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

\textbf{Quiz 4}\quad \textsl{Nov. 14, 1997}

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

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

\bigskip
\textit{b)} Find the corrseponding linear system near each critical
point and determine its eigenvalues.

\bigskip
\textit{c)} Discuss the type and stability of each critical point of
the original system.

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