Problem 4. Suppose that you have two spatial locations A and B. You have a population of self-driving vehicles, that switch from location A to B, with probability kABAt,and from location B to A with probability KBAAT. This can be represented by a "reversible chemical reaction", with “reaction rates" kAB and and kba A KAB, B B KBA, A kbA, The population of self-driving vehicles in each location A and B is given by XA(t) and XB(t), respectively. For At arbitrarily small, given that kABand kBA are non-negative con- stant values, the evolution of the population of vehicles in site A and B are given by, A(t) -KABTA(t) + KBATB(t) (1) IB(t) KABTA(t) – KBATB(t) (2) = a xB(0) = b i) Find the solution to the IVP.
Problem 4. Suppose that you have two spatial locations A and B. You have a population of self-driving vehicles, that switch from location A to B, with probability kABAt,and from location B to A with probability KBAAT. This can be represented by a "reversible chemical reaction", with “reaction rates" kAB and and kba A KAB, B B KBA, A kbA, The population of self-driving vehicles in each location A and B is given by XA(t) and XB(t), respectively. For At arbitrarily small, given that kABand kBA are non-negative con- stant values, the evolution of the population of vehicles in site A and B are given by, A(t) -KABTA(t) + KBATB(t) (1) IB(t) KABTA(t) – KBATB(t) (2) = a xB(0) = b i) Find the solution to the IVP.
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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Transcribed Image Text:Problem 4. Suppose that you have two spatial locations A and B. You have a population
of self-driving vehicles, that switch from location A to B, with probability KABAT,and from
location B to A with probability kBAAt. This can be represented by a "reversible chemical
reaction", with "reaction rates" kAB and and kBA
A KAB, B
kBA
В
The population of self-driving vehicles in each location A and B is given by XA(t) and
XB(t), respectively. For At arbitrarily small, given that kABand kba are non-negative con-
stant values, the evolution of the population of vehicles in site A and B are given by,
*a(t)
-KABTA(t) + KBATB(t)
(1)
KABTA(t) – KBATB(t)
(2)
TA(0) :
= a xB(0) = b
(3)
i) Find the solution to the IVP.
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