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dy dt = x + ky where k is a (real) parameter. (a) Write the system in matrix form d = AY. (b) Write the determinant and trace of A in terms of k and use these to find all values of k where the system has a bifurcation. in (c) Determine the type of equilibrium at the origin for all values of k which are not the hifungo

dy dt = x + ky where k is a (real) parameter. (a) Write the system in matrix form d = AY. (b) Write the determinant and trace of A in terms of k and use these to find all values of k where the system has a bifurcation. in (c) Determine the type of equilibrium at the origin for all values of k which are not the hifungo

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 31E
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This question concerns the linear system of differential equations dx kx + (k² + k)y dt dy dt = x + ky where k is a (real) parameter. (a) Write the system in matrix form d (b) Write the determinant and trace of A in terms of k and use these to find all values of k where the system has a bifurcation. = AY. (c) Determine the type of equilibrium at the origin for all values of k which are not the bifurcation values given in (b).
Transcribed Image Text:This question concerns the linear system of differential equations dx kx + (k² + k)y dt dy dt = x + ky where k is a (real) parameter. (a) Write the system in matrix form d (b) Write the determinant and trace of A in terms of k and use these to find all values of k where the system has a bifurcation. = AY. (c) Determine the type of equilibrium at the origin for all values of k which are not the bifurcation values given in (b).
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