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{\bf Math 226.01: Differential Equations and Linear Algebra }
\\
{\bf Quiz 3}
\\
{\bf September 17, 1998}
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\vspace*{.4cm}

\underline{{\bf Name:}\hspace*{10cm}}


Given the differential equation
\[
     y'=(y-1)(y-2)(y-4)^2.
\]
a) 
\hfill\begin{minipage}[t]{18cm}
Find the (constant) equilibrium solutions and classify each of them as 
asymptotically stable, unstable, or semistable.
\end{minipage}
\\[1ex]
b)
\hfill\begin{minipage}[t]{18cm}
Sketch the equilibrium solutions and also the two solutions $y_1$ and $y_2$ 
which satisfy the initial condition $y_1(0)=3$ and $y_2(0)= 1.5$.
You may put all five curves into one graph and neglect concavity. 
\end{minipage}



\vfill
\underline{{\bf Answer:}\hspace*{10cm}}

Sign the pledge:
``On my honor, I have neither given nor received unauthorized aid on this Exam.''

\underline{{\bf Signature:}\mbox{\hspace*{10cm}}}

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