1.1

<body topmargin=0 leftmargin=0 marginheight=0 marginwidth=0> <table cellpadding=0 cellspacing=0 border=0><tr> <td valign="top" colspan=3 height=24 BGCOLOR="#003366" TEXT="#F7F7FF"> <div> <FONT SIZE="4" COLOR="#FFFFFF" FACE="Bell MT" ><A HREF="index.htm" TARGET="_top" TITLE="Ecuaciones diferenciales"><U><B>Ecuaciones diferenciales</B></U></A><B>  | </B></FONT><A HREF="index.htm" TARGET="_top" TITLE="Ecuaciones diferenciales"><U><B>Home</B></U></A><B> | </B><A HREF="id118.htm" TARGET="_top" TITLE="C o n t e n i d o"><U><B>Contenido</B></U></A><B> | </B><A HREF="id31.htm" TARGET="_top" TITLE="B o y c e y D i P r i m a"><U><B>Boyce y DiPrima</B></U></A><B> </B></div> <div> <B>1.1</B>   |   <A HREF="id132.htm" TARGET="_top" TITLE="2.1"><U>2.1</U></A>   |   <A HREF="id133.htm" TARGET="_top" TITLE="2.2"><U>2.2</U></A>   |   <A HREF="id135.htm" TARGET="_top" TITLE="2.3"><U>2.3</U></A>   |   <A HREF="id137.htm" TARGET="_top" TITLE="2.4"><U>2.4</U></A>   |   <A HREF="id136.htm" TARGET="_top" 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<div>  <script async src="//pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script>  <ins class="adsbygoogle" style="display:inline-block;width:728px;height:90px" data-ad-client="ca-pub-1578463498418701" data-ad-slot="5388515922"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script>  </div> <bR> <div> <B>Enunciados</B></div> <div> <FONT SIZE="4" COLOR="#009900" FACE="Bell MT" ><B>E</B></FONT>n cada uno de los problemas <FONT SIZE="4" COLOR="#CC0033" FACE="Bell MT" >1</FONT> a <FONT SIZE="4" COLOR="#CC0033" FACE="Bell MT" >6</FONT>, determine el orden de la ecuación diferencial dada; diga también si la ecuación es lineal o no lineal:</div> <div> <FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><IMG SRC="cf5d12b0.gif" border=0 width="209" height="43" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </FONT><A HREF="#1" TITLE="1.1"><U><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="d31db2b0.gif" border=0 width="219" height="43" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#2" TITLE="1.1"><U><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="d32ef2b0.gif" border=0 width="239" height="43" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#3" TITLE="1.1"><U><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <IMG SRC="d3474290.gif" border=0 width="116" height="41" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#4" TITLE="1.1"><U><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="d35c92b0.gif" border=0 width="201" height="43" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#5" TITLE="1.1"><U><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="d36dd2b0.gif" border=0 width="221" height="43" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#6" TITLE="1.1"><U><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> </div> <div> <FONT SIZE="4" COLOR="#009900" FACE="Bell MT" ><B>E</B></FONT>n cada uno de los problemas <FONT SIZE="4" COLOR="#CC0033" FACE="Bell MT" >7</FONT> a <FONT SIZE="4" COLOR="#CC0033" FACE="Bell MT" >14</FONT>, verifique la función o funciones que se dan son una solución de la ecuación diferencial:</div> <div> <IMG SRC="d3b28190.gif" border=0 width="296" height="25" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#7" TITLE="1.1"><U><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>      <IMG SRC="d3c451b0.gif" border=0 width="325" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#8" TITLE="1.1"><U><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>      <IMG SRC="d3dc8180.gif" border=0 width="200" height="24" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#9" TITLE="1.1"><U><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <IMG SRC="d3e91190.gif" border=0 width="401" height="25" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#10" TITLE="1.1"><U><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="d3f95190.gif" border=0 width="405" height="25" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#11" TITLE="1.1"><U><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <IMG SRC="d40b3190.gif" border=0 width="435" height="25" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#12" TITLE="1.1"><U><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="d41b7170.gif" border=0 width="439" height="23" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#13" TITLE="1.1"><U><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <IMG SRC="d421c250.gif" border=0 width="284" height="37" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#14" TITLE="1.1"><U><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <IMG SRC="d05612d0.gif" border=0 width="865" height="45" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><IMG SRC="d436f150.gif" border=0 width="111" height="21" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </FONT><A HREF="#15" TITLE="1.1"><U><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="d4469150.gif" border=0 width="105" height="21" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#16" TITLE="1.1"><U><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="d458f150.gif" border=0 width="143" height="21" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#17" TITLE="1.1"><U><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="d46a1150.gif" border=0 width="161" height="21" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#18" TITLE="1.1"><U><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> </div> <div> <IMG SRC="d0a672d0.gif" border=0 width="871" height="45" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><IMG SRC="d47b0180.gif" border=0 