Option B
__8. The set of all critical points of the autonomous equation p' = p2-2p + 1...
_D_6 The set of critical points of the autonomous equation y' = y(2-y) are: A (0.2.-2) B (0) C2) D.(0.2) (0,3,-3) D_7. The set of critical points (or equilibrium points) of the equation y'=yl - 9y is: A (0) C.-99) D_8. Which of the following is a stable point of ' (-1)? A0 B. 1 C andu1 D. Neither is stable F 9 True or False) The equation y + xy +x+yi b le Writer for true or F forse...
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 following autonomous first-order differential equation. Find the critical points and phase portrait of the given differential equation. 0
Consider the following autonomous first-order differential equation. Find the critical points and phase portrait of the given differential equation. 0
Without solving explicitly, classify the critical points of the given first-order autonomous differential equation as either asymptotically stable or unstable. All constants are assumed to be positive. (Enter the critical points for each stability category as a comma- separated list. If there are no critical points in a certain category, enter NONE.) dv m = tg - ky dt asymptotically stable VE unstable V mg k х Need Help? Read 1 Talk to a Tutor 2. (-/1 Points] DETAILS ZILLDIFFEQ9...
For the autonomous first-order order differential equation dy=-18y+2y3, please 1. dx a. find its critical points; b. draw its phase portrait; c. clasify each critical point as asymptotcally stable, unstable, or semi-stable.
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)....
e critical points for the autonomous equation y'=y (ay) e whether they lead to equilibrium solubions which are shable, unstable or semesbable equilíbria. A solue g =- Jy y (0)=50 X+goo o solve y + y = x 0 Prove that the equation cosy dx - (x sing-y dy=0 s excent and then solve. 2 Prove that the ogrubion (easing) dx+cos ydy=0 is nob excent and then find an anbegrubina factor which will make it exact. Prove that exy dx...
1. Consider the polynomial p.(t)=1+t2 and pz(t)=1 – 12. Is {P1, P2} a linearly independent set in P = Span{1,1, 12? Why or Why not?
3) Let T: P2 → P3 be such that T (p) = 2p(x) - xp(x). Let Sy be the standard basis for P, and S, the standard basis for Pz. a) Find T (2 + 5x). b) Find [T(S)]sz: c) Use [T(S)]s to find [T(3 – x2)]sz. d) Verify that Vp € P2, [T (p)]sz = [T(S)][p]sz:
consider the autonomous equation
2. Consider the autonomous equation y=-(y2-6y-8) (a) Use the isocline method to sketch a direction field for the equation (b) Sketch the solution curves corresponding to the following intitial conditions: (1) y(0) 1 (2) y(0) =3 (3) y(0)=5 (4) 3y(0) 2 (5) y(0) = 4 (c) What are equilibrium solutions, and classify its equilibrium them as: sink (stable), source, node. (d) What is limy(t) if y(0) = 6? too
2. Consider the autonomous equation y=-(y2-6y-8) (a)...