Problem 4. Suppose that you have two spatial locations A and B. You have a populationof self-driving vehicles, that switch from location A to B, with probability KABAT,and fromlocation B to A with probability kBAAt. This can be represented by a "reversible chemicalreaction", with "reaction rates" kAB and and kBAA KAB, BkBAВThe population of self-driving vehicles in each location A and B is given by XA(t) andXB(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.

Answered: Image /qna-images/answer/acc5a6b5-4c36-4f44-ac2a-d55ba03ed997.jpg

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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