width="176" height="24" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </FONT><A HREF="#19" TITLE="1.1"><U><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="d48b1180.gif" border=0 width="177" height="24" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#20" TITLE="1.1"><U><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <FONT SIZE="4" COLOR="#009900" FACE="Bell MT" ><B>E</B></FONT>n cada uno de los problemas <FONT SIZE="4" COLOR="#CC0033" FACE="Bell MT" >21</FONT> a <FONT SIZE="4" COLOR="#CC0033" FACE="Bell MT" >26</FONT>, determine el orden de la ecuación diferencial parcial dada; diga también si la ecuación diferencial es lineal o no lineal. Las derivadas parciales se denotan por medio de subíndices:</div> <div> <FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><IMG SRC="d49a91b0.gif" border=0 width="169" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </FONT><A HREF="#21" TITLE="1.1"><U><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="d4a711b0.gif" border=0 width="113" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#22" TITLE="1.1"><U><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="d4b751b0.gif" border=0 width="117" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#23" TITLE="1.1"><U><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>    <IMG SRC="d4cf51b0.gif" border=0 width="245" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#24" TITLE="1.1"><U><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <IMG SRC="d4dd91b0.gif" border=0 width="217" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#25" TITLE="1.1"><U><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="d4e9b180.gif" border=0 width="155" height="24" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#26" TITLE="1.1"><U><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <FONT SIZE="4" COLOR="#009900" FACE="Bell MT" ><B>E</B></FONT>n cada uno de los problemas <FONT SIZE="4" COLOR="#CC0033" FACE="Bell MT" >27</FONT> a <FONT SIZE="4" COLOR="#CC0033" FACE="Bell MT" >32</FONT>, verifique que la  función o funciones dadas son una solución de la ecuación diferencial parcial correspondiente:</div> <div> <FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><IMG SRC="d4fd31d0.gif" border=0 width="467" height="29" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </FONT><A HREF="#27" TITLE="1.1"><U><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>  </div> <div> <IMG SRC="d518c1f0.gif" border=0 width="652" height="31" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#28" TITLE="1.1"><U><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <FONT SIZE="4" COLOR="#009900" FACE="Bell MT" ><B>E</B></FONT>n cada uno de los problemas <FONT SIZE="4" COLOR="#CC0033" FACE="Bell MT" >33</FONT> a <FONT SIZE="4" COLOR="#CC0033" FACE="Bell MT" >40</FONT>, use una computadora para hacer un esquema del campo direccional de la ecuación diferencial dada. Con base en el campo direccional, determine el comportamiento de <I>y</I> cuando <IMG SRC="d17330f0.gif" border=0 width="51" height="15" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0">:</div> <div> <FONT SIZE="4" COLOR="#000000" FACE="Georgia" ><IMG SRC="d527c150.gif" border=0 width="124" height="21" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </FONT><A HREF="#33" TITLE="1.1"><U><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="d536b150.gif" border=0 width="107" height="21" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#34" TITLE="1.1"><U><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="d548f150.gif" border=0 width="143" height="21" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#35" TITLE="1.1"><U><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="d5590180.gif" border=0 width="144" height="24" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#36" TITLE="1.1"><U><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="d5679180.gif" border=0 width="121" height="24" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#37" TITLE="1.1"><U><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <IMG SRC="d5774150.gif" border=0 width="116" height="21" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#38" TITLE="1.1"><U><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="d5880170.gif" border=0 width="128" height="23" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#39" TITLE="1.1"><U><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="d5989170.gif" border=0 width="137" height="23" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#40" TITLE="1.1"><U><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <bR> <DIV ALIGN="LEFT"></DIV> <div> <B>Soluciones</B></div> <div>  <A NAME="1"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>1</div> <div> <IMG SRC="cf474710.gif" border=0 width="628" height="113" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="2"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>2</div> <div> <IMG SRC="cf697710.gif" border=0 width="663" height="113" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="3"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>3</div> <div> <IMG SRC="cf77d710.gif" border=0 width="637" height="113" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="4"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>4</div> <div> <IMG SRC="cf8216f0.gif" border=0 width="545" height="111" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="5"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>5</div> <div> <IMG SRC="cf984710.gif" border=0 