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1. (25 pts) An autonomous differential equation has an unstable equilibrium solution at y = -1,...
15 pts] Sketch some representative solution curves for the autonomous first order differential equation y'- y(2-y) (1 -y). Find all equilibrium solutions, label all pertinent coordinates. Note: An Autonomous equation means that dy/dt does not depend on time t. Hint: Follow the method demonstrated in Example 1.3.6 (p.28). The hand-draw slop field is optional and not necessary. This method gives a qualitative analysis for the future of all possible solutions without solving the equation quantitatively 15 pts] Sketch some representative...
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 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)...
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 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,...
Find the stable equilibrium solution of the following differential equation: + y - 1 = e2( y − 1). The stable equilibrium solution is y = Check Find the general solution to the differential equation: x + y - x115 = 0. Answer: y(x) = Check Solve the initial-value problem: dy = e ** - y, yO= dx Answer: y(x) = Check
(4 points) Write down a first order autonomous differential equation which has equilibrium solutions at y = 1, y = 2 and y = 3. Is the differential equation linear?
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.
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...
For the equation (dp/dt)=(P+2)(P^2-6P+5) find the equilibrium points and make a phase 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.