2. Consider the system dP P(1000/Q – P) dt OP Q(20P – Q), dt where P is the price of a single item on the market and Q is the quantity of the item available on the market. Find the equilibrium points of this system. (a) Classify each equilibrium point with respect to its stability, if possible. If a point cannot be readily classified, explain why. (b) Perform a graphical stability analysis to determine what will happen to the levels of P and Q as time increases.

2. Consider the system dP P(1000/Q – P) dt OP Q(20P – Q), dt where P is the price of a single item on the market and Q is the quantity of the item available on the market. Find the equilibrium points of this system. (a) Classify each equilibrium point with respect to its stability, if possible. If a point cannot be readily classified, explain why. (b) Perform a graphical stability analysis to determine what will happen to the levels of P and Q as time increases.

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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Question

2. Consider the system
dP
P(1000/Q – P)
dt
OP
Q(20P – Q),
dt
where P is the price of a single item on the market and Q is the quantity of the item available
on the market. Find the equilibrium points of this system.
(a) Classify each equilibrium point with respect to its stability, if possible. If a point cannot
be readily classified, explain why.
(b) Perform a graphical stability analysis to determine what will happen to the levels of P
and Q as time increases.

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