<exercise>
<statement>
<p>
Explain how to use an appropriate Existence and Uniqueness Theorem to determine
the largest possible domain guaranteed for a unique solution to each IVP.
</p>
<ol>
<xsl:for-each select="ivps/*">
<li>
<m>
<xsl:value-of select="ode"/>\hspace{2em}
<xsl:value-of select="y"/>(<xsl:value-of select="t0"/>)=
<xsl:value-of select="y0"/><xsl:if test="yp0">,
<xsl:value-of select="y"/>'(<xsl:value-of select="t0"/>)=
<xsl:value-of select="yp0"/></xsl:if><xsl:if test="ypp0">,
<xsl:value-of select="y"/>'(<xsl:value-of select="t0"/>)=
<xsl:value-of select="ypp0"/></xsl:if>
</m>
</li>
</xsl:for-each>
</ol>
</statement>
<answer>
<ol>
<xsl:for-each select="ivps/*">
<li>
<xsl:if test="interval">
By the Linear ODE Existence and Uniqueness Theorem, the IVP has
a unique solution defined on the interval <m><xsl:value-of select="interval"/></m>.
</xsl:if>
<xsl:if test="domain">
By the First Order ODE Existence and Uniqueness Theorem, the IVP has
a unique solution defined <xsl:value-of select="domain"/>.
</xsl:if>
</li>
</xsl:for-each>
</ol>
</answer>
</exercise>
