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Unformatted text preview: saddle. For the case , 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. —— algebraic equations . The characteristic equation for the system is , with roots . With , the equations reduce to the single equation . A correspondi...
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