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Unformatted text preview: distinct, the general solution is
x The entire line along the eigendirection
consists of equilibrium points.
All other solutions diverge. The direction field changes across the line
Eliminating the exponential terms in the solution, the trajectories are given by
10. The characteristic equation is given by The equation has complex roots
solution vector must satisfy
A corresponding eigenvector is
general solution is . For
, the components of the
. Thus the corresponding eigenvector is
results in the single equation
Since the eigenvalues are distinct, the x 11. Setting x results in the algebraic equations ________________________________________________________________________
page 368 —————————————————————————— CHAPTER 7. —— .
For a nonzero solution, we must have
of the characteristic equation are
and . Setting . The roots
, we .
This system is reduces to the equations A corresponding solution vector is given by
the reduced system of equations is Setting , A corresponding solution vector is given by
, the reduced system of equations is Finally, setting A corresponding solution vector is give...
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- Spring '08