Differential Equations with Boundary-Value Problems (MindTap Course List)
9th Edition
ISBN: 9781305965799
Author: Dennis G. Zill
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Question
Chapter 10.2, Problem 22E
To determine
To show: The critical point
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Determine the type of the critical point (I1,I2) =
of the nonlinear
system
X = f(x), where x=
f(x) =
-312+21,22]
Source Node.
Source Spiral.
None of the options displayed
Saddle Node.
Sink Spiral.
Center.
There is no way to determine the type of the critical point with the information
provided.
Sink Node
Check if the system with the following input-output relation are i) Memory/memory lessii) Causal /non-causala) y(t) =x^4(t) + x(t-3)
b) y(n) = x(n-2) +3y(n-1)c) y(t) = A cos (2ㅠft + x(t))
nt) Consider the discrete-time dynamical system x+1 = 0.57x, +0.
What is the equilibrium for this system?
What is the updating function rule f(x)?
What is the derivative of the updating function?
Is the equilibrium stable, unstable, or neither?
1.4
Chapter 10 Solutions
Differential Equations with Boundary-Value Problems (MindTap Course List)
Ch. 10.1 - In Problems 16 write the given nonlinear...Ch. 10.1 - Prob. 2ECh. 10.1 - In Problems 16 write the given nonlinear...Ch. 10.1 - Prob. 4ECh. 10.1 - In Problems 16 write the given nonlinear...Ch. 10.1 - In Problems 16 write the given nonlinear...Ch. 10.1 - Prob. 7ECh. 10.1 - Prob. 8ECh. 10.1 - Prob. 9ECh. 10.1 - Prob. 10E
Ch. 10.1 - Prob. 11ECh. 10.1 - Prob. 12ECh. 10.1 - Prob. 13ECh. 10.1 - Prob. 14ECh. 10.1 - Prob. 15ECh. 10.1 - In Problems 716 find all critical points of the...Ch. 10.1 - In Problems 2326 solve the given nonlinear plane...Ch. 10.1 - In Problems 2326 solve the given nonlinear plane...Ch. 10.1 - In Problems 2326 solve the given nonlinear plane...Ch. 10.1 - In Problems 2326 solve the given nonlinear plane...Ch. 10.1 - Prob. 27ECh. 10.1 - Prob. 28ECh. 10.1 - Prob. 29ECh. 10.1 - Prob. 30ECh. 10.2 - In Problems 916 classify the critical point (0, 0)...Ch. 10.2 - Prob. 10ECh. 10.2 - Prob. 11ECh. 10.2 - Prob. 12ECh. 10.2 - In Problems 916 classify the critical point (0, 0)...Ch. 10.2 - In Problems 916 classify the critical point (0, 0)...Ch. 10.2 - In Problems 916 classify the critical point (0, 0)...Ch. 10.2 - Prob. 16ECh. 10.2 - Prob. 17ECh. 10.2 - Determine a condition on the real constant so...Ch. 10.2 - Prob. 19ECh. 10.2 - Prob. 20ECh. 10.2 - Prob. 21ECh. 10.2 - Prob. 22ECh. 10.2 - Prob. 23ECh. 10.2 - In Problems 23-26 a nonhomogeneous linear system...Ch. 10.2 - Prob. 25ECh. 10.2 - Prob. 26ECh. 10.3 - Prob. 1ECh. 10.3 - Prob. 2ECh. 10.3 - Prob. 3ECh. 10.3 - Prob. 4ECh. 10.3 - Prob. 5ECh. 10.3 - In Problems 310, without solving explicitly,...Ch. 10.3 - In Problems 310, without solving explicitly,...Ch. 10.3 - Prob. 8ECh. 10.3 - Prob. 9ECh. 10.3 - In Problems 310, without solving explicitly,...Ch. 10.3 - Prob. 11ECh. 10.3 - In Problems 1120 classify (if possible) each...Ch. 10.3 - Prob. 13ECh. 10.3 - Prob. 14ECh. 10.3 - Prob. 15ECh. 10.3 - Prob. 16ECh. 10.3 - Prob. 17ECh. 10.3 - Prob. 18ECh. 10.3 - Prob. 19ECh. 10.3 - Prob. 20ECh. 10.3 - Prob. 21ECh. 10.3 - Prob. 22ECh. 10.3 - Prob. 23ECh. 10.3 - Prob. 24ECh. 10.3 - Prob. 25ECh. 10.3 - Prob. 26ECh. 10.3 - Prob. 27ECh. 10.3 - Show that the dynamical system x = x + xy y = 1 y...Ch. 10.3 - Prob. 29ECh. 10.3 - Prob. 30ECh. 10.3 - Prob. 31ECh. 10.3 - Prob. 32ECh. 10.3 - Prob. 33ECh. 10.3 - Prob. 34ECh. 10.3 - Prob. 35ECh. 10.3 - Prob. 36ECh. 10.3 - When a nonlinear capacitor is present in an...Ch. 10.3 - Prob. 38ECh. 10.3 - Prob. 39ECh. 10.4 - Prob. 1ECh. 10.4 - Prob. 2ECh. 10.4 - Prob. 3ECh. 10.4 - Prob. 4ECh. 10.4 - Prob. 5ECh. 10.4 - Prob. 6ECh. 10.4 - Prob. 7ECh. 10.4 - Prob. 8ECh. 10.4 - Prob. 9ECh. 10.4 - Competition Models A competitive interaction is...Ch. 10.4 - Prob. 12ECh. 10.4 - Prob. 13ECh. 10.4 - Prob. 14ECh. 10.4 - Prob. 15ECh. 10.4 - Additional Mathematical Models Damped Pendulum If...Ch. 10.4 - Prob. 17ECh. 10.4 - Prob. 18ECh. 10.4 - Prob. 19ECh. 10.4 - Prob. 20ECh. 10.4 - Prob. 21ECh. 10.4 - Prob. 22ECh. 10 - Prob. 1RECh. 10 - Prob. 2RECh. 10 - Prob. 3RECh. 10 - Prob. 4RECh. 10 - Prob. 5RECh. 10 - Prob. 6RECh. 10 - Prob. 7RECh. 10 - Prob. 8RECh. 10 - Prob. 9RECh. 10 - Prob. 10RECh. 10 - Prob. 11RECh. 10 - Discuss the geometric nature of the solutions to...Ch. 10 - Classify the critical point (0, 0) of the given...Ch. 10 - Prob. 14RECh. 10 - Prob. 15RECh. 10 - Prob. 16RECh. 10 - Prob. 17RECh. 10 - Prob. 18RECh. 10 - Prob. 19RECh. 10 - Prob. 20RE
