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      <header alignment="Center" color="#a9a9a9">&amp;[DATE] &amp;[TIME] - &amp;[FILENAME]</header>
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  <region id="0" left="9" top="18" width="301" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p bold="true">Gewöhnliche Differenzialgleichungen
Beispiele für DGL 2. Ordnung</p>
    </text>
    <text lang="eng">
      <p bold="true">Ordinary Differential Equations
Examples for second order ODEs</p>
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  <region id="1" left="432" top="18" width="301" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Section Math ODE.sm">Gewöhnliche Differenzialgleichungen</p>
    </text>
    <text lang="eng">
      <p href="Section Math ODE.sm">Ordinary Differential Equations</p>
    </text>
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  <region id="2" left="432" top="36" width="94" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Mathematik.sm">Mathematik</p>
    </text>
    <text lang="eng">
      <p href="Mathematik.sm">Mathematics</p>
    </text>
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  <region id="3" left="432" top="54" width="61" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Handbook.sm">Inhalt</p>
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    <text lang="eng">
      <p href="Handbook.sm">Contents</p>
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    <text lang="ger">
      <p>Die folgenden Beispiele sind einem Forum-Beitrag von Vyacheslav Mezentsev entnommen:</p>
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    <text lang="eng">
      <p>The following examples are taken from a forum post by Vyacheslav Mezentsev:</p>
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    <text lang="ger">
      <p>Die Struktur der Beispiele ist immer gleich:</p>
    </text>
    <text lang="eng">
      <p>The examples all follow the pattern outlined here:</p>
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      <p>Differenzialgleichung und Anfangsbedingungen</p>
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      <p>differential equation and initial conditions</p>
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        <p>Maxima Solution</p>
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      <p>Aufbereitung für die numerische Lösung:
Vektor der Ableitungen und der Anfangswerte
der unbekannten Funktionen y </p>
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    <text lang="eng">
      <p>prepare ODE for solution:
provide vector y'(x,y) and 
initial conditions </p>
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    <text lang="ger">
      <p>Integrationsbereich und Schrittzahl</p>
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    <text lang="eng">
      <p>range and step of the  independent variable
</p>
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      <p>Lösung und Ergebnisdarstellung</p>
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            <e type="operand">1</e>
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            <e type="operand">k1</e>
            <e type="operator" args="2">*</e>
            <e type="function" preserve="true" args="1">cos</e>
            <e type="operand">2</e>
            <e type="operator" args="1">-</e>
            <e type="operand">2</e>
            <e type="operand">k1</e>
            <e type="operator" args="2">*</e>
            <e type="function" preserve="true" args="1">cos</e>
            <e type="operator" args="2">+</e>
            <e type="bracket">(</e>
            <e type="operator" args="2">*</e>
            <e type="operator" args="2">+</e>
            <e type="operand">2</e>
            <e type="operand">k1</e>
            <e type="operator" args="2">*</e>
            <e type="function" preserve="true" args="1">sin</e>
            <e type="operand">2</e>
            <e type="operator" args="2">^</e>
            <e type="operator" args="2">+</e>
            <e type="bracket">(</e>
            <e type="operator" args="2">*</e>
            <e type="operator" args="2">-</e>
            <e type="bracket">(</e>
            <e type="operator" args="2">*</e>
            <e type="operand">4</e>
            <e type="operand">k1</e>
            <e type="operator" args="2">*</e>
            <e type="function" preserve="true" args="1">cos</e>
            <e type="operand">1</e>
            <e type="operand">1</e>
            <e type="operand">2</e>
            <e type="operand">2</e>
            <e type="operand">k1</e>
            <e type="operator" args="2">*</e>
            <e type="function" preserve="true" args="1">cos</e>
            <e type="operator" args="2">*</e>
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            <e type="bracket">(</e>
            <e type="operand">2</e>
            <e type="operand">k1</e>
            <e type="operator" args="2">*</e>
