2.2

<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="Georgia" ><B>M</B></FONT><FONT SIZE="4" COLOR="#FFFFFF" FACE="Georgia" ><B>atemáticas de la U</B></FONT><B> (MatU)  | </B><A HREF="http://www.jcbmat.com/" TARGET="_top" TITLE="http://www.jcbmat.com/"><U><B>Home</B></U></A><B> | </B><A HREF="index.htm" TARGET="_top" TITLE="Ecuaciones diferenciales"><U><B>Ecuaciones diferenciales</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="id182.htm" TARGET="_top" TITLE="Z i l l (Ed.7)"><U><B>D. G.. Zill</B></U></A><B>  |</B></div> <bR> <bR> <bR> <bR> <div> </div> </td> </tr><tr> <td valign="top" rowspan="2" width=160 BGCOLOR="#FFFFFF" TEXT="#080000"> <div> <B> <script async src="//pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script>  <ins class="adsbygoogle" style="display:inline-block;width:160px;height:600px" data-ad-client="ca-pub-1578463498418701" data-ad-slot="3073775660"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script>  </B></div> </td> <td valign="top" height=432 BGCOLOR="#FFFFFF" TEXT="#080000"> <div> <B>Ejercicios </B><B>2.2</B></div> <div> <B>Variables se</B><B>p</B><B>arables</B></div> <bR> <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> <div>  <A NAME="enunciados_2_2"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></div> <div> <B>Enunciados y enlaces a las soluciones de los problemas de los Ejercicios 2.2</B></div> <bR> <div> <FONT SIZE="5" COLOR="#006699" FACE="Bell MT" ><B>S</B></FONT>olución en imagen <IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> y o video <FONT SIZE="3" COLOR="#330033" FACE="Georgia" ><IMG SRC="c4218180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT> de los problemas de los Ejercicios 2.2:</div> <div> <FONT SIZE="4" COLOR="#009900" FACE="Bell MT" ><B>          </B></FONT><FONT SIZE="4" COLOR="#CC0033" FACE="Bell MT" ><B>E</B></FONT>n los problemas <FONT SIZE="4" COLOR="#CC0033" FACE="Bell MT" >1</FONT> a <FONT SIZE="4" COLOR="#CC0033" FACE="Bell MT" >22</FONT>, resuelva la ecuación diferencial dada por separación de variables:</div> <div> <IMG SRC="162675300.gif" border=0 width="117" height="48" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT>          <IMG SRC="16277c300.gif" border=0 width="124" height="48" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT>          <IMG SRC="1628871d0.gif" border=0 width="135" height="29" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT>          <IMG SRC="17ddac200.gif" border=0 width="172" height="32" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT>         <IMG SRC="17de63300.gif" border=0 width="99" height="48" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT></div> <div> <FONT SIZE="4" COLOR="#111111" FACE="Bell MT" ><IMG SRC="17df87300.gif" border=0 width="135" height="48" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#111111" FACE="Bell MT" >          <IMG SRC="17e073300.gif" border=0 width="115" height="48" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="3" COLOR="#330033" FACE="Georgia" >          <IMG SRC="17e1bd300.gif" border=0 width="189" height="48" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="3" COLOR="#330033" FACE="Georgia" >          <IMG SRC="17e2ab380.gif" border=0 width="171" height="56" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="17e39b380.gif" border=0 width="155" height="56" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0">          <IMG SRC="17e4d11c0.gif" border=0 width="209" height="28" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0">          <IMG SRC="17e5fb1c0.gif" border=0 width="251" height="28" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><IMG SRC="c4118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="17e944290.gif" border=0 width="324" height="41" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="3" COLOR="#330033" FACE="Georgia" ><A HREF="https://www.youtube.com/watch?v=7pwzs7Gdsco" TARGET="_top" TITLE="https://www.youtube.com/watch?v=7pwzs7Gd"><U><IMG SRC="c4218180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>          <IMG SRC="17ea1c2b0.gif" border=0 width="284" height="43" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="3" COLOR="#330033" FACE="Georgia" ><A HREF="https://www.youtube.com/watch?v=qz3y8bJRYVc" TARGET="_top" TITLE="https://www.youtube.com/watch?v=qz3y8bJR"><U><IMG SRC="c4218180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>          <IMG SRC="17eb6b300.gif" border=0 width="107" height="48" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="3" COLOR="#330033" FACE="Georgia" ><A HREF="https://www.youtube.com/watch?v=luchZlwA7EQ" TARGET="_top" TITLE="https://www.youtube.com/watch?v=luchZlwA"><U><IMG SRC="c4218180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT></div> <div> <IMG SRC="17eca7300.gif" border=0 width="167" height="48" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="3" COLOR="#330033" FACE="Georgia" ><A HREF="https://www.youtube.com/watch?v=v4jJWx6Qnn4" TARGET="_top" TITLE="https://www.youtube.com/watch?v=v4jJWx6Q"><U><IMG SRC="c4218180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>         <IMG SRC="17ed8b300.gif" border=0 width="139" height="48" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="3" COLOR="#330033" FACE="Georgia" ><A HREF="https://www.youtube.com/watch?v=bA06Z1ZdcNk" TARGET="_top" TITLE="https://www.youtube.com/watch?v=bA06Z1Zd"><U><IMG SRC="c4218180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>          <IMG SRC="17eeaf300.gif" border=0 width="175" height="48" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="3" COLOR="#330033" FACE="Georgia" ><A HREF="https://www.youtube.com/watch?v=qUfwtVFRtqk" TARGET="_top" TITLE="https://www.youtube.com/watch?v=qUfwtVFR"><U><IMG SRC="c4218180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>          <IMG SRC="17efd1330.gif" border=0 width="209" height="51" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="3" COLOR="#330033" FACE="Georgia" ><A