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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
, the algebraic equations reduce to
. An eigenvector is
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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- Spring '08