<exercise>
<statement>
<p>
Consider the following
autonomous ODE.
</p>
<me><xsl:value-of select="ode"/></me>
<ol>
<li>
<p>Draw a slope field and phase line for the ODE.</p>
</li>
<li>
<p>
Mark each equilibrium of the ODE, and label each
as sink/source/neither and stable/unstable.
</p>
</li>
<li>
<p>
Suppose you have the initial condition
<m>x(<xsl:value-of select="t0"/>)=<xsl:value-of select="x0"/></m>.
Explain where the value of <m>x</m> limits as <m>t</m> grows very large,
under both theoretical and real-world contexts.
</p>
</li>
</ol>
</statement>
<answer>
<p>
The equilibrium <m><xsl:value-of select="a"/></m> is <xsl:value-of select="a_label"/>.
</p>
<xsl:if test="z_label != 'NA'">
<p>
The equilibrium <m>0</m> is <xsl:value-of select="z_label"/>.
</p>
</xsl:if>
<p>
The equilibrium <m><xsl:value-of select="b"/></m> is <xsl:value-of select="b_label"/>.
</p>
<p>
Mathematically, <m>x</m> limits to <m><xsl:value-of select="math_lim"/></m>.
</p>
<p>
Under real-world conditions, <m>x</m> limits to <m><xsl:value-of select="real_lim"/></m>.
</p>
</answer>
</exercise>
