The following problem can be interpreted as describing theinteraction of two species with populations x and y. For the criticalpoint (0,6) find the corresponding linear system. Find theeigenvalues and eigenvectors of the linear system.dxx(12 — x − 9y),dtNumber of eigenvectors: Twor1=72stable center=Choose oneunstable spiral pointstable spiral pointunstable saddle pointstable saddle pointasymptotically stable nodeunstable node=dydt=??y (6 - y - 12x)

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Answered: The following problem can be…

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 following coefficient matrix, which contains a parameter a. 3 - x' 4 4 9. 4 Determine the eigenvalues in terms of a. r2 Find the critical value or values of a, where the qualitative nature of the phase portrait for the system changes. Number of critical values: Choose one one two ||
Consider the following system of first order homogeneous equations -1 2 E. 0. Find the eigenvalues of the coefficient matrix A. a n= 1, r, = 2 T1=1, b. 1=-1, Oc n= 1, =2 C. T2=-2 O d. Ti=1, T= 2 72= Previous page
Consider the system of ODEs: x' = -3x – y y' = 4x + 2y Find the equilibrium solution(s) and classify them based on the eigenvalues and eigenvectors of the associated coefficient matrix. You do NOT need to solve the system. Please type in your step-by-step solution.
6. The nonlinear system y₁ = -y₁ - y2, y₂ = y₁ + y₂, has steady states at (0,0), (1, -1), and (-1,1). Classify each steady state as a source (all eigenvalues have positive real part), sink (all eigenvalues have negative real part), saddle (one eigenvalue with positive real part and one with negative real part), or center (all eigenvalues purely imaginary).
can you please do c and d
Suppose that a 2 x 2 matrix A with real entries has an eigenvalue X = 1 + 3i with corresponding 4 i [12] eigenvector 1 + 2i Which of the following is NOT a solution of the linear system y' = Ay? y(t) = et y(t) = et y(t) = et y(t) = et 4 cos(3t) sin(3t) [cos(3t) + 2 sin(3t). 4 cos(3t) + sin(3t) cos(3t) 2 sin (3t) - cos(3t) + 4 sin(3t) 2 cos(3t) + sin(3t) cos (3t) - 4 sin (3t) -2 cos(3t) - sin(3t)
Find the General Solution of the given systems. Make sure to indicate your Eigenvalues and Eigenvectors.
Jj.24.
The coefficient matrix has a zero eigenvalue. As a result, the pattern of trajectories is different from those in the examples in the text. For each system: Find the general solution of the given system of equations.

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