Fundamentals of Differential Equations and Boundary Value Problems
7th Edition
ISBN: 9780321977106
Author: Nagle, R. Kent
Publisher: Pearson Education, Limited
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 12.RP, Problem 18RP
In Problems 17 and 18 , determine the stability of the zero solution to the given system.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
3. Find the general solution of the following system of linear equations. Give the final answer in the
form =... and y=... (
x = x+y
y' = 4x - 2y
with (0) 1 and y(0) = -2
8. Use any method to find the general solution of the system
x +
2
[1/₂].
III. Solve the following linear systems of differential equations.
dr₁
dt
(a)
(b)
dx2
dt
dx₁
dt
dx₂
dt
= x1 + 2x₂
=
=
=
4x1 + 3x2
x₁ - 4x₂
4x₁ - 7x₂
(c)
(d)
dx₁
dt
dx₂
dt
dx₁
dt
dx₂
dt
= -4x1 + 2x2
=
=
=
5
2²1 +22
-2x1 - 2x₂
2x16x₂
X(0) = [-2]
X(0) = [1¹]
Chapter 12 Solutions
Fundamentals of Differential Equations and Boundary Value Problems
Ch. 12.2 - In Problem 16, classify the critical point at the...Ch. 12.2 - Prob. 2ECh. 12.2 - Prob. 3ECh. 12.2 - Prob. 4ECh. 12.2 - Prob. 5ECh. 12.2 - Prob. 6ECh. 12.2 - Prob. 7ECh. 12.2 - Prob. 8ECh. 12.2 - Prob. 9ECh. 12.2 - In Problem 712, find and classify the critical...
Ch. 12.2 - In Problem 712, find and classify the critical...Ch. 12.2 - In Problem 712, find and classify the critical...Ch. 12.2 - Prob. 13ECh. 12.2 - In Problems 13-20, classify the critical point at...Ch. 12.2 - Prob. 15ECh. 12.2 - Prob. 16ECh. 12.2 - Prob. 17ECh. 12.2 - In Problems 13-20, classify the critical point at...Ch. 12.2 - Prob. 19ECh. 12.2 - Prob. 20ECh. 12.2 - Show that when the system x(t)=ax+by+p,...Ch. 12.2 - Prob. 22ECh. 12.2 - Prob. 23ECh. 12.2 - Prob. 24ECh. 12.2 - Prob. 25ECh. 12.2 - Show when the roots of the characteristic equation...Ch. 12.2 - Prob. 27ECh. 12.3 - In Problems 1 -8, show that the given system is...Ch. 12.3 - Prob. 2ECh. 12.3 - Prob. 3ECh. 12.3 - Prob. 4ECh. 12.3 - Prob. 5ECh. 12.3 - Prob. 6ECh. 12.3 - Prob. 7ECh. 12.3 - Prob. 8ECh. 12.3 - In Problems 9 -12, find all the critical points...Ch. 12.3 - Prob. 10ECh. 12.3 - Prob. 11ECh. 12.3 - In Problems 9 -12, find all the critical points...Ch. 12.3 - In Problems 13-16, convert the second-order...Ch. 12.3 - In Problems 13-16, convert the second-order...Ch. 12.3 - Prob. 15ECh. 12.3 - Prob. 16ECh. 12.3 - Prob. 17ECh. 12.3 - Prob. 18ECh. 12.3 - Prob. 19ECh. 12.3 - Prob. 20ECh. 12.3 - van der Pols Equation. a. Show that van der Pols...Ch. 12.3 - Consider the system dxdt=(+)x+y, dydt=x+(+)y,...Ch. 12.3 - Prob. 23ECh. 12.3 - Show that coexistence occurs in the competing...Ch. 12.3 - When one of the populations in a competing species...Ch. 12.4 - Prob. 1ECh. 12.4 - Prob. 2ECh. 12.4 - Prob. 3ECh. 12.4 - Prob. 4ECh. 12.4 - Prob. 5ECh. 12.4 - Prob. 6ECh. 12.4 - Prob. 7ECh. 12.4 - Prob. 8ECh. 12.4 - Prob. 9ECh. 12.4 - Prob. 10ECh. 12.4 - Prob. 11ECh. 12.4 - Prob. 12ECh. 12.4 - Prob. 13ECh. 12.4 - Prob. 14ECh. 12.4 - Prob. 15ECh. 12.4 - Prob. 16ECh. 12.4 - Prob. 17ECh. 12.4 - Prob. 18ECh. 12.4 - Prob. 19ECh. 12.4 - Prob. 20ECh. 12.4 - Prob. 21ECh. 