A population is governed by the nonlinear equationx = x² - 3x3 +2.Show that there is an equilibrium state at x = 1 and by considering a small pertur-bation determine whether it is a stable or unstable state. Find any other equilibriumstates and determine their stability.

To analyze the given nonlinear equationx˙=x4−3x3+2,we start by finding the equilibrium states, which…

Answered: A population is governed by the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The demand and supply functions for two interdependent commodities are given by:Qd1 = 205 − 2.5P1 − P2Qs1 = 1.5P1 − 30Qd2 = 147.5 − 0.5P1− 1.5P2Qs2 =P2 − 60Determine the equilibrium price and quantity for this two-commodity model.
D(x) is the price, in dollars per unit, that consumers are willing to pay for x units of an item, and S(x) is the price, in dollars per unit, that producers are willing to accept for x units. If the equilibrium price is $12 and the equilibrium quantity is 144 units, find the Consumer Surplus at the equilibrium point and then answer the question about Producer Surplus. 144 D(x)= S(x) = Vx %3D You must write a complete solution for part (a) and submit with your written work. Note: Consumer and Producer Surplus formulas are: Consumer Surplus: D(x)dx- PQ, Producer Surplus: PQ- | Sx)dx. [4 points] (a) The Consumer Surplus is S (Round to the nearest cent as needed.) (b) Which expression will give the correct value of the Producer Surplus? [2 points] O A. T 1 1A-(12|144) 0. -144 -(12)(144) |O B. 21 (12)(144)- [144 -0 OC. 3 2. 2, 21 144 3. (12)(144) D. 31 (12)(144)- 2. 144 E. (12)(144)- [12 -0 (Select the correct answer.) Click to select your answer(s).
For the following graph of f(x), identify where f(x) is not differentiable and why. -5 -4 2- 3 4 X f(x) is not differentiable at x = 0 because f(x) is not defined at x = 0. f(x) is not differentiable at x = 0 because f(x) has a corner at x = 0. f(x) is not differentiable at x = 0 because f(x) has a cusp at x = 0. Of(x) is not differentiable at x = 0 because f(x) has a jump at x = 0.
Derive the two expressions for the IS and LM equilibrium relationships respectively. Sketch a graph of the two relationships.

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A population is governed by the nonlinear equation x = x² - 3x3 +2. Show that there is an equilibrium state at x = 1 and by considering a small pertur- bation determine whether it is a stable or unstable state. Find any other equilibrium states and determine their stability.