

Briefly describe whether each of the following statements describes a change in supply or a change in the quantity supplied. a To take advantage of higher prices for umbrellas in winter, Shelter...

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...

1. If the current 180 day inter-bank Eurodollar rate is 15% (all rates are started on an annualized basis, and next periods LIBOR is 13%, then a Eurocurrency loan priced at LIBOR plus 1% will cost...

Paints makes and sells paint to home improvement stores. Jamison's only plant can produce up to 12 million cans of paint per year. Current annual production is 10 million cans. Fixed manufacturing,...

Not sure how to answer this next part. Thank you for the help :) 1. Prepare the adjusting entry to record bad debts under each separate assumption a. Bad debts are estimated to be 3% of credit sales....