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Unformatted text preview: ”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€” CHAPTER 7. â€”â€” x , which is a constant vector. A second linearly independent solution is obtained from the
system
.
The equations reduce to the single equation
Let
, and a second linearly independent solution is . We obtain x Dropping the last term, the general solution is
x
Imposing the initial conditions, we require that
,
which results in and Therefore the solution of the IVP is
x ________________________________________________________________________
page 420 â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€” CHAPTER 7. â€”â€” 12. The characteristic equation of the system is
. The
eigenvalues are
and
. The eigenvector associated with
is
Setting
, the components of the eigenvectors must
satisfy the relation An eigenvector vector is given by
Since the last equation has two
free variables, a third linearly independent eigenvector associated with
is
Therefore the general solution may be written as
x
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This note was uploaded on 03/11/2014 for the course MA 303 taught by Professor Staff during the Spring '08 term at Purdue.
 Spring '08
 Staff

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