Differential Equations with Boundary-Value Problems (MindTap Course List)
9th Edition
ISBN: 9781305965799
Author: Dennis G. Zill
Publisher: Cengage Learning
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Chapter 10.3, Problem 12E
In Problems 11–20 classify (if possible) each critical point of the given plane autonomous system as a stable node, a stable spiral point, an unstable spiral point, an unstable node, or a saddle point.
12.
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9. discuss the behavior of the dynamical system Xk+1= Axk where
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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
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- 2. Classify (if possible) each critical point of the given plane autonomous system as a stable node, an unstable node, a stable spiral point, an unstable spiral point or a saddle point. (a) x = x³ - y y = x - y³ (b) x = y - x² + 2 y = 2xy - y (c) x = x (10-x-2y) y=y (16-y - x)arrow_forward6. Let A = {X € R³ : X and (1,2,3), (1, 0, -1) are linearly depedent} Show that A is closed in R³.arrow_forwardCheck 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))arrow_forward
- 9. discuss the behavior of the dynamical system xk+1= AXk where -0.3] 2 ] (b) A = 1.5 (a) A = 1.2 0.3 0.41 -0.3 1.1arrow_forward6. Consider the dynamical system dx - = x (x² − 4x) - dt where X a parameter. Determine the fixed points and their nature (i.e. stable or unstable) and draw the bifurcation diagram.arrow_forward3. Find all Critical points of the given plane autonomous system. 3.1 x² = x (1-x² - 3y²) y₁ = y (3 - x² - 3 y²) x' = - 2x+y+10 y' = 2x -y-15 y 3.2 y + 5arrow_forward
- (10) Consider the system y-(9) 0 Determine whether the critical point constitutes a node, saddle point, center, or spiral.arrow_forwardQuestion No. 2) Explain the importance of fixed point in discrete dynamical Systems with the help of two practical examples.arrow_forwardon the circle have single stable fixed point and no other fixed points? (ii) tuso stable fixed points and ho other fixed points? 4) Could a system (i) a (6) What are the answers to question (2) and (ii) for systems on the line x = P(x).arrow_forward
- 1. Disk Method a. y = x2,x = 0, x = 2, y = 0, about the x аxisarrow_forwardTr.28.arrow_forwardProblem 5. Let C be the square oriented counterclockwise with corners (0,0).(7,0).(7,7), and (0,7). If we label the edges of the square as C1, C3, C3, C, starting from the bottom edge going counterclockwise, then the edges may be linearly parameterized, with 0arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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