width="644" height="113" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="6"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>6</div> <div> <IMG SRC="cfa5f710.gif" border=0 width="607" height="113" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div> <FONT SIZE="4" COLOR="#0099FF" FACE="Georgia" ><B>E</B></FONT>n cada uno de los problemas <FONT SIZE="4" COLOR="#CC0033" FACE="Georgia" >7</FONT> a <FONT SIZE="4" COLOR="#CC0033" FACE="Georgia" >14</FONT>, verifique la función o funciones que se dan son una solución de la ecuación diferencial:</div> <div>  <A NAME="7"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>7</div> <div> <IMG SRC="cfb79eb0.gif" border=0 width="377" height="235" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="8"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>8</div> <div> <IMG SRC="cfcb52b0.gif" border=0 width="693" height="299" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="9"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>9</div> <div> <IMG SRC="cfdc3b30.gif" border=0 width="451" height="179" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="10"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>10</div> <div> <IMG SRC="cfeff540.gif" border=0 width="767" height="340" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="11"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>11</div> <div> <IMG SRC="d0093810.gif" border=0 width="659" height="385" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="12"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>12</div> <div> <IMG SRC="d01c4390.gif" border=0 width="708" height="313" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="13"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>13</div> <div> <IMG SRC="d0237170.gif" border=0 width="823" height="279" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="14"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>14</div> <div> <IMG SRC="d0493f90.gif" border=0 width="659" height="249" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div> <IMG SRC="65e612d0.gif" border=0 width="865" height="45" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="15"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>15</div> <div> <IMG SRC="d060ccb0.gif" border=0 width="524" height="203" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="16"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>16</div> <div> <IMG SRC="d0765e40.gif" border=0 width="613" height="228" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </div> <bR> <div>  <A NAME="17"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>17</div> <div> <IMG SRC="d0821e80.gif" border=0 width="545" height="232" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </div> <bR> <div>  <A NAME="18"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>18</div> <div> <IMG SRC="d094d030.gif" border=0 width="589" height="259" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div> <IMG SRC="64ab12b0.gif" border=0 width="689" height="43" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="19"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>19</div> <div> <IMG SRC="d0bb4050.gif" border=0 width="692" height="261" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="20"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>20</div> <div> <IMG SRC="d0c14050.gif" border=0 width="532" height="261" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div> <FONT SIZE="4" COLOR="#0099FF" FACE="Bell MT" ><B>E</B></FONT>n cada uno de los problemas <FONT SIZE="4" COLOR="#CC0033" FACE="Bell MT" >21</FONT> a <FONT SIZE="4" COLOR="#CC0033" FACE="Bell MT" >26</FONT>, determine el orden de la ecuación diferencial parcial dada; diga también si la ecuación diferencial es lineal o no lineal. Las derivadas parciales se denotan por medio de subíndices:</div> <div>  <A NAME="21"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>21</div> <div> <IMG SRC="d0d29690.gif" border=0 width="553" height="105" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="22"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>22</div> <div> <IMG SRC="d0e59680.gif" border=0 width="857" height="104" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="23"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>23</div> <div> <IMG SRC="d0f29680.gif" border=0 width="553" height="104" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="24"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>24</div> <div> <IMG SRC="d1043690.gif" border=0 width="579" height="105" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="25"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>25</div> <div> <IMG SRC="d11ac690.gif" border=0 width="684" height="105" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="26"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>26</div> <div> <IMG SRC="d1267670.gif" border=0 width="615" height="103" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div> <FONT SIZE="4" COLOR="#009900" FACE="Bell MT" ><B>E</B></FONT>n cada uno de los problemas <FONT SIZE="4" COLOR="#CC0033" FACE="Bell MT" >27</FONT> a <FONT SIZE="4" COLOR="#CC0033" FACE="Bell MT" >32</FONT>, verifique que la  función o funciones dadas son una solución de la ecuación diferencial parcial correspondiente:</div> <div>  <A NAME="27"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>27</div> <div> <IMG SRC="d1413110.gif" border=0 width="531" height="529" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="28"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>28</div> <div> <IMG SRC="d16079f0.gif" border=0 width="775" height="415" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div> <FONT