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4. Consider the linear system of differential equations -1 (5)-(G 2)6) = a (1) where a € R is a parameter. (a) Find the eigenvalues and the corresponding eigenvectors of the matrix of the system, and write the general solution of system (1). (b) Characterise the steady state (0,0) as a varies from -∞ to +∞0. (c) Sketch the phase portrait of the system as accurately as possible for the following values of the parameter a. In each case explain your reasoning. (i) a = -1, (ii) a = 0.

4. Consider the linear system of differential equations -1 (5)-(G 2)6) = a (1) where a € R is a parameter. (a) Find the eigenvalues and the corresponding eigenvectors of the matrix of the system, and write the general solution of system (1). (b) Characterise the steady state (0,0) as a varies from -∞ to +∞0. (c) Sketch the phase portrait of the system as accurately as possible for the following values of the parameter a. In each case explain your reasoning. (i) a = -1, (ii) a = 0.

Advanced Engineering Mathematics
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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4. Consider the linear system of differential equations a -1 (H-G 200) = 1 a (1) where a € IR is a parameter. (a) Find the eigenvalues and the corresponding eigenvectors of the matrix of the system, and write the general solution of system (1). (b) Characterise the steady state (0,0) as a varies from -∞ to +∞0. (c) Sketch the phase portrait of the system as accurately as possible for the following values of the parameter a. In each case explain your reasoning. (i) a = -1, (ii) a = 0.
Transcribed Image Text:4. Consider the linear system of differential equations a -1 (H-G 200) = 1 a (1) where a € IR is a parameter. (a) Find the eigenvalues and the corresponding eigenvectors of the matrix of the system, and write the general solution of system (1). (b) Characterise the steady state (0,0) as a varies from -∞ to +∞0. (c) Sketch the phase portrait of the system as accurately as possible for the following values of the parameter a. In each case explain your reasoning. (i) a = -1, (ii) a = 0.
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