2. (8 points) Solve the linear, 1st order ODE with initial value: dy dr 3. (7...
nd the critical points and phase portrait of the given autonomous rst-order differential equation. Classify each critical point as asymptotically stable, unstable, or semi-stable. By hand, sketch typical solution curves in the regions in the xy-plane determined by the graphs of the equilibrium solutions(a) dy/dx= y2-y3(b) dy/dx=(y-2)4
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...
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.
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...
dP 7. For the equation = (P+2)(P2 - 6P+5)find the equilibrium points and make a phase dt portrait of the differential equation. Classify each equilibrium point as asymptotically stable, unstable or semi-stable. Sketch typical solution curves determined by the graphs of equilibrium solutions. (6pts)
Consider the autonomous first-order differential equation y = 10 + 3y – v2 Find the DISTINCT critical points and classify each as (1) AS for Asymptotically Stable, (2) US for Unstable or (3) SS for Semi-Stable. Enter your answer as a comma separated list of pairs consisting on a critical point and its stability type (e.g. your answer might look like (2,AS), (-3,SS), (7,US)) Critical Point and Stability: For the initial value problem y' = 10 + 3y – y,...
4. (25 points) Solve the following ODE using classical 4th-order Runge- Kutta method within the domain of x = 0 to x= 2 with step size h = 1: dy 3 dr=y+ 6x3 dx The initial condition is y(0) = 1. If the analytical solution of the ODE is y = 21.97x - 5.15; calculate the error between true solution and numerical solution at y(1) and y(2).
Solve the initial value problem. 9 dy 3 +5y 3 e 0, y(0)=7 dx The solution is y(x) =I
solve 5c 5. (24 points) Find the solution of each of the following initial value problems: a) xy' + 3y = x V),y (1) = 0 (Bernoulli equation) 18 b) y" – 4y' – 12y = 3e5, y (0) =- (Hint: use the method of undetermined 7 coefficients) c) (2xy - 9x?) dx + (2y + x2 + 1) dy = 0,y (0) = - 3 (Hint: first show this is an exact DE)
Choose option Stable, Unstable, Semistable, Neither (2 points) The phase plot for an ODE-= f(y) is shown below. dy/dx -2 -1 2 (a) Which of these could be a plot of solutions y vs r corresponding to this ODE? 8 A. You can click the graphs above to enlarge them A. A B. B 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...