In this problem, the coefficient matrix contains a parameter a.(a) Find the eigenvalues of the given system in terms of a.λ = a +x'- (-22) xX' =Xαiα =(b) Find the critical value of a where the qualitative nature of the phase portrait for the system changes.

(a) The coefficient matrix for given system is A = α2-2α The…

Answered: In this problem, the coefficient matrix…

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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Consider the system of differential equations For this system, the smaller eigenvalue is (-39/10) [Note-- you may want to view a phase plane plot (right click to open in a new window).] If y'= Ay is a differential equation, how would the solution curves behave? • All of the solutions curves would converge towards 0. (Stable node) All of the solution curves would run away from 0. (Unstable node) and the larger eigenvalue is The solution curves would race towards zero and then veer away towards infinity. (Saddle) The solution curves converge to different points. The solution to the above differential equation with initial values (0) = 4, y(0) = 3 is (t)= (49/12)*e^((-9/10)*t)-(1/12)*e^((-19/10)*t) y(t) = (49/12)*e^((-9/10)*t)+(5/12)*e^((-19/10)*t) da dt dy dt = -1.4x +0.75y, = 1.66667 3.4y. (-9/10)
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In this problem, the coefficient matrix contains a parameter a. (a) Find the eigenvalues of the given system in terms of a. λ = a + X' x = α (_2₂²), -2 X (b) Find the critical value of a where the qualitative nature of the phase portrait for the system changes.