Ecuaciones separables

<body topmargin=0 leftmargin=0 marginheight=0 marginwidth=0> <table cellpadding=0 cellspacing=0 border=0><tr> <td valign="top" colspan=3 height=98 BGCOLOR="#006600" TEXT="#F7F7FF" bgproperties="fixed" background="05700732dwnpjk.jpg"> <div> <FONT SIZE="6" COLOR="#FFFFFF" FACE="Times New Roman" ><B>C á l c u l o   2 1</B></FONT><FONT SIZE="6" COLOR="#FFCC66" FACE="Arial" ><B> </B></FONT><FONT SIZE="2" COLOR="#FFFFCC" FACE="Arial" >   </FONT><B>  |   </B><A HREF="index.htm" TARGET="_top" TITLE="A n á l i s i s M a t e m á t i c o"><U><B>Home</B></U></A><B> |  </B><A HREF="id98.htm" TARGET="_top" TITLE=" | Contenido |"><U><B>Contenido</B></U></A><B> |  </B><A HREF="id373.htm" TARGET="_top" TITLE="Ecuaciones diferenciales"><U><B>Ecuaciones diferenciales</B></U></A><B> |</B></div> <div> <A HREF="id377.htm" TARGET="_top" TITLE="Integración directa"><U>Integración directa</U></A>   |   Ecuaciones separables   |   <A HREF="id379.htm" TARGET="_top" TITLE="Ecuaciones lineales"><U>Ecuaciones lineales</U></A>   |   <A HREF="id380.htm" TARGET="_top" TITLE="Ecuaciones exactas"><U>Ecuaciones exactas</U></A>   |   <A HREF="id381.htm" TARGET="_top" TITLE="Ecuaciones homogéneas"><U>Ecuaciones homogéneas</U></A>   |   <A HREF="id382.htm" TARGET="_top" TITLE="Ecuaciones de Bernoulli"><U>Ecuaciones de Bernoulli</U></A></div> <div> </div> </td> </tr><tr> <td valign="top" rowspan="2" width=245 BGCOLOR="#006600" TEXT="#F7F7FF"> <div> <B> <TABLE BORDER="4" CELLPADDING="4" CELLSPACING="1" WIDTH="60" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP BGCOLOR=#0099CC HEIGHT= 53 ><NOBR><div> <B><IMG SRC="195f262f0.gif" border=0 width="38" height="47" ALT="Imagen de mapa de bits" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> </NOBR></tD> </tR> </TABLE></B></div> <bR> </td> <td valign="top" height=361 colspan=2 BGCOLOR="#FFFFFF" TEXT="#080000"> <div> <U>Ecuaciones separables</U></div> <div>  <A NAME="ecuaci_n_separable"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><FONT SIZE="3" COLOR="#00CC00" FACE="Times New Roman" ><B>Ecuación separable: </B></FONT></div> <div> <IMG SRC="196055430.gif" border=0 width="597" height="67" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> Como se puede observar, en este tipo de ecuaciones cada miembro de la igualdad involucra solo una de las variables. Para resolver ecuaciones separables se integra en ambos miembros de la igualdad. La solución, por lo general, es una función implícita. </div> <div> <FONT SIZE="3" COLOR="#0099FF" FACE="Times New Roman" ><B>E</B></FONT>s importante que se repasen las<A HREF="http://ed21.webcindario.com/id352.htm" TARGET="_top" TITLE="http://ed21.webcindario.com/id352.htm"><U><I> técnicas de integración</I></U></A>. </div> <bR> <DIV ALIGN="LEFT"></DIV> <div> <TABLE BORDER="1" CELLPADDING="1" CELLSPACING="1" WIDTH="612" BORDERCOLORLIGHT="#006600" BORDERCOLORDARK="#009900" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP COLSPAN=3 BGCOLOR=#FFFFCC HEIGHT= 57 ><NOBR><div>  <A NAME="ejercicios_resultos"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" ><B>Ejercicios resueltos</B></FONT></div> <bR> <div> <FONT SIZE="3" COLOR="#FF6600" FACE="Times New Roman" ><B>E</B></FONT>n los ejercicios <FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" >1</FONT> a <FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" >15</FONT>, resuelva la ecuación diferencial dada, por separación de variables:</div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 51 WIDTH="198"><div> <A HREF="#1" TITLE="Ecuaciones separables"><U><IMG SRC="196150150.gif" border=0 width="80" height="21" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> <tD VALIGN=TOP WIDTH="198"><div> <A HREF="#2" TITLE="Ecuaciones separables"><U><IMG SRC="19624f2c0.gif" border=0 