Consider the autonomous first-order differential equation y = 10 + 3y – v2 Find the DISTINCT...
MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the following autonomous first-order differential equation. dy = y219 - y2) Find the critical points and phase portrait of the given differential equation. dx 6 3 3 0 0 ol -6 -6 -3 Classify each critical point as asymptotically stable, unstable, or semi-stable. (List the critical points according to their stability, Enter your answers as a comma-separated list. If there are no critical points in a certain category, enter NONE.) asymptotically stable...
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...
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)...
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.)dPdt = P(a − bP)(1 − cP−1), P > 0, a < bc
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.
1. (10 points) Consider the autonomous equation dy = y2 + 3y + 2 dc (a) (6 points) Determine the equilibrium solutions of the equation, and classify each as asymptotically stable or unstable. (b) (4 points) Sketch at least three solutions to the equation, choosing initial points not corresponding to the equilibrium solutions. Include the equilibrium solutions in your sketch.
1. For the differential equation (y-y-6) șin(y/2) a) Find the critical points for y in (-6,6) and lassify the critical points as asymptotically stable, or unstable, or semi stable. b) Sketch approximate but clear solutions corresponding to the initial conditions 1.0 -0.8 -0.6 -0.4 0.2 0.2 0.4 0.6 0.8 1.0 -2 .6 1. For the differential equation (y-y-6) șin(y/2) a) Find the critical points for y in (-6,6) and lassify the critical points as asymptotically stable, or unstable, or semi...
Question 3 (20 points) Consider the following differential equation = y(y2 - 4). (a) Find all critical values. (6) Draw the phase diagram to classify each as stable, semi-stable or unstable.
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...
4. The origin (0,0) is a critical point of the first order autonomous system x'(t)- Ax(t) The origin can classified as asymptotically stable if Re(A) < 0 and stable if Re(A)0 for all eigenvalues λ of A. The origin is unstable if there exists an eigenvalue λ of A where Re(A) >0. For the following systems, classify the origin 1 -3x(C) b, x'(t)=11-3 1-3x(t)