# Since the right hand side is related to one of the

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Unformatted text preview: ng the initial conditions, we require that Hence the solution of the IVP is x 13. Setting x results in the algebraic equations . The characteristic equation is , with a single root of . With ________________________________________________________________________ page 421 —————————————————————————— CHAPTER 7. —— , the system reduces to a single equation Hence one solution is . An eigenvector is given by x . In order to find a second linearly independent solution, we search for a generalized eigenvector whose components satisfy . These equations reduce to . Let , some arbitrary constant. Then Before proceeding, note that if we set , the original equation is transformed into a constant coefficient equation with independent variable . Recall that a second solution is obtained by multiplication of the first solution by the factor . This implies that we must multiply first solution by a factor of . Hence a second linearly independent solution is x Dropping the last term, the general solution is x 15. The characte...
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