            <e type="function" preserve="true" args="1">sin</e>
            <e type="operand">2</e>
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            <e type="operator" args="2">*</e>
            <e type="operator" args="2">+</e>
            <e type="operand">2</e>
            <e type="operand">k1</e>
            <e type="operator" args="2">*</e>
            <e type="function" preserve="true" args="1">cos</e>
            <e type="operand">4</e>
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            <e type="operand">2</e>
            <e type="operand">k1</e>
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            <e type="function" preserve="true" args="1">cos</e>
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            <e type="operand">2</e>
            <e type="operand">k1</e>
            <e type="operator" args="2">*</e>
            <e type="function" preserve="true" args="1">cos</e>
            <e type="operator" args="2">*</e>
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            <e type="bracket">(</e>
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            <e type="operand">1</e>
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            <e type="operand">k1</e>
            <e type="operator" args="2">*</e>
            <e type="function" preserve="true" args="1">cos</e>
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            <e type="bracket">(</e>
            <e type="operand">4</e>
            <e type="operand">k1</e>
            <e type="operator" args="2">*</e>
            <e type="function" preserve="true" args="1">cos</e>
            <e type="operator" args="2">*</e>
            <e type="operator" args="2">+</e>
            <e type="bracket">(</e>
            <e type="operator" args="2">*</e>
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            <e type="operand">2</e>
            <e type="operand">2</e>
            <e type="operand">k1</e>
            <e type="operator" args="2">*</e>
            <e type="function" preserve="true" args="1">sin</e>
            <e type="operand">4</e>
            <e type="operator" args="2">^</e>
            <e type="operand">2</e>
            <e type="operand">k1</e>
            <e type="operator" args="2">*</e>
            <e type="function" preserve="true" args="1">cos</e>
            <e type="operand">3</e>
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            <e type="operand">3</e>
            <e type="operator" args="1">-</e>
            <e type="operand">2</e>
            <e type="operand">k1</e>
            <e type="operator" args="2">*</e>
            <e type="function" preserve="true" args="1">cos</e>
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            <e type="bracket">(</e>
            <e type="operator" args="2">*</e>
            <e type="operator" args="2">+</e>
            <e type="bracket">(</e>
            <e type="operator" args="2">*</e>
            <e type="operator" args="2">+</e>
            <e type="operand">3</e>
            <e type="operand">2</e>
            <e type="operand">k1</e>
            <e type="operator" args="2">*</e>
            <e type="function" preserve="true" args="1">cos</e>
            <e type="operator" args="2">*</e>
            <e type="operator" args="2">-</e>
            <e type="bracket">(</e>
            <e type="operator" args="2">*</e>
            <e type="operator" args="2">+</e>
            <e type="operand">5</e>
            <e type="operand">4</e>
            <e type="operand">2</e>
            <e type="operand">k1</e>
            <e type="operator" args="2">*</e>
            <e type="function" preserve="true" args="1">cos</e>
            <e type="operator" args="2">*</e>
            <e type="operand">3</e>
            <e type="operator" args="1">-</e>
            <e type="operand">2</e>
            <e type="operand">2</e>
            <e type="operand">k1</e>
            <e type="operator" args="2">*</e>
            <e type="function" preserve="true" args="1">cos</e>
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            <e type="operator" args="2">+</e>
            <e type="bracket">(</e>
            <e type="operator" args="2">*</e>
            <e type="operator" args="2">+</e>
            <e type="bracket">(</e>
            <e type="operand">2</e>
            <e type="operand">k1</e>
            <e type="operator" args="2">*</e>
            <e type="function" preserve="true" args="1">sin</e>
            <e type="operand">2</e>
            <e type="operator" args="2">^</e>
            <e type="operator" args="2">*</e>
            <e type="operator" args="2">+</e>
            <e type="operand">13</e>
            <e type="operand">2</e>
            <e type="operand">k1</e>
            <e type="operator" args="2">*</e>
            <e type="function" preserve="true" args="1">cos</e>
            <e type="operand">2</e>
            <e type="operator" args="2">^</e>
            <e type="operator" args="2">*</e>
