1 In class, we analyzed a model of glycolysis:i = -x + ay + ²y,ý = b – ay – x²y .Show that solutions of this ODE are confined to the setQ = {(r, y) E R² | a20,0 0 around (b, b/(a + b²)), with ɛ being very small. Arewe guaranteed that Q = Q\ B would contain a closed trajectory?

Answered: Image /qna-images/answer/ec7a6318-5ae9-466f-8dd8-620ee14839b8.jpg

Answered: In class, we analyzed a model of…

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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22.Prove that for the system dxdt=F(x,y),dydt=G(x,y) there is at most one trajectory passing through a given point (x0, y0). Hint: Let C0 be the trajectory generated by the solution x = ϕ0(t), y = ψ0(t), with ϕ0(t0) = x0, ψ0(t0) = y0, and let C1 be the trajectory generated by the solution x = ϕ1(t), y = ψ1(t), with ϕ1(t1) = x0, ψ1(t1) = y0. Use the fact that the system is autonomous, and also the existence and uniqueness theorem, to show that C0 and C1 are the same.
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In class, we analyzed a model of glycolysis: i = -x + ay + ²y, ý = b – ay – x²y . Show that solutions of this ODE are confined to the set Q = {(r, y) E R² | a20,0 0 around (b, b/(a + b²)), with ɛ being very small. Are we guaranteed that Q = Q\ B would contain a closed trajectory?