8.1(a)

<body topmargin=0 leftmargin=0 marginheight=0 marginwidth=0> <table cellpadding=0 cellspacing=0 border=0><tr> <td valign="top" colspan=3 height=77 BGCOLOR="#006600" TEXT="#F7F7FF"> <div> <B>| </B><A HREF="index.htm" TARGET="_top" TITLE="Ejercicios resueltos de ecuaciones di"><U><B>Ejercicios resueltos de ecuaciones diferenciales</B></U></A><B>  |  </B><A HREF="http://ed21.webcindario.com/index.htm" TARGET="_top" TITLE="http://ed21.webcindario.com/index.htm"><U><B>Análisis matemático</B></U></A><B> |  </B><A HREF="id31.htm" TARGET="_top" TITLE="Boyce y DiPrima"><U><B>Boyce y DiPrima</B></U></A><B> |</B></div> <div> <A HREF="id44.htm" TARGET="_top" TITLE="1.1"><U>1.1</U></A>   |   <A HREF="id46.htm" TARGET="_top" TITLE="2.1(a)"><U>2.1(a)</U></A>   |   <A HREF="id64.htm" TARGET="_top" TITLE="2.1(b)"><U>2.1(b)</U></A>   |   <A HREF="id47.htm" TARGET="_top" TITLE="2.2(a)"><U>2.2(a)</U></A>   |   <A HREF="id55.htm" TARGET="_top" TITLE="2.2(b)"><U>2.2(b)</U></A>   |   <A HREF="id65.htm" TARGET="_top" TITLE="2.2(c)"><U>2.2(c)</U></A>   |   <A HREF="id57.htm" TARGET="_top" TITLE="2.3"><U>2.3</U></A>   |   <A HREF="id60.htm" TARGET="_top" TITLE="2.4"><U>2.4</U></A>   |   <A HREF="id58.htm" TARGET="_top" TITLE="2.5(a)"><U>2.5(a)</U></A>   |   <A HREF="id88.htm" TARGET="_top" TITLE="2.5(b)"><U>2.5(b)</U></A>   |   <A HREF="id89.htm" TARGET="_top" TITLE="2.6(a)"><U>2.6(a)</U></A>   |   <A HREF="id83.htm" TARGET="_top" TITLE="2.8"><U>2.8</U></A>   |   <A HREF="id61.htm" TARGET="_top" TITLE="3.1(a)"><U>3.1(a)</U></A>   |   <A HREF="id62.htm" TARGET="_top" TITLE=" 3.1(b)"><U> 3.1(b)</U></A>   |   <A HREF="id63.htm" TARGET="_top" TITLE="7.2(a)"><U>7.2(a)</U></A>   |   <B>8.1(a)</B></div> <div> </div> </td> </tr><tr> <td valign="top" rowspan="2" width=14 BGCOLOR="#006600" TEXT="#F7F7FF"> <bR> </td> <td valign="top" height=382 BGCOLOR="#FFFFFF" TEXT="#080000"> <bR> <div> <B>Problemas </B><B>8.1(a)</B></div> <div> <FONT SIZE="3" COLOR="#0099FF" FACE="Times New Roman" ><B> <A NAME="1_y_2"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B>E</B></FONT>n los problemas <FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" >1</FONT> y <FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" >2</FONT>:</div> <div> a<FONT SIZE="3" COLOR="#000000" FACE="Times New Roman" >)  Encuentre valores aproximados de la solución del problema dado con valor inicial. en </FONT></div> <div>    <I>t</I> = 0.1, 0.2, 0.3 y 0.4 al aplicar el método de Euler con<I> h</I> = 0.1.</div> <div> <FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" >b</FONT>)  Repetir el inciso a) con <I>h</I> = 0.05. Compare los resultados con los del inciso a).</div> <div> <FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" >c</FONT>)  Repita el inciso a) con <I>h</I> = 0.025. Compare los resultados con los del inciso a) y b).</div> <div> <IMG SRC="3a8982b0.gif" border=0 width="408" height="43" ALT="Documento Microsoft Office Word" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>       Compare estos valores con los resultados de los incisos a), b) y c).</div> <bR> <div> <IMG SRC="3a9ce1d0.gif" border=0 width="718" height="797" ALT="Documento Microsoft Office Word" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="3aa76970.gif" border=0 width="374" height="663" ALT="Documento Microsoft Office Word" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="3abb07b0.gif" border=0 width="432" height="379" ALT="Documento Microsoft Office Word" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="3acbf7b0.gif" border=0 width="447" height="379" ALT="Documento Microsoft Office Word" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <DIV ALIGN="LEFT"></DIV> <div> <TABLE