            <e type="operator" args="2">+</e>
            <e type="operator" args="2">/</e>
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        </math>
      </region>
      <region id="34" left="18" top="1143" width="348" height="80" color="#000000" bgColor="#ffffff" fontSize="10">
        <math evaluate="false" error="9">
          <input>
            <e type="operand">0</e>
            <e type="function" args="1">y.2</e>
            <e type="operand">y.0</e>
            <e type="operator" args="2">≡</e>
            <e type="operand">x</e>
            <e type="function" args="1">y.2</e>
            <e type="operand">x</e>
            <e type="function" preserve="true" args="2">diff</e>
            <e type="operand">x</e>
            <e type="operand">0</e>
            <e type="function" preserve="true" args="3">lim</e>
            <e type="operand">y'.0</e>
            <e type="operator" args="2">≡</e>
            <e type="operand">2</e>
            <e type="operand">1</e>
            <e type="function" preserve="true" args="4">sys</e>
            <e type="operand">k1</e>
            <e type="operand">k2</e>
            <e type="operand">2</e>
            <e type="operand">1</e>
            <e type="function" preserve="true" args="4">sys</e>
            <e type="function" preserve="true" args="2">Solve</e>
            <e type="function" preserve="true" args="1">Assign</e>
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          <result action="symbolic">
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          </result>
        </math>
      </region>
      <region id="35" left="9" top="1224" width="15475" height="86" color="#000000" bgColor="#ffffff" fontSize="10">
        <math evaluate="false">
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            <e type="operand">x</e>
            <e type="function" args="1">y.2</e>
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            <e type="operand">2</e>
            <e type="operand">2</e>
            <e type="operand">r2</e>
            <e type="operator" args="2">*</e>
            <e type="function" preserve="true" args="1">cos</e>
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            <e type="operand">2</e>
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            <e type="operand">4</e>
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            <e type="function" preserve="true" args="1">sin</e>
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            <e type="operand">2</e>
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            <e type="operator" args="2">*</e>
            <e type="function" preserve="true" args="1">sin</e>
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            <e type="operand">2</e>
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            <e type="operand">2</e>
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            <e type="function" preserve="true" args="1">sin</e>
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            <e type="function" preserve="true" args="1">sin</e>
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            <e type="operator" args="2">*</e>
            <e type="operator" args="2">+</e>
            <e type="operand">2</e>
            <e type="operand">x</e>
            <e type="function" args="1">y.3</e>
            <e type="operator" args="2">*</e>
            <e type="operator" args="2">+</e>
            <e type="operand">2</e>
            <e type="operand">e</e>
            <e type="operand">x</e>
            <e type="operator" args="1">-</e>
            <e type="operator" args="2">^</e>
            <e type="operator" args="2">*</e>
            <e type="operand">x</e>
            <e type="function" preserve="true" args="1">cos</e>
            <e type="operator" args="2">*</e>
            <e type="operator" args="2">≡</e>
            <e type="operand">x</e>
            <e type="function" args="1">y.3</e>
            <e type="operand">x</e>
            <e type="function" preserve="true" args="3">ODE.2</e>
            <e type="function" preserve="true" args="1">Assign</e>
          </input>
          <result action="symbolic">
            <e type="operand">x</e>
            <e type="function" preserve="true" args="1">sin</e>
            <e type="operand">x</e>
            <e type="operand">k1</e>
            <e type="operator" args="2">+</e>
            <e type="bracket">(</e>
            <e type="operator" args="2">*</e>
            <e type="operand">x</e>
            <e type="function" preserve="true" args="1">cos</e>
            <e type="operand">1</e>
            <e type="operand">k2</e>
            <e type="operator" args="2">+</e>
            <e type="bracket">(</e>
            <e type="operator" args="2">*</e>
            <e type="operator" args="2">+</e>
            <e type="operand">e</e>
            <e type="operand">x</e>
            <e type="operator" args="2">^</e>
            <e type="operator" args="2">/</e>
          </result>
        </math>
      </region>
      <region id="56" left="18" top="2214" width="349" height="79" color="#000000" bgColor="#ffffff" fontSize="10">
        <math evaluate="false">
          <input>
            <e type="operand">0</e>
            <e type="function" args="1">y.3</e>
            <e type="operand">1</e>
            <e type="operator" args="2">≡</e>
            <e type="operand">x</e>
            <e type="function" args="1">y.3</e>
            <e type="operand">x</e>
            <e type="function" preserve="true" args="2">diff</e>
            <e type="operand">x</e>
            <e type="operand">0</e>
            <e type="function" preserve="true" args="3">lim</e>
            <e type="operand">0</e>
            <e type="operator" args="2">≡</e>
            <e type="operand">2</e>
            <e type="operand">1</e>
            <e type="function" preserve="true" args="4">sys</e>
            <e type="operand">k1</e>
            <e type="operand">k2</e>
            <e type="operand">2</e>
            <e type="operand">1</e>
            <e type="function" preserve="true" args="4">sys</e>
            <e type="function" preserve="true" args="2">Solve</e>
            <e type="function" preserve="true" args="1">Assign</e>
          </input>
          <result action="symbolic">
            <e type="operand">1</e>
            <e type="operand">0</e>
            <e type="operand">2</e>
            <e type="operand">1</e>
            <e type="function" preserve="true" args="4">sys</e>
            <e type="operand">1</e>
            <e type="operand">1</e>
            <e type="function" preserve="true" args="3">mat</e>
          </result>
        </math>
      </region>
      <region id="57" left="387" top="2232" width="111" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
        <math evaluate="false">
          <input>
            <e type="operand">x</e>
            <e type="function" args="1">y.3</e>
          </input>
          <result action="symbolic">
            <e type="operand">x</e>
            <e type="function" args="1">y.3</e>
          </result>
        </math>
      </region>
      <region id="58" left="18" top="2295" width="308" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
        <text lang="ger">
          <p>Alternative Lösung mit desolve()</p>
        </text>
        <text lang="eng">
          <p>Alternative solution using desolve()</p>
        </text>
      </region>
      <region id="59" left="18" top="2331" width="282" height="36" color="#000000" bgColor="#ffffff" fontSize="10">
        <math>
          <input>
            <e type="operand">x</e>
            <e type="function" args="1">y.3</e>
            <e type="operand">x</e>
            <e type="operand">0</e>
            <e type="operator" args="2">≡</e>
            <e type="operand">1</e>
            <e type="function" args="3">atvalue</e>
            <e type="function" preserve="true" args="1">Maxima</e>
          </input>
          <result action="symbolic">
            <e type="operand">1</e>
          </result>
        </math>
      </region>
      <region id="60" left="18" top="2367" width="310" height="48" color="#000000" bgColor="#ffffff" fontSize="10">
        <math>
          <input>
            <e type="operand">x</e>
            <e type="function" args="1">y.3</e>
            <e type="operand">x</e>
            <e type="function" preserve="true" args="2">diff</e>
            <e type="operand">x</e>
            <e type="operand">0</e>
            <e type="operator" args="2">≡</e>
            <e type="operand">0</e>
            <e type="function" args="3">atvalue</e>
            <e type="function" preserve="true" args="1">Maxima</e>
          </input>
          <result action="symbolic">
            <e type="operand">0</e>
          </result>
        </math>
      </region>
      <region id="61" left="18" top="2421" width="766" height="62" color="#000000" bgColor="#ffffff" fontSize="10">
        <math>
          <input>
            <e type="operand">x</e>
            <e type="function" args="1">y.3</e>
            <e type="operand">x</e>
            <e type="operand">2</e>
            <e type="function" preserve="true" args="3">diff</e>
            <e type="operand">2</e>
            <e type="operand">x</e>
            <e type="function" args="1">y.3</e>
            <e type="operand">x</e>
            <e type="function" preserve="true" args="2">diff</e>
            <e type="operator" args="2">*</e>
            <e type="operator" args="2">+</e>
            <e type="operand">2</e>
            <e type="operand">x</e>
            <e type="function" args="1">y.3</e>
            <e type="operator" args="2">*</e>
            <e type="operator" args="2">+</e>
            <e type="operand">2</e>
            <e type="operand">e</e>
            <e type="operand">x</e>
            <e type="operator" args="1">-</e>
            <e type="operator" args="2">^</e>
            <e type="operator" args="2">*</e>
            <e type="operand">x</e>
            <e type="function" preserve="true" args="1">cos</e>
            <e type="operator" args="2">*</e>
            <e type="operator" args="2">≡</e>
            <e type="operand">x</e>
            <e type="function" args="1">y.3</e>
            <e type="function" args="2">desolve</e>
            <e type="function" preserve="true" args="1">Maxima</e>
          </input>
          <result action="symbolic">
            <e type="operand">x</e>
            <e type="function" args="1">y.3</e>
            <e type="operand">x</e>
            <e type="function" preserve="true" args="1">sin</e>
            <e type="operand">1</e>
            <e type="operand">x</e>
            <e type="operator" args="2">+</e>
            <e type="bracket">(</e>
            <e type="operator" args="2">*</e>
            <e type="operand">x</e>
            <e type="function" preserve="true" args="1">cos</e>
            <e type="operator" args="2">+</e>
            <e type="operand">e</e>
            <e type="operand">x</e>
            <e type="operator" args="2">^</e>
            <e type="operator" args="2">/</e>
            <e type="operator" args="2">≡</e>
          </result>
        </math>
      </region>
      <region id="62" left="18" top="2493" width="335" height="52" color="#000000" bgColor="#ffffff" fontSize="10">
        <math>
          <input>
            <e type="operand" style="string">%</e>
            <e type="function" preserve="true" args="1">Maxima</e>
            <e type="function" preserve="true" args="1">Assign</e>
          </input>
          <result action="symbolic">
            <e type="operand">x</e>
            <e type="function" preserve="true" args="1">sin</e>
            <e type="operand">1</e>
            <e type="operand">x</e>
            <e type="operator" args="2">+</e>
            <e type="bracket">(</e>
            <e type="operator" args="2">*</e>
            <e type="operand">x</e>
            <e type="function" preserve="true" args="1">cos</e>
            <e type="operator" args="2">+</e>
            <e type="operand">e</e>
            <e type="operand">x</e>
            <e type="operator" args="2">^</e>
            <e type="operator" args="2">/</e>
          </result>
        </math>
      </region>
      <region id="63" top="2547" color="#000000" bgColor="#ffffff">
        <area terminator="true" />
      </region>
    </region>
    <region id="64" left="9" top="2574" width="270" height="71" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">x</e>
          <e type="operand">y</e>
          <e type="function" args="2">D</e>
          <e type="operand">y</e>
          <e type="operand">2</e>
          <e type="function" preserve="true" args="2">el</e>
          <e type="operand">2</e>
          <e type="operand">e</e>
          <e type="operand">x</e>
          <e type="operator" args="1">-</e>
          <e type="operator" args="2">^</e>
          <e type="operand">x</e>
          <e type="function" preserve="true" args="1">cos</e>
          <e type="operator" args="2">*</e>
          <e type="operand">y</e>
          <e type="operand">2</e>
          <e type="function" preserve="true" args="2">el</e>
          <e type="operand">y</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="2">el</e>
          <e type="operator" args="2">+</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">-</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">*</e>
          <e type="operand">2</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="4">mat</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region id="65" left="288" top="2583" width="287" height="62" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">L</e>
          <e type="operand">y.0</e>
          <e type="operand">y'.0</e>
          <e type="operand">2</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="4">mat</e>
          <e type="operand">0</e>
          <e type="operand">1</e>
          <e type="operand">50</e>
          <e type="operand">x</e>
          <e type="operand">y</e>
          <e type="function" args="2">D</e>
          <e type="function" preserve="true" args="5">rkfixed</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region id="66" left="9" top="2655" width="284" height="34" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">y.num</e>
          <e type="operand">L</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="2">col</e>
          <e type="operand">L</e>
          <e type="operand">2</e>
          <e type="function" preserve="true" args="2">col</e>
          <e type="function" preserve="true" args="2">augment</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region id="67" left="9" top="2700" width="678" height="245" color="#000000" bgColor="#ffffff" fontSize="10">
