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ubuntu2004
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<?xml version='1.0' encoding='UTF-8'?>

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<exercise xmlns="https://spatext.clontz.org" version="0.0">

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  <statement>

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      <p>

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          Explain how to use an appropriate Existence and Uniqueness Theorem to determine

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          the largest possible domain guaranteed for a unique solution to each IVP.

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      </p>

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      <ol>

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          {{#ivps}}

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              <li>

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                  <m>

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                      {{ode}};\qquad

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                      {{y}}({{t0}})={{y0}}

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                      {{#yp0}},{{y}}'({{t0}})={{yp0}}{{/yp0}}

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                      {{#ypp0}},{{y}}''({{t0}})={{ypp0}}{{/ypp0}}

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                  </m>

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              </li>

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          {{/ivps}}

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      </ol>

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  </statement>

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  <answer>

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      <ol>

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          {{#ivps}}

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              <li>

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                  {{#interval}}

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                      By the Linear ODE Existence and Uniqueness Theorem, the IVP has

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                      a unique solution defined on the interval <m>{{interval}}</m>.

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                  {{/interval}}

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                  {{#domain}}

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                      By the First Order ODE Existence and Uniqueness Theorem, the IVP has

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                      a unique solution defined {{domain}}.

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                  {{/domain}}

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              </li>

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          {{/ivps}}

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      </ol>

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  </answer>

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</exercise>

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