Ecuaciones lineales

<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>   |   <A HREF="id378.htm" TARGET="_top" TITLE="Ecuaciones separables"><U>Ecuaciones separables</U></A>   |   Ecuaciones lineales   |   <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 lineales</U></div> <div>  <A NAME="arriba"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="198c24800.gif" border=0 width="548" height="128" ALT="Documento Microsoft Office Word" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <B><IMG SRC="198d6d1d0.gif" border=0 width="621" height="541" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <DIV ALIGN="LEFT"></DIV> <div> <TABLE BORDER="1" CELLPADDING="1" CELLSPACING="1" WIDTH="506" BORDERCOLORLIGHT="#0000FF" BORDERCOLORDARK="#66FFFF" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 394 WIDTH="498"><div>  <A NAME="p_r_o_c_e_d_i_m_i_e_n_t_o"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><FONT SIZE="3" COLOR="#FF6600" FACE="Times New Roman" ><B>P r o c e d i m i e n t o</B></FONT></div> <bR> <div> <B>   </B><FONT SIZE="3" COLOR="#00CC00" FACE="Times New Roman" ><B>P</B></FONT><FONT SIZE="3" COLOR="#000000" FACE="Times New Roman" >ara resolver una ecuación diferencial lineal de primer orden, se procede de la siguiente manera:</FONT></div> <bR> <div> <IMG SRC="198ee7150.gif" border=0 width="487" height="277" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> </tD> </tR> </TABLE></div> <div> <TABLE BORDER="1" CELLPADDING="1" CELLSPACING="1" WIDTH="612" BORDERCOLORLIGHT="#009900" BORDERCOLORDARK="#00CC00" 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_resueltos"><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> <B>E</B><FONT SIZE="3" COLOR="#000000" FACE="Times New Roman" >n los ejercicios </FONT>1<FONT SIZE="3" COLOR="#000000" FACE="Times New Roman" > a </FONT>9<FONT SIZE="3" COLOR="#000000" FACE="Times New Roman" >, encuentre la solución general de la ecuación diferencial dada</FONT></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 31 WIDTH="198"><div> <A HREF="#1" TITLE="Ecuaciones lineales"><U><IMG SRC="198f84180.gif" border=0 width="132" height="24" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> <tD VALIGN=TOP WIDTH="202"><div> <A HREF="#2" TITLE="Ecuaciones lineales"><U><IMG SRC="199077180.gif" border=0 width="119" height="24" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> <tD VALIGN=TOP WIDTH="194"><div> <A HREF="#3" TITLE="Ecuaciones lineales"><U><IMG SRC="19917d180.gif" border=0 width="125" height="24" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 46 ><NOBR><div> <A HREF="#4" TITLE="Ecuaciones lineales"><U><IMG SRC="1992bc270.gif" border=0 width="188" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> <tD VALIGN=TOP WIDTH="202"><div> <A HREF="#5" TITLE="Ecuaciones lineales"><U><IMG SRC="199364180.gif" border=0 width="100" height="24" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> <tD VALIGN=TOP><NOBR><div> <A HREF="#6" TITLE="Ecuaciones lineales"><U><IMG SRC="1994ad150.gif" border=0 width="173" height="21" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 47 ><NOBR><div> <A HREF="#7" TITLE="Ecuaciones lineales"><U><IMG SRC="1995891d0.gif" border=0 width="137" height="29" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> <A HREF="#8" TITLE="Ecuaciones lineales"><U><IMG SRC="1996c9180.gif" border=0 width="201" height="24" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> <tD VALIGN=TOP WIDTH="194"><div> <A HREF="#9" TITLE="Ecuaciones lineales"><U><IMG SRC="199769280.gif" border=0 width="105" height="40" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> </tR> </TABLE></div> <div> <TABLE BORDER="1" CELLPADDING="1" CELLSPACING="1" WIDTH="612" BORDERCOLORLIGHT="#009900" BORDERCOLORDARK="#00CC00" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 39 ><NOBR><div> <B>Edwards y Penney (E&P)</B></div> <div> <B>1.5</B></div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> <B>Boyce y DiPrima (B&D)</B></div> <div> <B>2.1, 2.2</B></div> </NOBR></tD> <tD VALIGN=TOP WIDTH="198"><div> <B>D.G. Zill (DGZ)</B></div> <div> <B>2.3</B></div> </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><IMG SRC="199884180.gif" border=0 width="132" height="24" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="19992d1b0.gif" border=0 width="557" height="283" ALT="MathType 5.0 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><IMG SRC="199a77180.gif" border=0 width="119" height="24" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="199ba01b0.gif" border=0 width="416" height="283" ALT="MathType 5.0 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><IMG SRC="199c7d180.gif" border=0 width="125" height="24" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="199dd5150.gif" border=0 width="469" height="277" ALT="MathType 5.0 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><IMG SRC="199ebc270.gif" border=0 width="188" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="199f1c350.gif" border=0 width="540" height="309" ALT="MathType 5.0 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><IMG SRC="19a064180.gif" border=0 width="100" height="24" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="19a189000.gif" border=0 width="393" height="256" ALT="MathType 5.0 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><IMG SRC="19a2ad150.gif" border=0 width="173" height="21" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="19a327250.gif" border=0 width="551" height="293" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="7"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="19a4891d0.gif" border=0 width="137" height="29" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="19a590230.gif" border=0 width="400" height="291" ALT="MathType 5.0 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><IMG SRC="19a6c9180.gif" border=0 width="201" height="24" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="19a7f75b0.gif" border=0 width="503" height="347" ALT="MathType 5.0 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><IMG SRC="19a8c4800.gif" border=0 width="452" height="384" ALT="Documento Microsoft Office Word" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <bR> </td> </tr><tr> <td valign="top" colspan=2 height=21 BGCOLOR="#006600" TEXT="#F7F7FF"> <div> <B>| </B><A HREF="id379_m.htm#p_r_o_c_e_d_i_m_i_e_n_t_o" TARGET="TRLX_Middle" TITLE="Ecuaciones lineales"><U><B> </B></U></A><A HREF="id379_m.htm#p_r_o_c_e_d_i_m_i_e_n_t_o" TARGET="TRLX_Middle" TITLE="Ecuaciones lineales"><U><B>Procedimiento</B></U></A><B> |  </B><A HREF="id379_m.htm#ejercicios_resueltos" TARGET="TRLX_Middle" TITLE="Ecuaciones lineales"><U><B>Ejercicios resueltos</B></U></A><B> |</B></div> </td> </tr></table></body>