SIZE="4" COLOR="#0099FF" FACE="Georgia" ><B>E</B></FONT>n cada uno de los problemas <FONT SIZE="4" COLOR="#CC0033" FACE="Georgia" >33</FONT> a <FONT SIZE="4" COLOR="#CC0033" FACE="Georgia" >40</FONT>, use una computadora para hacer un esquema del campo direccional de la ecuación diferencial dada. Con base en el campo direccional, determine el comportamiento de <I>y</I> cuando <IMG SRC="64d330f0.gif" border=0 width="51" height="15" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <FONT SIZE="4" COLOR="#3366FF" FACE="Bell MT" ><U>Nota</U>: </FONT>el campo direccional se puede trazar en <B>Maple </B>con la siguiente instrucción<FONT SIZE="4" COLOR="#000000" FACE="Georgia" >  <IMG SRC="7229a110.gif" border=0 width="410" height="17" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT></div> <div>  <A NAME="33"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>33</div> <div> <IMG SRC="d19af940.gif" border=0 width="943" height="148" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <DIV ALIGN="LEFT"></DIV> <div> <IMG SRC="64e751b0.gif" border=0 width="373" height="283" ALT="Imagen de mapa de bits" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="34"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>34</div> <div> <IMG SRC="d1cc52d0.gif" border=0 width="197" height="45" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> El esquema del campo direccional sugiere que cuando la variable independiente <I>x</I> tiende al infinito, la  función <I>y</I> tiende a -2, a menos infinito o a más infinito. </div> <DIV ALIGN="LEFT"></DIV> <div> <IMG SRC="65013180.gif" border=0 width="275" height="280" ALT="Imagen de mapa de bits" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="35"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>35</div> <div> <IMG SRC="d1fc52d0.gif" border=0 width="197" height="45" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> El esquema del campo direccional sugiere que cuando <I>x</I> tiende al infinito, la <I>y</I> también tiende al infinito. (<I> y</I> es asintótica a <I>x</I> - 3  cuando  <I>x</I> tiende a infinito).</div> <DIV ALIGN="LEFT"></DIV> <div> <IMG SRC="65221f00.gif" border=0 width="289" height="240" ALT="Imagen de mapa de bits" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="36"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>36</div> <div> <IMG SRC="d22c52f0.gif" border=0 width="197" height="47" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> Como bien sugiere el esquema del campo direccional, cuando <I>x</I> tiende al infinito, <I>y</I> tiende a 0.</div> <DIV ALIGN="LEFT"></DIV> <div> <IMG SRC="65426fc0.gif" border=0 width="294" height="252" ALT="Imagen de mapa de bits" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="37"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>37</div> <div> <IMG SRC="d5ac52f0.gif" border=0 width="197" height="47" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> El esquema del campo direccional sugiere que cuando la variable independiente <I>x</I> tiende al infinito, la  <I>y</I> tiende a 0, a menos infinito o a más infinito. </div> <DIV ALIGN="LEFT"></DIV> <div> <IMG SRC="656301b0.gif" border=0 width="304" height="283" ALT="Imagen de mapa de bits" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="38"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>38</div> <div> <IMG SRC="d2ac52d0.gif" border=0 width="197" height="45" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> El esquema del campo direccional sugiere que cuando <I>x</I> tiende al infinito, la <I>y</I> también tiende al infinito o al menos infinito.</div> <DIV ALIGN="LEFT"></DIV> <div> <IMG SRC="65810070.gif" border=0 width="272" height="263" ALT="Imagen de mapa de bits" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="39"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>39</div> <div> <IMG SRC="d2dc52d0.gif" border=0 width="197" height="45" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> El esquema del campo direccional sugiere que cuando la variable independiente <I>x</I> tiende al infinito, la  <I>y</I> tiende a 0, a 4 o a menos infinito.</div> <DIV ALIGN="LEFT"></DIV> <div> <IMG SRC="65a36180.gif" border=0 width="310" height="280" ALT="Imagen de mapa de bits" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="40"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>40</div> <div> <IMG SRC="d30c52d0.gif" border=0 width="197" height="45" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> El esquema del campo direccional sugiere que cuando la variable independiente <I>x</I> tiende al infinito, la  <I>y</I> tiende a 0, a 5 o a más infinito.</div> <DIV ALIGN="LEFT"></DIV> <div> <IMG SRC="65c1c0f0.gif" border=0 width="284" height="271" ALT="Imagen de mapa de bits" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script>  <ins class="adsbygoogle" style="display:inline-block;width:970px;height:250px" data-ad-client="ca-pub-1578463498418701" data-ad-slot="8553279920"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script>  </div> <bR> </td> </tr><tr> <td valign="top" colspan=2 height=24 BGCOLOR="#003366" TEXT="#F7F7FF"> <div> <B> <form action="http://www.google.com.co" id="cse-search-box" target="_blank"> <div> <input type="hidden" name="cx" value="partner-pub-6266400581769473:6497222116" /> <input type="hidden" name="ie" value="UTF-8" /> <input type="text" name="q" size="100" /> <input type="submit" name="sa" value="Buscar" /> </div> </form> <script type="text/javascript" src="http://www.google.com.co/coop/cse/brand?form=cse-search-box&lang=es"></script>  </B></div> </td> </tr></table></body>