<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>1409-2433</journal-id>
<journal-title><![CDATA[Revista de Matemática Teoría y Aplicaciones]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. Mat]]></abbrev-journal-title>
<issn>1409-2433</issn>
<publisher>
<publisher-name><![CDATA[Centro de Investigaciones en Matemática Pura y Aplicada (CIMPA) y Escuela de Matemática, San José, Costa Rica.]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1409-24332016000100063</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Solución analítica de la ecuación diferencial ordinaria autónoma de orden k]]></article-title>
<article-title xml:lang="en"><![CDATA[Analytical solution of the k-th order autonomous ordinary differential equation]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Orozco López]]></surname>
<given-names><![CDATA[Ronald]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad del Atlántico  ]]></institution>
<addr-line><![CDATA[ Barranquilla]]></addr-line>
<country>CO</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2016</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2016</year>
</pub-date>
<volume>23</volume>
<numero>1</numero>
<fpage>63</fpage>
<lpage>84</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S1409-24332016000100063&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S1409-24332016000100063&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S1409-24332016000100063&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[ResumenEl objetivo principal de este trabajo es hallar la solución analítica de la ecuación autónoma y(k) = f (y) y demostrar su convergencia usando polinomios autónomos de orden k, definidos aquí, además de la fórmula de Faá di Bruno para composición de funciones y polinomios de Bell. Los polinomios autónomos de orden k están definidos en término de los valores de frontera de la ecuación. Además valores especiales de los polinomios autónomos de orden 1 son dados.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[AbstractThe main objective of this paper is to find the analytical solution of the autonomous equation y(k) = f (y) and prove its convergence using autonomous polynomials of order k, define here in addition of the formula of Faá di Bruno for composition of functions and Bell polynomials. Autonomous polynomials of order k are defined in terms of the boundary values of the equation. Also special values of autonomous polynomials of order 1 are given.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[ecuación autónoma]]></kwd>
<kwd lng="es"><![CDATA[polinomios de Bell]]></kwd>
<kwd lng="es"><![CDATA[polinomios autónomos]]></kwd>
<kwd lng="en"><![CDATA[Autonomous equation]]></kwd>
<kwd lng="en"><![CDATA[Bell polynomials]]></kwd>
<kwd lng="en"><![CDATA[Autonomous polynomials]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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