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Unformatted text preview: e 388 —————————————————————————— CHAPTER 7. ——
11 . 12. Solution of the ODEs is based on the analysis of the algebraic equations
.
The characteristic equation is
, with roots
. Setting
, the two equations reduce to
. The corresponding
eigenvector is
One of the complexvalued solutions is given by
x Hence the general solution is
x . Let x The solution of the initial value problem is
x With x , the solution is ________________________________________________________________________
page 389 —————————————————————————— CHAPTER 7. —— x . ________________________________________________________________________
page 390 —————————————————————————— CHAPTER 7. ——
. 13 . The characteristic equation of the coefficient matrix is
roots
. , with . When
and
, the equilibrium point
is a stable spiral and an
unstable spiral, respectively. The equilibrium point is a center when
. _________________________________________________________...
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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 UniversityWest Lafayette.
 Spring '08
 Staff

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