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Unformatted text preview: saddle. For
, the roots are both positive, and the equilibrium point
is an unstable node. Finally, when
, both roots are negative, with the
equilibrium point being a stable node. ________________________________________________________________________
page 394 —————————————————————————— CHAPTER 7. —— 20. The characteristic equation is , with roots The roots are complex when
. Since the real part is negative, the origin
is a stable spiral. Otherwise the roots are real. When
, both roots
are negative, and hence the equilibrium point is a stable node. For
, the roots
are of opposite sign and the origin is a saddle. 22. Based on the method in Prob. of Section , setting x results in the ________________________________________________________________________
page 395 —————————————————————————— CHAPTER 7. ——
The characteristic equation for the system is
, with roots
, the equations reduce to the single equation
. A correspondi...
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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