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 10.1, Problem 12E
To determine
All the critical points of the given plane system.
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Problem 5. Find and Classify the critical point of (x,y)=192x³+y²–4xy²
on the triangle with vertices (0,0), (4,2) and (-2,2).
2) 3
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dr
subject to x = 1 and y = 0 at t = 0
6. (2x +3y = 0
/2x
x+2y =-1
9. (1
1
-X+-y 5
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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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- 3. 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_forwardQ.No.4 Differentiate the following Y= (x²+3)x1 Y= ax²+b/ cx Y= 7x*+2x³-3x+37arrow_forwardIn Problems 15–22, find (a) v x w, (b) w X v, (c) w X w, and (d) v x v. 15. v = 2i - 3j + k 2j 17. v = i+j w = 2i +j + k 18. v = i - 4j + 2k w = 3i + 2j + k 16. v = -i + 3j + 2k w = 3i - 2j - k 20. v = 31 + j+ 3k w = i - k w = 3i - - k 22. v = 2i - 3j w = 3j - 2k 19. v = 2i j+ 2k w =j- k 21. v = i -j -k w = 4i - 3karrow_forward
- b) Show that Δ2y0 = y2-2y1 + y0.arrow_forward9. discuss the behavior of the dynamical system Xk+1= Axk where -0.31 (@) A = [ (b) A = ["0.3 11 1.5 0.3 (b) A = 0.3 1 3Darrow_forward11. What is the general solution of* (2x – y)dx + (4x + y - 6)dy = 0 (2 +y – 3) = c(2x + y - 4)2 (x – y + 3)? = c(2æ + y – 4)3 Option 1 Option 2 (2 - y - 3) = c(2r - y- 4) (x+y - 3) = c(x + 2y – 4)?arrow_forward
- 13. Find the equation of the orthogonal trajectories of the system of parabolas y² = 2x + 2. a. y = ce-x b. y = cex c. y = ce²x d. y = ce-2xarrow_forward(5) y + Y 1+x DE -(1+x)²y5) 2 with y(1) = 1arrow_forward3. 2хydx - (3xу + 2y?)dy %3D0 o (x - 2y)*(2x +y) = c (х — у)"(х + у) %3 с (х + 2y) (2х- у)* %3 с (x – 2y)* = c(2x + y)arrow_forward
- 2. Which of the following is a general solution to the following: x²y" + xy' + (36x² - 1) y (Hint: As discussed in the lecture, use Y, only when J, and J-, are linearly dependent). A. y = c₁J₁(2x) + C₂J_1(2x) 6 B. y = C₁J₁(x) + C₂Y₁(x) 3 3 C. y = c₁₂/₁(6x) + C₂Y₁(6x) 0 D. y = c₁J₁(6x) + c₂] _1(6x) 2arrow_forwardSolve for the critical points and determine whether they are minimum point, maximum point or point of reflection. 1. y = 3x2 – 6x 2. y = x3 – 6x2 + 1 3. y = x3 – x2 – x 4. y = (x3–4)2/3 5. y = x4 + 1/x2 6. y = 1/4x4 – x3 + x2arrow_forward20. In question number 19, what is its particular solution? * (D² – D- 2)y = 1 – 2x – 9e* Yp = 3e- + x – 2 Yp = 3xe-* +x – 1 Option 1 Option 2 Yp = 3e-* – 2x – 2 Yp = 3xe 2x – 1arrow_forward
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