12.5 - In Problems 1-8, use Lyapunovs direct method to...Ch. 12.5 - In Problems 1-8, use Lyapunovs direct method to...Ch. 12.5 - In Problems 1-8, use Lyapunovs direct method to...Ch. 12.5 - Prob. 4ECh. 12.5 - In Problems 1-8, use Lyapunovs direct method to...Ch. 12.5 - Prob. 6ECh. 12.5 - Prob. 7ECh. 12.5 - Prob. 8ECh. 12.5 - In problem 9-14, use Lyapunovs direct method to...Ch. 12.5 - In problem 9-14, use Lyapunovs direct method to...Ch. 12.5 - Prob. 11ECh. 12.5 - Prob. 12ECh. 12.5 - Prob. 13ECh. 12.5 - Prob. 14ECh. 12.5 - Prob. 15ECh. 12.5 - Prob. 16ECh. 12.5 - Prove that the zero solution for a conservative...Ch. 12.6 - Semistable Limit cycle. For the system...Ch. 12.6 - Prob. 2ECh. 12.6 - Prob. 3ECh. 12.6 - Prob. 4ECh. 12.6 - In Problems 512, either by hand or using a...Ch. 12.6 - Prob. 6ECh. 12.6 - Prob. 7ECh. 12.6 - Prob. 8ECh. 12.6 - In Problems 5-12, either by hand or using computer...Ch. 12.6 - Prob. 10ECh. 12.6 - Prob. 11ECh. 12.6 - In Problems 5-12, either by hand or using computer...Ch. 12.6 - In Problems 13-18, show that the given system or...Ch. 12.6 - In Problems 13-18, show that the given system or...Ch. 12.6 - Prob. 15ECh. 12.6 - In Problems 13-18, show that the given system or...Ch. 12.6 - Prob. 17ECh. 12.6 - Prob. 18ECh. 12.6 - Prob. 19ECh. 12.6 - Prob. 20ECh. 12.6 - Prob. 21ECh. 12.6 - Prob. 22ECh. 12.6 - Prob. 23ECh. 12.6 - Prob. 24ECh. 12.6 - Prob. 25ECh. 12.6 - Prob. 26ECh. 12.6 - Prob. 27ECh. 12.6 - Prob. 28ECh. 12.7 - Prob. 1ECh. 12.7 - Prob. 2ECh. 12.7 - Prob. 3ECh. 12.7 - Prob. 4ECh. 12.7 - Prob. 5ECh. 12.7 - Prob. 6ECh. 12.7 - Prob. 9ECh. 12.7 - Prob. 10ECh. 12.7 - Prob. 11ECh. 12.7 - Prob. 12ECh. 12.7 - Prob. 13ECh. 12.7 - Prob. 14ECh. 12.7 - Prob. 15ECh. 12.7 - Prob. 16ECh. 12.7 - Prob. 17ECh. 12.7 - Prob. 18ECh. 12.8 - Calculate the Jacobian eigenvalues at the critical...Ch. 12.8 - Prob. 2ECh. 12.8 - Prob. 3ECh. 12.8 - Prob. 4ECh. 12.RP - In Problems 1-6, find all the critical points for...Ch. 12.RP - Prob. 2RPCh. 12.RP - Prob. 3RPCh. 12.RP - Prob. 4RPCh. 12.RP - In Problems 1-6, find all the critical points for...Ch. 12.RP - In Problems 1-6, find all the critical points for...Ch. 12.RP - Prob. 7RPCh. 12.RP - In Problems 7 and 8, use the potential plane to...Ch. 12.RP - In Problems 9-12, use Lyapunovs direct method to...Ch. 12.RP - Prob. 10RPCh. 12.RP - In Problems 9-12, use Lyapunovs direct method to...Ch. 12.RP - Prob. 12RPCh. 12.RP - Prob. 13RPCh. 12.RP - In Problem 13 and 14, sketch the phase plane...Ch. 12.RP - In Problems 15 and 16, determine whether the given...Ch. 12.RP - Prob. 16RPCh. 12.RP - In Problems 17 and 18, determine the stability of...Ch. 12.RP - In Problems 17 and 18, determine the stability of...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- In each of Problems (2) through (9), find the general solution of the given system. Calculations are greatly facilitated by using a computer algebra system. 2.x² - (²-2) x + ( ) X' = 3arrow_forward1. Find steady states of the equation: 2xn (а) хр+1 Xn+1 K (b) Xn+1 where k1, k2 and K are constants. ki + k2/Xnarrow_forwardFind the real-valued general solution to the following systems of equations 2 -5 x'(t) = ({arrow_forward
