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\textbf{Math 325: Differential Equations}
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\textbf{Quiz 5}\quad \textsl{February 23, 2001}
 
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You may  use your own calculator.
You may not use anything else.  You may not pass a calculator 
to another person.

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Show all your work.  Erase or cross out any work you do not want graded.

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a)  Find the general solution of the system of differential equations
$$
{\mathbf x}'=
\left[\begin{array}{rr} 1 & \sqrt 8\\ \sqrt 8 & -1\end{array} \right]
{\mathbf x}.
$$

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b) 
How will the solution of the initial value problem
$$
{\mathbf x}'=
\left[\begin{array}{rr} 1 & \sqrt 8\\ \sqrt 8 & -1\end{array} \right]
{\mathbf x},
\qquad {\mathbf x}(0)= \left[\begin{array}{r} 1\\0 \end{array} \right]
$$
behave as $t\to\infty$?

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