HREF="https://www.youtube.com/watch?v=BmMuA10iGrQ" TARGET="_top" TITLE="https://www.youtube.com/watch?v=BmMuA10i"><U><IMG SRC="c4218180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT></div> <div> <IMG SRC="17f0c9330.gif" border=0 width="201" height="51" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="3" COLOR="#330033" FACE="Georgia" ><A HREF="https://www.youtube.com/watch?v=Hklie0y2QiA" TARGET="_top" TITLE="https://www.youtube.com/watch?v=Hklie0y2"><U><IMG SRC="c4218180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>         <IMG SRC="17f19b300.gif" border=0 width="155" height="48" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="3" COLOR="#330033" FACE="Georgia" ><A HREF="https://www.youtube.com/watch?v=eMOXAF4f6sY" TARGET="_top" TITLE="https://www.youtube.com/watch?v=eMOXAF4f"><U><IMG SRC="c4218180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>          <IMG SRC="17f2bb300.gif" border=0 width="187" height="48" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="3" COLOR="#330033" FACE="Georgia" ><A HREF="https://www.youtube.com/watch?v=iey-LAfeTq8" TARGET="_top" TITLE="https://www.youtube.com/watch?v=iey-LAfe"><U><IMG SRC="c4218180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>          </div> <div> <FONT SIZE="4" COLOR="#009900" FACE="Bell MT" ><B>          </B></FONT><B>E</B><FONT SIZE="4" COLOR="#111111" FACE="Bell MT" >n los problemas </FONT>23<FONT SIZE="4" COLOR="#111111" FACE="Bell MT" > a </FONT>28<FONT SIZE="4" COLOR="#111111" FACE="Bell MT" >, </FONT><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >encuentre una solución explícita del problema con valores iniciales dado:</FONT></div> <div> <IMG SRC="17f601300.gif" border=0 width="257" height="48" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="3" COLOR="#330033" FACE="Georgia" ><A HREF="https://www.youtube.com/watch?v=a3TCfTXx598" TARGET="_top" TITLE="https://www.youtube.com/watch?v=a3TCfTXx"><U><IMG SRC="c4218180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>         <IMG SRC="17f7d5330.gif" border=0 width="213" height="51" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="3" COLOR="#330033" FACE="Georgia" ><A HREF="https://www.youtube.com/watch?v=L9bOq3m822k" TARGET="_top" TITLE="https://www.youtube.com/watch?v=L9bOq3m8"><U><IMG SRC="c4218180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT></div> <bR> <DIV ALIGN="LEFT"></DIV> <div> <B>Lista de reproducción sobre las soluciones del Ejercicio 2.2</B></div> <bR> <div>  <iframe width="560" height="315" src="https://www.youtube.com/embed/videoseries?list=PLq_SQwoOZHo2wybWfwhkVX2rCuoCJwYMd" frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>  </div> <bR> <div> <B>    E</B><FONT SIZE="4" COLOR="#111111" FACE="Georgia" >n los problemas </FONT>1<FONT SIZE="4" COLOR="#111111" FACE="Georgia" > a </FONT>22<FONT SIZE="4" COLOR="#111111" FACE="Georgia" >, resuelva la ecuación diferencial dada por separación de variables:</FONT></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> <B><IMG SRC="983874c0.gif" border=0 width="647" height="332" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div>  <A NAME="2"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>2</div> <div> <B><IMG SRC="98419e80.gif" border=0 width="537" height="232" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div>  <A NAME="3"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>3</div> <div> <B><IMG SRC="986834c0.gif" border=0 width="643" height="332" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div>  <A NAME="4"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>4</div> <div> <B><IMG SRC="98780980.gif" border=0 width="640" height="408" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div>  <A NAME="5"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>5</div> <div> <B><IMG SRC="988747b0.gif" border=0 width="628" height="379" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div>  <A NAME="6"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>6</div> <div> <B><IMG SRC="98938440.gif" border=0 width="568" height="324" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></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> <B><IMG SRC="98a845f0.gif" border=0 width="644" height="351" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div>  <A NAME="8"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>8</div> <div> <B><IMG SRC="98b43c10.gif" border=0 width="835" height="705" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div>  <A NAME="9"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>9</div> <div> <B><IMG SRC="98cf9940.gif" border=0 width="761" height="660" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div>  <A NAME="10"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>10</div> <div> <B><IMG SRC="98d31730.gif" border=0 width="817" height="883" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div>  <A NAME="11"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>11</div> <div> <B><IMG SRC="98e315f0.gif" border=0 width="817" height="863" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div>  <A NAME="12"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>12</div> <div> <B><IMG SRC="98fac540.gif" border=0 width="684" height="340" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <DIV ALIGN="LEFT"></DIV> <div> <IMG SRC="15528c8c0.gif" border=0 width="140" height="140" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div> <A HREF="http://twitter.com/Calculo21" TARGET="_top" TITLE="http://twitter.com/Calculo21"><U><IMG SRC="97d28280.jpg" border=0 width="40" height="40" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="http://www.facebook.com/juan.beltran.58511" TARGET="_top" TITLE="http://www.facebook.com/juan.beltran.585"><U><IMG SRC="97e28280.gif" border=0 width="40" height="40" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A 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