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# 24 the characteristic equation of the system is with

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Unformatted text preview: e 388 —————————————————————————— CHAPTER 7. —— 11 . 12. Solution of the ODEs is based on the analysis of the algebraic equations . The characteristic equation is , with roots . Setting , the two equations reduce to . The corresponding eigenvector is One of the complex-valued solutions is given by x Hence the general solution is x . Let x The solution of the initial value problem is x With x , the solution is ________________________________________________________________________ page 389 —————————————————————————— CHAPTER 7. —— x . ________________________________________________________________________ page 390 —————————————————————————— CHAPTER 7. —— . 13 . The characteristic equation of the coefficient matrix is roots . , with . When and , the equilibrium point is a stable spiral and an unstable spiral, respectively. The equilibrium point is a center when . _________________________________________________________...
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