\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} The horizontal and vertical axes on
the graph below have different scales. $x$ goes from $-10$ to $10$ and
$y$ goes from $-1$ to $3.5$.  The graph is a direction field for the
differential equation $
y'={1\over{10}}\left(1-{1\over{10}}yx^2\right).$

\bigskip

\centerline{\epsfxsize=3in{\epsfbox{w6W.eps}}}

\medskip

\noindent a) Sketch the solution curve which passes
through $(0,1)$ {\bf on the graph above}.

\medskip

\noindent b) How many critical points does this solution curve seem to have?
What types of critical points do they seem to be? If $(x_0,y_0)$ is a
critical point, find an exact algebraic relationship between $x_0$ and
$y_0$.

\medskip

\noindent {\bf Comment} The equation {\it can't}\/ be solved in terms
of standard functions. Information from the graph and the differential
equation should be used.

%An ``explicit'' solution for this initial value problem can be
%given. Both the exponential function and the Gamma function appear!
%The solution is certainly {\it not}\/ ``elementary''! I think the
%domain of the solution is $(a,\infty)$ for some negative $a$ (not
%obvious!). Using the DEplot command of Maple can have some weird
%output unless the stepsize is made small.

\vfil\eject\end

