4.2

<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> <div> <A HREF="id187.htm" TARGET="_top" TITLE="1.1"><U>1.1</U></A>   |   <A HREF="id282.htm" TARGET="_top" TITLE="Zill 1.2"><U>Zill 1.2</U></A>   |   <A HREF="id283.htm" TARGET="_top" TITLE="1.3"><U>1.3</U></A>   |   <A HREF="id184.htm" TARGET="_top" TITLE="2.2"><U>2.2</U></A>   |   <A HREF="id185.htm" TARGET="_top" TITLE="2.3"><U>2.3</U></A>   |   <A HREF="id186.htm" TARGET="_top" TITLE="2.4"><U>2.4</U></A>   |   <A HREF="id284.htm" TARGET="_top" TITLE="2.5"><U>2.5</U></A>   |   <A HREF="id272.htm" TARGET="_top" TITLE="3.1"><U>3.1</U></A>   |   <A HREF="id279.htm" TARGET="_top" TITLE="4.1"><U>4.1</U></A>   |   <B>4.2</B>   |   <A HREF="id286.htm" TARGET="_top" TITLE="4.3"><U>4.3</U></A>   |   <A HREF="id287.htm" TARGET="_top" TITLE="4.4"><U>4.4</U></A>   |   <A HREF="id288.htm" TARGET="_top" TITLE="4.5"><U>4.5</U></A>   |   <A HREF="id289.htm" TARGET="_top" TITLE="4.6"><U>4.6</U></A>   |   <A HREF="id271.htm" TARGET="_top" TITLE="7.1"><U>7.1</U></A></div> <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>4.2</B></div> <div> <B>Reducción de orden</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> <bR> <div> <B>Procedimiento 1. Reducción de orden</B></div> <div> <B><IMG SRC="16a5a32c0.gif" border=0 width="931" height="300" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <div> <B>Procedimiento 2. Uso de la fórmula</B></div> <div> <B><IMG SRC="16a668bd0.gif" border=0 width="616" height="189" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <DIV ALIGN="LEFT"></DIV> <div> <B>Enunciados de los problemas del Ejercicio 4.2</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 4.2:</div> <bR> <div> <FONT SIZE="4" COLOR="#CC0033" FACE="Georgia" ><B>    E</B></FONT>n los problemas <FONT SIZE="4" COLOR="#CC0033" FACE="Georgia" >1</FONT> a <FONT SIZE="4" COLOR="#CC0033" FACE="Georgia" >16</FONT> la función indicada <I>y</I><FONT SIZE="2" COLOR="#000000" FACE="Georgia" >1</FONT>(<I>x</I>) es una solución de la ecuación diferencial dada. Use la reducción de </div> <div> orden o la fórmula, como se indica, para encontrar una segunda solución <I>y</I><FONT SIZE="2" COLOR="#000000" FACE="Georgia" >2</FONT>(<I>x</I>).</div> <div> <IMG SRC="16a7f91c0.gif" border=0 width="249" height="28" 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=fBGD86n7BzE" TARGET="_top" TITLE="https://www.youtube.com/watch?v=fBGD86n7"><U><IMG SRC="c4218180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>         <IMG SRC="16a8071c0.gif" border=0 width="263" height="28" 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=7MfluZFfB5Q" TARGET="_top" TITLE="https://www.youtube.com/watch?v=7MfluZFf"><U><IMG SRC="c4218180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>         <IMG SRC="16a9f81c0.gif" border=0 width="248" height="28" 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=cVBdcvcQzKU" TARGET="_top" TITLE="https://www.youtube.com/watch?v=cVBdcvcQ"><U><IMG SRC="c4218180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT></div> <div> <IMG SRC="16aaef1c0.gif" border=0 width="239" height="28" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="https://www.youtube.com/watch?v=pvQT_BWNfZE" TARGET="_top" TITLE="https://www.youtube.com/watch?v=pvQT_BWN"><U><IMG SRC="c4218180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>         <IMG SRC="16abe71c0.gif" border=0 width="231" height="28" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="https://www.youtube.com/watch?v=GA-O4CbkRBg" TARGET="_top" TITLE="https://www.youtube.com/watch?v=GA-O4Cbk"><U><IMG SRC="c4218180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>          <IMG SRC="16ace11d0.gif" border=0 width="225" height="29" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="https://www.youtube.com/watch?v=qQ1GMrlACbc" TARGET="_top" TITLE="https://www.youtube.com/watch?v=qQ1GMrlA"><U><IMG SRC="c4218180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <IMG SRC="16ad251f0.gif" border=0 width="293" height="31" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="https://www.youtube.com/watch?v=mA2njJXLvoU" TARGET="_top" TITLE="https://www.youtube.com/watch?v=mA2njJXL"><U><IMG SRC="c4218180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>          <IMG SRC="16ae031f0.gif" border=0 width="259" height="31" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="https://www.youtube.com/watch?v=b6U3WE07FhE" TARGET="_top" TITLE="https://www.youtube.com/watch?v=b6U3WE07"><U><IMG SRC="c4218180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>         <IMG SRC="16af211d0.gif" border=0 width="289" height="29" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="https://www.youtube.com/watch?v=lWLMhIqwtwQ" TARGET="_top" TITLE="https://www.youtube.com/watch?v=lWLMhIqw"><U><IMG SRC="c4218180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <IMG SRC="16b0231d0.gif" border=0 width="291" height="29" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="https://www.youtube.com/watch?v=-HEF0B2G3Lk" TARGET="_top" TITLE="https://www.youtube.com/watch?v=-HEF0B2G"><U><IMG SRC="c4218180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>         <IMG SRC="16b1e91c0.gif" border=0 width="233" height="28" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="https://www.youtube.com/watch?v=Fm1j8bpnb5A" TARGET="_top" TITLE="https://www.youtube.com/watch?v=Fm1j8bpn"><U><IMG SRC="c4218180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>         <IMG SRC="16b2011d0.gif" border=0 width="257" height="29" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="https://www.youtube.com/watch?v=sjsa3lB1fR0" TARGET="_top" TITLE="https://www.youtube.com/watch?v=sjsa3lB1"><U><IMG SRC="c4218180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <IMG SRC="16b35c1d0.gif" border=0 width="348" height="29" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="https://www.youtube.com/watch?v=PNbb6XLqqzg" TARGET="_top" TITLE="https://www.youtube.com/watch?v=PNbb6XLq"><U><IMG SRC="c4218180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <bR> <bR> <DIV ALIGN="LEFT"></DIV> <div> <B>Lista de reproducción sobre las soluciones del Ejercicio 4.2</B></div> <bR> <div>  <iframe width="560" height="315" src="https://www.youtube.com/embed/videoseries?list=PLq_SQwoOZHo2gsBHG3ZrLHJJI51CtOr0-" frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>  </div> <bR> <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 HREF="https://www.youtube.com/user/MatematicaAplicadas" TARGET="_top" TITLE="https://www.youtube.com/user/MatematicaA"><U><IMG SRC="97f28280.jpg" border=0 width="40" height="40" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <bR> <div> Por: <FONT SIZE="4" COLOR="#FF9900" FACE="Georgia" >Juan Carlos </FONT><FONT SIZE="4" COLOR="#0000FF" FACE="Georgia" >Beltrán</FONT> <FONT SIZE="4" COLOR="#FF0000" FACE="Georgia" >Beltrán </FONT></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> <div> <A HREF="http://jcbmat.com/" TARGET="_top" TITLE="http://jcbmat.com/"><U><B><IMG SRC="1558e5530.gif" border=0 width="741" height="83" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></U></A></div> <div>         </div> </td> <td valign="top" rowspan="2" width=105 BGCOLOR="#FFFFFF" TEXT="#080000"> <div> <A HREF="https://www.youtube.com/user/MatematicaAplicadas" TARGET="_top" TITLE="https://www.youtube.com/user/MatematicaA"><U><IMG SRC="154c64580.gif" border=0 width="100" height="600" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <bR> </td> </tr><tr> <td valign="top" height=24 BGCOLOR="#003366" TEXT="#F7F7FF"> <bR> </td> </tr></table></body>