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\textbf{Math 325: Differential Equations}
\hfill\makebox[2.5in][r]{Name:\hrulefill}

\textbf{Quiz 5}\quad \textsl{Nov. 22, 1996}

Consider the non-linear system
\begin{eqnarray*}
\frac{dx}{dt} &=&  x(3 -  x - y) \\
\frac{dy}{dt} &=&  y(4 - 2y - x)\\
\end{eqnarray*}

\textit{a)} Find all critical points of this system.

\textit{b)} Classify each critical point by type and stability.

\textit{c)} Describe what happens to the solution that passes through the
point $(1,1)$ in the phase plane as $t\to\infty$.

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