      <plot type="2d" render="lines" scale_x="10.7191527289318" scale_y="23.4518702799918" scale_z="235.526442983348" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="-298" transpose_y="-91" transpose_z="0">
        <input>
          <e type="operand">y.num</e>
          <e type="operand">x</e>
          <e type="function" args="1">y.3</e>
          <e type="operand">2</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="4">sys</e>
        </input>
      </plot>
    </region>
    <region id="68" top="2988" color="#000000" bgColor="#ffffff">
      <area terminator="true" />
    </region>
  </region>
  <region id="69" left="9" top="3006" width="188" height="34" border="true" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">y''</e>
        <e type="operand">4</e>
        <e type="operand">y</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="operand">e</e>
        <e type="operand">3</e>
        <e type="operand">x</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">^</e>
        <e type="operand">13</e>
        <e type="operand">x</e>
        <e type="operator" args="2">*</e>
        <e type="operand">7</e>
        <e type="operator" args="2">-</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">≡</e>
      </input>
    </math>
  </region>
  <region id="70" left="225" top="3006" width="52" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">y.0</e>
        <e type="operand">2</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="71" left="297" top="3006" width="69" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">y'.0</e>
        <e type="operand">3</e>
        <e type="operator" args="1">-</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="72" top="3042" color="#000000" bgColor="#ffffff">
    <area collapsed="true" />
    <region id="73" top="3060" color="#000000" bgColor="#ffffff">
      <area collapsed="true">
        <title lang="ger">
          <p>Maxima Solution</p>
        </title>
      </area>
      <region id="74" left="18" top="3078" width="146" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
        <math>
          <input>
            <e type="operand">k1</e>
            <e type="operand">k2</e>
            <e type="function" preserve="true" args="2">Clear</e>
          </input>
          <result action="numeric">
            <e type="operand">1</e>
          </result>
        </math>
      </region>
      <region id="75" left="18" top="3105" width="757" height="62" color="#000000" bgColor="#ffffff" fontSize="10">
        <math>
          <input>
            <e type="operand">x</e>
            <e type="function" args="1">y.4</e>
            <e type="operand">x</e>
            <e type="operand">2</e>
            <e type="function" preserve="true" args="3">diff</e>
            <e type="operand">4</e>
            <e type="operand">x</e>
            <e type="function" args="1">y.4</e>
            <e type="operator" args="2">*</e>
            <e type="operator" args="2">+</e>
            <e type="operand">e</e>
            <e type="operand">3</e>
            <e type="operand">x</e>
            <e type="operator" args="2">*</e>
            <e type="operator" args="2">^</e>
            <e type="operand">13</e>
            <e type="operand">x</e>
            <e type="operator" args="2">*</e>
            <e type="operand">7</e>
            <e type="operator" args="2">-</e>
            <e type="bracket">(</e>
            <e type="operator" args="2">*</e>
            <e type="operator" args="2">≡</e>
            <e type="operand">x</e>
            <e type="function" args="1">y.4</e>
            <e type="operand">x</e>
            <e type="function" preserve="true" args="3">ODE.2</e>
            <e type="function" preserve="true" args="1">Assign</e>
          </input>
          <result action="symbolic">
            <e type="operand">k1</e>
            <e type="operand">2</e>
            <e type="operand">x</e>
            <e type="operator" args="2">*</e>
            <e type="function" preserve="true" args="1">sin</e>
            <e type="operator" args="2">*</e>
            <e type="operand">k2</e>
            <e type="operand">2</e>
            <e type="operand">x</e>
            <e type="operator" args="2">*</e>
            <e type="function" preserve="true" args="1">cos</e>
            <e type="operator" args="2">*</e>
            <e type="operator" args="2">+</e>
            <e type="operand">1</e>
            <e type="operator" args="1">-</e>
            <e type="operand">x</e>
            <e type="operator" args="2">+</e>
            <e type="bracket">(</e>
            <e type="operand">e</e>
            <e type="operand">3</e>
            <e type="operand">x</e>
            <e type="operator" args="2">*</e>
            <e type="operator" args="2">^</e>
            <e type="operator" args="2">*</e>
            <e type="operator" args="2">+</e>
          </result>
        </math>
      </region>
      <region id="76" left="18" top="3168" width="379" height="80" color="#000000" bgColor="#ffffff" fontSize="10">
        <math>
          <input>