BORDER="1" CELLPADDING="1" CELLSPACING="0" WIDTH="512" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP COLSPAN=3 HEIGHT= 29 ><NOBR><div> <B><IMG SRC="3b609160.gif" border=0 width="521" height="22" ALT="Documento Microsoft Office Word" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP BGCOLOR=#FFFFCC HEIGHT= 20 WIDTH="80"><div> <I><B>t</B></I></div> </tD> <tD VALIGN=TOP BGCOLOR=#FFFFCC WIDTH="217"><div> <FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" ><B>a</B></FONT>)  <I><B>h</B></I><B> = 0.1</B></div> </tD> <tD VALIGN=TOP BGCOLOR=#FFFFCC WIDTH="201"><div> <FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" ><B>b</B></FONT>)  <I><B>h</B></I><B> = 0.05</B></div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 20 WIDTH="80"><div> 0.1</div> </tD> <tD VALIGN=TOP WIDTH="217"><div> 1.1</div> </tD> <tD VALIGN=TOP WIDTH="201"><div> 1.105</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 20 WIDTH="80"><div> 0.2</div> </tD> <tD VALIGN=TOP WIDTH="217"><div> 1.22</div> </tD> <tD VALIGN=TOP WIDTH="201"><div> 1.23205</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 20 WIDTH="80"><div> 0.3</div> </tD> <tD VALIGN=TOP WIDTH="217"><div> 1.364</div> </tD> <tD VALIGN=TOP WIDTH="201"><div> 1.3857805</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 20 WIDTH="80"><div> 0.4</div> </tD> <tD VALIGN=TOP WIDTH="217"><div> 1.5368</div> </tD> <tD VALIGN=TOP WIDTH="201"><div> 1.57179435</div> </tD> </tR> </TABLE></div> <div> <IMG SRC="3bac7630.gif" border=0 width="455" height="611" ALT="Documento Microsoft Office Word" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="3bbfec40.gif" border=0 width="510" height="708" ALT="Documento Microsoft Office Word" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="3bcfbc50.gif" border=0 width="507" height="709" ALT="Documento Microsoft Office Word" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="3bdffc30.gif" border=0 width="511" height="707" ALT="Documento Microsoft Office Word" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <DIV ALIGN="LEFT"></DIV> <div> <TABLE BORDER="1" CELLPADDING="1" CELLSPACING="0" WIDTH="660" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP COLSPAN=4 HEIGHT= 29 ><NOBR><div> <B><IMG SRC="3be10160.gif" border=0 width="528" height="22" ALT="Documento Microsoft Office Word" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP BGCOLOR=#FFFFCC HEIGHT= 20 WIDTH="80"><div> <I><B>t</B></I></div> </tD> <tD VALIGN=TOP BGCOLOR=#FFFFCC WIDTH="217"><div> <FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" ><B>a</B></FONT>)  <I><B>h</B></I><B> = 0.1</B></div> </tD> <tD VALIGN=TOP BGCOLOR=#FFFFCC WIDTH="201"><div> <FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" ><B>b</B></FONT>)  <I><B>h</B></I><B> = 0.05</B></div> </tD> <tD VALIGN=TOP BGCOLOR=#FFFFCC WIDTH="144"><div> <FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" ><B>c</B></FONT>)  <I><B>h</B></I><B> = 0.025</B></div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 26 WIDTH="80"><div> 0.1</div> </tD> <tD VALIGN=TOP WIDTH="217"><div> 1.1</div> </tD> <tD VALIGN=TOP WIDTH="201"><div> 1.105</div> </tD> <tD VALIGN=TOP WIDTH="144"><div> <IMG SRC="3c257130.gif" border=0 width="87" height="19" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 26 WIDTH="80"><div> 0.2</div> </tD> <tD VALIGN=TOP WIDTH="217"><div> 1.22</div> </tD> <tD VALIGN=TOP WIDTH="201"><div> 1.23205</div> </tD> <tD VALIGN=TOP WIDTH="144"><div> <IMG SRC="3c157130.gif" border=0 width="87" height="19" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 26 WIDTH="80"><div> 0.3</div> </tD> <tD VALIGN=TOP WIDTH="217"><div> 1.364</div> </tD> <tD VALIGN=TOP WIDTH="201"><div> 1.3857805</div> </tD> <tD VALIGN=TOP WIDTH="144"><div> <IMG SRC="3c057130.gif" border=0 width="87" height="19" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 26 WIDTH="80"><div> 0.4</div> </tD> <tD VALIGN=TOP WIDTH="217"><div> 1.5368</div> </tD> <tD VALIGN=TOP WIDTH="201"><div> 1.57179435</div> </tD> <tD VALIGN=TOP WIDTH="144"><div> <IMG SRC="3bf57130.gif" border=0 width="87" height="19" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </tD> </tR> </TABLE></div> <div> <IMG SRC="3c3a6e80.gif" border=0 width="678" height="488" ALT="Documento Microsoft Office Word" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <DIV ALIGN="LEFT"></DIV> <div> <TABLE BORDER="1" CELLPADDING="1" CELLSPACING="0" WIDTH="594" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP COLSPAN=5 HEIGHT= 39 WIDTH="580"><div> <B>Tabla comparativa de los valores aproximados obtenidos en </B><FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" ><B>a</B></FONT><B>), </B><FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" ><B>b</B></FONT><B>) y </B><FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" ><B>c</B></FONT><B>) con los valores reales obtenidos en </B><FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" ><B>d</B></FONT><B>)</B></div> </tD> </tR> <tR> <tD VALIGN=TOP BGCOLOR=#FFFFCC HEIGHT= 20 WIDTH="80"><div> <I><B>t</B></I></div> </tD> <tD VALIGN=TOP BGCOLOR=#FFFFCC WIDTH="123"><div> <FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" ><B>a</B></FONT>)  <I><B>h</B></I><B> = 0.1</B></div> </tD> <tD VALIGN=TOP BGCOLOR=#FFFFCC WIDTH="123"><div> <FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" ><B>b</B></FONT>)  <I><B>h</B></I><B> = 0.05</B></div> </tD> <tD VALIGN=TOP BGCOLOR=#FFFFCC WIDTH="123"><div> <FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" ><B>c</B></FONT>)  <I><B>h</B></I><B> = 0.025</B></div> </tD> <tD VALIGN=TOP BGCOLOR=#FFFFCC><NOBR><div> <B>d</B><FONT SIZE="3" COLOR="#000000" FACE="Times New Roman" ><B>) Valores reales</B></FONT></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 26 WIDTH="80"><div> 0.1</div> </tD> <tD VALIGN=TOP WIDTH="123"><div> 1.1</div> </tD> <tD VALIGN=TOP WIDTH="123"><div> 1.105</div> </tD> <tD VALIGN=TOP><NOBR><div> <IMG SRC="3c557130.gif" border=0 width="87" height="19" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> <tD VALIGN=TOP WIDTH="123"><div> 1.110701379</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 26 WIDTH="80"><div> 0.2</div> </tD> <tD VALIGN=TOP WIDTH="123"><div> 1.22</div> </tD> <tD VALIGN=TOP WIDTH="123"><div> 1.23205</div> </tD> <tD VALIGN=TOP><NOBR><div> <IMG SRC="3c657130.gif" border=0 width="87" height="19" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> <tD VALIGN=TOP WIDTH="123"><div> 1.245912349</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 26 WIDTH="80"><div> 0.3</div> </tD> <tD VALIGN=TOP WIDTH="123"><div> 1.364</div> </tD> <tD VALIGN=TOP WIDTH="123"><div> 1.3857805</div> </tD> <tD VALIGN=TOP><NOBR><div> <IMG SRC="3c757130.gif" border=0 width="87" height="19" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> <tD VALIGN=TOP WIDTH="123"><div> 1.411059400</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 26 WIDTH="80"><div> 0.4</div> </tD> <tD VALIGN=TOP WIDTH="123"><div> 1.5368</div> </tD> <tD VALIGN=TOP WIDTH="123"><div> 1.57179435</div> </tD> <tD VALIGN=TOP><NOBR><div> <IMG SRC="3c857130.gif" border=0 width="87" height="19" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> <tD VALIGN=TOP WIDTH="123"><div> 1.612770464</div> </tD> </tR> </TABLE></div> <bR> <bR> </td> <td valign="top" rowspan="2" width=14 BGCOLOR="#006600" TEXT="#F7F7FF"> <bR> </td> </tr><tr> <td valign="top" height=21 BGCOLOR="#006600" TEXT="#F7F7FF"> <div> <B>|  </B><A HREF="id69_m.htm#1_y_2" TARGET="TRLX_Middle" TITLE="8.1(a)"><U><B>1 y 2</B></U></A><B> |</B></div> </td> </tr></table></body>