width="79" height="44" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> <tD VALIGN=TOP WIDTH="198"><div> <A HREF="#3" TITLE="Ecuaciones separables"><U><IMG SRC="196368280.gif" border=0 width="104" height="40" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 47 WIDTH="198"><div> <A HREF="#4" TITLE="Ecuaciones separables"><U><IMG SRC="196459180.gif" border=0 width="89" height="24" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> <tD VALIGN=TOP><NOBR><div> <A HREF="#5" TITLE="Ecuaciones separables"><U><IMG SRC="196597180.gif" border=0 width="151" height="24" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> <tD VALIGN=TOP WIDTH="198"><div> <A HREF="#6" TITLE="Ecuaciones separables"><U><IMG SRC="196668280.gif" border=0 width="104" height="40" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> </tR> <tR> <tD VALIGN=TOP COLSPAN=2 HEIGHT= 54 WIDTH="399"><div> <A HREF="#7" TITLE="Ecuaciones separables"><U><IMG SRC="1967e7180.gif" border=0 width="231" height="24" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> <tD VALIGN=TOP WIDTH="198"><div> <A HREF="#8" TITLE="Ecuaciones separables"><U><IMG SRC="1968672f0.gif" border=0 width="103" height="47" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 56 WIDTH="198"><div> <A HREF="#9" TITLE="Ecuaciones separables"><U><IMG SRC="196978280.gif" border=0 width="120" height="40" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> <tD VALIGN=TOP><NOBR><div> <A HREF="#10" TITLE="Ecuaciones separables"><U><IMG SRC="196a9e310.gif" border=0 width="158" height="49" ALT="Documento Microsoft Office Word" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> <tD VALIGN=TOP WIDTH="198"><div> <A HREF="#11" TITLE="Ecuaciones separables"><U><IMG SRC="196b75270.gif" border=0 width="117" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 31 ><NOBR><div> <A HREF="#12" TITLE="Ecuaciones separables"><U><IMG SRC="196cb1180.gif" border=0 width="177" height="24" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> <tD VALIGN=TOP COLSPAN=2 WIDTH="399"><div> <A HREF="#13" TITLE="Ecuaciones separables"><U><IMG SRC="196dfb180.gif" border=0 width="251" height="24" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 50 ><NOBR><div> <A HREF="#14" TITLE="Ecuaciones separables"><U><IMG SRC="196eb1280.gif" border=0 width="177" height="40" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> <tD VALIGN=TOP WIDTH="198"><div> <A HREF="#15" TITLE="Ecuaciones separables"><U><IMG SRC="196f6f2b0.gif" border=0 width="111" height="43" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> <tD VALIGN=TOP WIDTH="198"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="50" ALIGN="bottom" WIDTH="198" HSPACE="0" VSPACE="0"></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 20 ><NOBR><div> <B>Boyce y DiPrima (B&D)</B></div> </NOBR></tD> <tD VALIGN=TOP WIDTH="198"><div> <B>Dennis G. Zill (DGZ)</B></div> </tD> <tD VALIGN=TOP WIDTH="198"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="20" ALIGN="bottom" WIDTH="198" HSPACE="0" VSPACE="0"></tD> </tR> </TABLE></div> <bR> <div> <B>S o l u c i o n e s</B></div> <bR> <div>  <A NAME="1"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" ><B><IMG SRC="197050150.gif" border=0 width="80" height="21" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></FONT></div> <div> <B><IMG SRC="19711b280.gif" border=0 width="539" height="296" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <div>  <A NAME="2"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" ><B><IMG SRC="19724f2c0.gif" border=0 width="79" height="44" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></FONT></div> <div> 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HREF="id378_m.htm#ejercicios_resultos" TARGET="TRLX_Middle" TITLE="Ecuaciones separables"><U><B>Ejercicios resueltos</B></U></A></div> </td> </tr></table></body>