- 2. Solve the following system of nonlinear equation using Newton's Method. (you can use MS Excel) X6 f.(x) = 0.5x1 + x2 + 0.5x3 = 0 -- %3D X7 2 f2(x) = x3 + X4 + 2x5 -- - X7 1 f3(x) = x1 + X2 + x5 - - = f.(x) = -28837x1 – 139009x2 – 78213x3 + 18927x4 + 8427x5 %3D 13492 10690*é = 0 fs(x) = x1 + x2 + X3 + X4 + X5 – 1 = 0 fo(x) = 400x,x? – 1.7837×10$x3X5 = 0 f,(x) = x1X3 – 2.6058x4 = 0 %3Darrow_forwardProblem 2. What solution of the linear system of differential equations x = x1 – 3.x2 x2 = 3x1 + x2 satisfies the initial conditions X1(0) = 4, X2(0) = 7?arrow_forwardQuestion 5. Determine all solutions to the first-order linear system x₁ = −x1 + x2 x = -2x1-3x2 + 23 - x = x1 + x2 − 2x3arrow_forward
- 4. For which values of a will the following system have (a): no solution, (b): Unique solution, (c): Infinitely many solutions? x + 2y- 3z = 4 3x y+ 5z = 2 - 4x + y+(a² – 14)z = a + 2arrow_forwardIn each of Problems (2) through (9), find the general solution of the given system. Calculations are greatly facilitated by using a computer algebra system.arrow_forward2. What is the solution set to the system of equations y = 2x + 3 and y = g(x) where g(x) is defined by the function below? G. 通 A.arrow_forward
- 1. For which values of k will the following system have no solution? Exactly one solution? Infinitely many solutions? x + ky - 2z = 0 x + 2ky – 2z = 5 x + ky + (k^2 –- 3k)z = k – 1arrow_forward2. Solve the following system of nonlinear equation using Newton's Method. (you can use MS Excel) x6 f₁(x) = 0.5x₁ + x₂ +0.5x3- = 0 f₂(x) = x3 + x4 + 2x5 f3(x) = x₁ + x₂ + x5 f4(x) = -28837x₁ - 139009x2 - 78213x3 + 18927x4 +8427x5 + 2 -1=0 X7 1 -1=0 fs(x) = x₁ + x₂ + x3 + x4 + x5-1=0 400x₁x2-1.7837x105x3x5 = 0 f(x) = f(x) = x₁x3 - 2.6058x4 = 0 13492 x7 106906 = 0 x7arrow_forwardFind a solution to the system [*] -3 1 1 -5 [] [] by solving the IVP with initial condition x (t) exp t) + 18 = 3 [8] = [³] y(0) t exp ☐t)arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill Education
Mathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
Thinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSON
Discrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,
Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education
Discrete Mathematics and Its Applications ( 8th I...
Math
ISBN:9781259676512
Author:Kenneth H Rosen
Publisher:McGraw-Hill Education
Mathematics for Elementary Teachers with Activiti...
Math
ISBN:9780134392790
Author:Beckmann, Sybilla
Publisher:PEARSON
Thinking Mathematically (7th Edition)
Math
ISBN:9780134683713
Author:Robert F. Blitzer
Publisher:PEARSON
Discrete Mathematics With Applications
Math
ISBN:9781337694193
Author:EPP, Susanna S.
Publisher:Cengage Learning,
Pathways To Math Literacy (looseleaf)
Math
ISBN:9781259985607
Author:David Sobecki Professor, Brian A. Mercer
Publisher:McGraw-Hill Education
Intro to the Laplace Transform & Three Examples; Author: Dr. Trefor Bazett;https://www.youtube.com/watch?v=KqokoYr_h1A;License: Standard YouTube License, CC-BY