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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 Spring '08
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