(i) (5 marks) Determine all equilibrium solutions to the ODE 8xy + 2x - y =...
Given the equation y' 9-16y, a) Find all Equilibrium solutions b) Determine whether each solution is stable, unstable or neither. c) Sketch the direction field.
Given the equation y' 9-16y, a) Find all Equilibrium solutions b) Determine whether each solution is stable, unstable or neither. c) Sketch the direction field.
4 Consider the autonomous differential equation y f(v) a) (3 points) Find all the equilibrium solutions (critical points). b) (3 points) Use the sign of y f(z) to determine where solutions are increasing / decreasing. Sketch several solution curves in each region determined by the critical points in c) (3 points) the ty-plane. d) (3 points) Classify each equilibrium point as asymptotically stable, unstable, or semi-stable and draw the corresponding phase line.
4 Consider the autonomous differential equation y f(v)...
Consider the autonomous differential equation y = f(y) = y4-4 уг = y"(y-2) (y+2). a) (3 points) Find all the equilibrium solutions (critical points). f(y) to determine where solutions are increasing / decreasing. Use the sign of y' e) (3 points) Sketch several solution curves in each region determined by the critical poins in the ty-plane
Consider the autonomous differential equation y = f(y) = y4-4 уг = y"(y-2) (y+2). a) (3 points) Find all the equilibrium solutions (critical points)....
For (b): choose stable/unstable/semistable/neither
(2 points) The phase plot for an ODE -f(y) is shown below dx dy/dx (a) Which of these could be a plot of solutions y vsx corresponding to this ODE? A. B. C. D. You can click the graphs above to enlarge them A. A B. B C. C D. D (b) The smallest equilibrium of this ODE is y and the largest equilibrium of this ODE is y - (c) For which of the following...
dy 2 points) The phase plot for an ODE fyis shown below dy/dx -2 -1 -1 (a) Which of these could be a plot of solutions y vs corresponding to this ODE? You can ciick the grapns above to enlarge them A. A ов, в ос. с D. D (b) The smallest equilibrium of this ODE is y which is choose uilibrium of this ODE is y and the which is choose (C) For which or the following value(s) of...
(2) (4 marks.) Find the general solution of the ODE e-2x Y"' + 4y + 4y = X > 1. 2
dy dx 2 points) The phase plot foan ODE shown below dy/dx hoyts dockland - Google Search -1 (a) Which of these could be a plot of solutions y vs x corresponding to this ODE? A. B. C. D. You can click the graphs above to enlarge them. A. A B. B C. C D. D (b) The smallest equilibrium of this ODE is y- and the largest equilibrium of this ODE is y (c) For which of the following...
Question 2 (12 marks) (a) Consider the sequence with terms 2n3 5"5 log n , n = 1,2,3,.... an 13 n8n (i) Determine whether {an} converges or diverges. If the sequence converges, find its lmit (ii) Determine whether diverges. Justify your answer an COnverges or n-1 (b) Consider the series (2n)! 2" (n!)? n=1 and determine whether it converges or diverges. Justify your answer
Question 2 (12 marks) (a) Consider the sequence with terms 2n3 5"5 log n , n...
The phase plot for an ODE dy dx =f(y) dydx=f(y) is shown
below.
4 3 2 1 2 1 1 1 1 2 3 (a) Which of these could be a plot of solutions y vs x corresponding to this ODE? 9 2 B. A. 2 2 3 C. D. You can click the graphs above to enlarge them. OA. A ов, в OC. C OD. D E which is choose (b) The smallest equilibrium of this ODE is y-...
6. Consider the autonomous differential equation (a) Find all of its equilibrium solutions. (b) Classify the stability of each equilibrium solution. Justify your answer. (c) If y(t) is a solution that satisfies y(-1) =-4, what is y(0)? Without solving the equation, briefly explain your conclusion. (d) If y() is a solution that satisis y(3) -3, then what is lim y(t)?
6. Consider the autonomous differential equation
(a) Find all of its equilibrium solutions. (b) Classify the stability of each equilibrium...