Determine the equilibrium, classify each equilibrium, draw a phase line. If y(0)=1 then lim y(t) = ? If y(0)=2 then what is the solution y(t) =? 3/3-4y Let dt 3/3-4y Let dt
Consider the ODE dy/dt = -y(1-(y/T))(1-(y/K)) where 0 < T < K. (a) Draw a phase line and determine the stability of each equilibrium point. (b) Draw a graph in the yt-plane showing several solutions and their long term behavior. (Remark: Solving this ODE isn’t necessary!)
Let y(t)y(t) be a solution of y˙=1/4y(1−y4) such that
y(0)=8.Determine limt→∞y(t) without finding y(t) explicitly.
9.0 Differential Eqns: Problem 6 Previous Problem List Next Results for this submission Answer Preview Entered The answer above is NOT correct. (1 point) Let y(t) be a solution of y such that y(0) 8. Determine lim y(t) without finding y(t explicitly. t oo lim y(t) t oo Preview My Answers Submit Answers Result ncorrect
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...
dx/dt = -2x-4y dy/dt = 0.5x draw the x(t) graph for the solution that starts at (x,y)=(1,1)
3. [20 pts.] (a) Find the equilibrium solutions of the equation y-υw-2)3. (b) Sketch the phase line of the equation, and determine the stability of the equilibria you found in (a). (c) How does the solution with y(0) =-1 behave as t -» +00? How does the solution with y(0) 1 behave as t - --0?
3. [20 pts.] (a) Find the equilibrium solutions of the equation y-υw-2)3. (b) Sketch the phase line of the equation, and determine the stability...
5.4 Equilibrium Solutions and Phase Portraits 1. 2 3 3 2 . (a) Draw direction field. Use the points: (0,0), (+1,0), (0, +1), (+1, +1). (b) Draw the phase portrait. (c) Classify the equilibrium solution with its stability. 11 and 2. Suppose 2 x 2 matrix A has eigenvalues – 3 and -1 with eigenvectors respectively. (a) Find the general solution of 7' = A. (b) Draw the phase portrait. (C) Classify the equilibrium solution with its stability. 3. Suppose...
3. Draw the direction field of the following differential equation: = (1-y)y dt What happens for the solution satisfying y(0)-2, 1, 0.5,-1 as t-> oo? If y(2)-β and limt→oo y(t) = 1. Find all possible values of β.
3. Draw the direction field of the following differential equation: = (1-y)y dt What happens for the solution satisfying y(0)-2, 1, 0.5,-1 as t-> oo? If y(2)-β and limt→oo y(t) = 1. Find all possible values of β.
The solution of the initial value problem y" + 4y = g(t); y(0) = -1, y'(0) = 4 is ОВ. cos 2t y = į SÓ 9(T) sin 2(t – 7)dt + 2 sin 2t – cos 2t y = {G(s) sin 2t + 2 sin 2t y = So 9(7) sin 2(t – 7)dt + 2 sin 2t – į cos 2t y = £g(t) sin 2t + 2 sin 2t – } oc OD COS 2t OE y...
Determine which differential equation corresponds to each phase line You should be able to state briefly how you know your choices are correct E dy/dt = 2y - y^2 dy/dt = y(y - 2) F dy/dt = y^2 | y - 2| B dy/dt = 3y - y^2 A dy/dt = y(2 - y)^2 D dy/dt= 4y - y^3 C dy/dt = y^2 - 3y H dy/dt = y^3 - 4y
(1 point) Let y(t) be a solution of ý = {y(1 – 3) such that y0) = 10. Determine lim y(t) without finding y(t) explicitly. ta lim Vt) = 1. 100