# Since the coefficient matrix is symmetric the

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Unformatted text preview: ristic equation is Hence the eigenvalues are 16 . Using the result in Prob. The discriminant vanishes when , the eigenvalues are . ________________________________________________________________________ page 422 —————————————————————————— CHAPTER 7. —— . The system of differential equations is The associated eigenvalue problem is . The characteristic equation is , with a single root of . Setting , the algebraic equations reduce to . An eigenvector is given by Hence one solution is . A second solution is obtained from a generalized eigenvector whose components satisfy . It follows that and A second linearly independent solution is Dropping the last term, the general solution is Imposing the initial conditions, we require that , which results in 18 and Therefore the solution of the IVP is . The eigensystem is obtained from analysis of the equation ________________________________________________________________________ page 423 —————...
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