            <e type="operand">0</e>
            <e type="function" args="1">y.4</e>
            <e type="operand">y.0</e>
            <e type="operator" args="2">≡</e>
            <e type="operand">x</e>
            <e type="function" args="1">y.4</e>
            <e type="operand">x</e>
            <e type="function" preserve="true" args="2">diff</e>
            <e type="operand">x</e>
            <e type="operand">0</e>
            <e type="function" preserve="true" args="3">lim</e>
            <e type="operand">y'.0</e>
            <e type="operator" args="2">≡</e>
            <e type="operand">2</e>
            <e type="operand">1</e>
            <e type="function" preserve="true" args="4">sys</e>
            <e type="operand">k1</e>
            <e type="operand">k2</e>
            <e type="operand">2</e>
            <e type="operand">1</e>
            <e type="function" preserve="true" args="4">sys</e>
            <e type="function" preserve="true" args="2">Solve</e>
            <e type="function" preserve="true" args="1">Assign</e>
          </input>
          <result action="symbolic">
            <e type="operand">1</e>
            <e type="operand">2</e>
            <e type="operator" args="2">/</e>
            <e type="operator" args="1">-</e>
            <e type="operand">3</e>
            <e type="operand">2</e>
            <e type="operand">1</e>
            <e type="function" preserve="true" args="4">sys</e>
            <e type="operand">1</e>
            <e type="operand">1</e>
            <e type="function" preserve="true" args="3">mat</e>
          </result>
        </math>
      </region>
      <region id="77" left="405" top="3195" width="351" height="51" color="#000000" bgColor="#ffffff" fontSize="10">
        <math>
          <input>
            <e type="operand">x</e>
            <e type="function" args="1">y.4</e>
          </input>
          <result action="symbolic">
            <e type="operand">2</e>
            <e type="operand">x</e>
            <e type="operator" args="2">*</e>
            <e type="function" preserve="true" args="1">sin</e>
            <e type="operator" args="1">-</e>
            <e type="operand">6</e>
            <e type="operand">2</e>
            <e type="operand">x</e>
            <e type="operator" args="2">*</e>
            <e type="function" preserve="true" args="1">cos</e>
            <e type="operator" args="2">*</e>
            <e type="operator" args="2">+</e>
            <e type="operand">2</e>
            <e type="operand">1</e>
            <e type="operator" args="1">-</e>
            <e type="operand">x</e>
            <e type="operator" args="2">+</e>
            <e type="bracket">(</e>
            <e type="operator" args="2">*</e>
            <e type="operand">e</e>
            <e type="operand">3</e>
            <e type="operand">x</e>
            <e type="operator" args="2">*</e>
            <e type="operator" args="2">^</e>
            <e type="operator" args="2">*</e>
            <e type="operator" args="2">+</e>
            <e type="operand">2</e>
            <e type="operator" args="2">/</e>
          </result>
        </math>
      </region>
      <region id="78" top="3249" color="#000000" bgColor="#ffffff">
        <area terminator="true" />
      </region>
    </region>
    <region id="79" left="9" top="3267" width="240" height="68" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">x</e>
          <e type="operand">y</e>
          <e type="function" args="2">D</e>
          <e type="operand">y</e>
          <e type="operand">2</e>
          <e type="function" preserve="true" args="2">el</e>
          <e type="operand">e</e>
          <e type="operand">3</e>
          <e type="operand">x</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">^</e>
          <e type="operand">13</e>
          <e type="operand">x</e>
          <e type="operator" args="2">*</e>
          <e type="operand">7</e>
          <e type="operator" args="2">-</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">*</e>
          <e type="operand">4</e>
          <e type="operand">y</e>
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      <p href="Section Math ODE.sm">Gewöhnliche Differenzialgleichungen</p>
    </text>
    <text lang="eng">
      <p href="Section Math ODE.sm">Ordinary Differential Equations</p>
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      <p href="Mathematik.sm">Mathematik</p>
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    <text lang="eng">
      <p href="Mathematik.sm">Mathematics</p>
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      <p href="Handbook.sm">Inhalt</p>
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    <text lang="eng">
      <p href="Handbook.sm">Contents</p>
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      <p italic="true">$Author: mkraska $
$Date: 2013-11-10 18:06:03 +0100 (So, 10. Nov 2013) $ </p>
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