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\textbf{Math 325: Differential Equations}
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\textbf{Quiz 3}\quad \textsl{February 9, 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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Consider the attached graph of two numerical solutions of a single
first order differential equation
$y'(x)=f(x,y)\/$ with initial condition  $y(0)=-1/2\/$.
The dotted curve was produced with Maple's {\bf dsolve} command
using the default accuracy settings.  The solid curve was produced 
by increasing the accuracy by two decimal points (i.e., setting
Digits := 12).

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a)  On which interval (approximately) is the first solution (the dotted
curve) likely to be accurate?  Explain.


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b)  Can you deduce anything about the solution  as  $x\to \infty\/$? 


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c) Which of the following differential equations could be the source
of the graph?  Justify your answer.
 
\begin{itemize}
\item[]  $y'=\sin ^2 x\/$ 
\item[]  $y'=y^3 \/$ 
\item[] $y'= \sin x + y\/$
\item[] $y'= e^{y^3}\/$
\end{itemize}

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