Knowledge Booster
Similar questions
- 23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes 1/2 of the food and 1/3 of the manufactured goods. Manufacturing consumes 1/2 of the food and 2/3 of the manufactured goods. Assuming the economy is closed and in equilibrium, find the relative outputs of the farming and manufacturing industries.arrow_forwardg(a,b) = a²b-2a² - 4a + 2ab. Determine all the critical points of g. And determine the relative minimum, relative maximum, or saddle point at each critical points using the second derivatives test.arrow_forwardnt) Consider the discrete-time dynamical system x+1 = 4x,(1-x₂). 3 If x₁ = ³, X₁+1 Is x₂ = an equilibrium for this system? X₁ 4 Write the updating function rule as f(x) = 4x(1-x). Compute the derivative: f'(x) = Evaluate the derivative at the equilibrium: Is the equilibruim stable, unstable or neither?arrow_forward
- Example: If y=2+x , find the critical points and recognize them.arrow_forwardConsider an arbitrary quadratic function f(x) = a.x² + bx +c where a, b, and c are constants with a + 0. Find the critical number(s) of f(x) and then find the conditions needed on a, b, and c that will make that/those critical number(s) correspond to a relative maximum or a relative minimum.arrow_forward3. Consider the competition system (x for coyotes and y for foxes) x' = 3x - 2xy - x², y'= 3y - 2xy - y². Find all fixed points. Denote by R the unique fixed point (ro, yo) with ro> 0 and yo > 0. Is it stable (co-existence) or unstable (one species extinction)?arrow_forward
- A linear function f (x, y) = ax + by + c has no critical points. Therefore, the global minimum and maximum values of f (x, y) on a closed and bounded domain must occur on the boundary of the domain. Furthermore, it can be easily seen that if the domain is a polygon, as in the figure, then the global minimum and maximum values of f must occur at a vertex of the polygon. Find the global minimum and maximum values of f (x, y) on the specified polygon. f(x, y) = 9y - 5x +9 (Give your answers as a whole numbers.) global minimum: global maximum:arrow_forwardConsider the linear model Y; = B + B1X1¡ + B2X2i + u; where error term and where E (u;|X1i, X2;) = 0, observations (Yi, X1i, X2;) are independent and identically distributed, 0 < E (Y4) < ∞, 0 < E (X;) < o, 0 < E(X) < ∞ and where X2; OLS estimators ß, and B, of the coefficients B, and B, unbiased and is the X. Are the consistent? Explain.arrow_forward5. For each linear system given, classify the critical (equilibrium) point (0,0) and use this information to match to the phase portrait. Classification Phase Portrait Linear System = -x+3y -3x - 5y 2r+24 x+y -2x + 3y -3x + 2y -4x+y x + 2y (d) 318 dt = = = (III) H (II) (IV) MUTT wwwarrow_forward
- a) Describe nonlinear phenomena, essential nonlinear phenomena. b) Describe common nonlinearities in control systems with examples. c) Describe classification of equilibria of a nonlinear system using phase-plane analysis d) Describe the concept of limit cycle with full explanation. e) Find and classify all equilibrium points for the system given below: 2x,x2 i, = (1 – x1)x1-1+x 1+x1 *z = (2 - *2 X2 -)x2 1+x1arrow_forward3. Find the critical points of if(x,y) = x²+x-3xy + y³-5, Use the second partial derivative test to determine for each of the critical points whether they correspond to a relative minimum, a relative maximum, or a saddle point.arrow_forwardThe homogenous D. E. with constant coefficient of at least order which has the solution y = 2x? + 3e* + ecosx is 5y(5) + 9y(4) + 12y" = 0 %3D (9)4 O + 3y(5) + 4y(4) + 2y" = 0 %3D y(6) 4y(5) + 9y(4) + 5y" = 0 %3D (9)4 O 5y5) + 7y(4) + 5y" = 0 (9)4 O - 5y(5) + 9y(4) + 10y" = 0arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning