<?xml version='1.0' encoding='UTF-8'?>
<exercise xmlns="https://spatext.clontz.org" version="0.0">
<statement>
<p>
For each of the following Initial Value Problems (IVPs), designate the following:
</p>
<ul>
<li>its Ordinary Differential Equation (ODE)</li>
<li>its Initial Value or Values (IVs)</li>
<li>the order of the IVP</li>
<li>its independent variable</li>
<li>its dependent variable</li>
<li>whether its solution is implicit or explicit</li>
</ul>
<p>
Then show how to verify that its solution is valid.
</p>
<ol>
{{#ivps}}
<li>
<ul>
<li>IVP:
<m>
{{ode}};\qquad
{{y}}({{t0}})=
{{y0}}{{#yp0}},
{{y}}'({{t0}})=
{{yp0}}
{{/yp0}}
</m>
</li>
<li>Solution: <m>{{sol}}</m></li>
</ul>
</li>
{{/ivps}}
</ol>
</statement>
<answer>
<ol>
{{#ivps}}
<li>
<ul>
<li>ODE: <m>{{ode}}</m></li>
<li>IV(s): <m>
{{y}}({{t0}})={{y0}}
{{#yp0}},{{y}}'({{t0}})={{yp0}}{{/yp0}}
</m></li>
<li>Order: {{order}}</li>
<li>Independent variable: <m>{{t}}</m></li>
<li>Dependent variable: <m>{{y}}</m></li>
<li>The solution <m>{{sol}}</m> is {{ex_im}}.</li>
</ul>
</li>
{{/ivps}}
</ol>
</answer>
</exercise>
