Unformatted text preview: nt on x x . It follows that , for . ________________________________________________________________________
page 365 —————————————————————————— CHAPTER 7. ——
Section 7.5
2. Setting x , and substituting into the ODE, we obtain the algebraic equations
. For a nonzero solution, we must have
A
I
. The roots of the
characteristic equation are
and
. For
, the two equations
reduce to
. The corresponding eigenvector is
Substitution of
results in the single equation
. A corresponding eigenvector is
Since the eigenvalues are distinct, the general solution is
x 3. Setting x results in the algebraic equations
. For a nonzero solution, we must have
A
I
. The roots of the
characteristic equation are
and
. For
, the system of equations
reduces to
. The corresponding eigenvector is
Substitution of
results in the single equation
. A corresponding eigenvector is
Since the eigenvalues are distinct, the general solution is
x ________________________________________________________________________
page 366 —————————————...
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 Spring '08
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 Linear Algebra, eigenvector

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