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\noindent Quiz 3

\noindent Math 230

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\noindent 1.  Consider the initial value problem
$$
\frac{dy}{dx} = \frac{y}{x+y},\quad y(1) = 2.
$$
\begin{itemize}
\item[(a)] Using Euler's method with a step size of .1, estimate y(1.2).
\vskip 3in
\item[(b)] Estimate the local truncation error that occurred in the first
step of part (a).
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\end{itemize}

\noindent 2.  Consider the differential equation 
$$
\frac{dy}{dx} = f(y)
$$
where the graph of $f$ is shown below:

\vskip 2in

\begin{itemize}
\item[(a)] Identify (approximately) the equilibrium solutions of $f$ and 
indicate whether each is stable, unstable or semistable.
\item[(b)] What is $\lim\limits_{x\to\infty} y(x)$ if y(0) = 1?  if y(0) = -1?
\end{itemize}


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