<?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>0035-001X</journal-id>
<journal-title><![CDATA[Revista mexicana de física]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. mex. fis.]]></abbrev-journal-title>
<issn>0035-001X</issn>
<publisher>
<publisher-name><![CDATA[Sociedad Mexicana de Física]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0035-001X2021000300442</article-id>
<article-id pub-id-type="doi">10.31349/revmexfis.67.443</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Factorization method for some inhomogeneous Liénard equations]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Cornejo-Pérez]]></surname>
<given-names><![CDATA[O.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Mancas]]></surname>
<given-names><![CDATA[S. C.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Rosu]]></surname>
<given-names><![CDATA[H. C.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Rico-Olvera]]></surname>
<given-names><![CDATA[C. A.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Autónoma de Querétaro Facultad de Ingeniería ]]></institution>
<addr-line><![CDATA[Santiago de Querétaro ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Embry-Riddle Aeronautical University  ]]></institution>
<addr-line><![CDATA[Daytona Beach FL]]></addr-line>
<country>USA</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Instituto Potosino de Investigación Científica y Tecnológica  ]]></institution>
<addr-line><![CDATA[San Luis Potosí S.L.P.]]></addr-line>
<country>México</country>
</aff>
<aff id="Af4">
<institution><![CDATA[,Universidad Autónoma de Querétaro Facultad de Ingeniería ]]></institution>
<addr-line><![CDATA[Santiago de Querétaro ]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2021</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2021</year>
</pub-date>
<volume>67</volume>
<numero>3</numero>
<fpage>442</fpage>
<lpage>446</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0035-001X2021000300442&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0035-001X2021000300442&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0035-001X2021000300442&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract We obtain closed-form solutions of several inhomogeneous Liénard equations by the factorization method. The two factorization conditions involved in the method are turned into a system of first-order differential equations containing the forcing term. In this way, one can find the forcing terms that lead to integrable cases. Because of the reduction of order feature of factorization, the solutions are simultaneously solutions of first-order differential equations with polynomial nonlinearities. The illustrative examples of Liénard solutions obtained in this way generically have rational parts, and consequently display singularities.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Factorization]]></kwd>
<kwd lng="en"><![CDATA[inhomogeneous]]></kwd>
<kwd lng="en"><![CDATA[Liénard equation]]></kwd>
<kwd lng="en"><![CDATA[Abel equation]]></kwd>
<kwd lng="en"><![CDATA[Riccati equation]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<label>1</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lakshmanan]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Rajasekar]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<source><![CDATA[Nonlinear Dynamics: Integrability, Chaos, and Patterns]]></source>
<year>2003</year>
<publisher-loc><![CDATA[Heidelberg ]]></publisher-loc>
<publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B2">
<label>2</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Harko]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Liang]]></surname>
<given-names><![CDATA[S.-D.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Exact solutions of the Liénard and generalized Liénard type ordinary nonlinear differential equations obtained by deforming the phase space coordinates of the linear harmonic oscillator]]></article-title>
<source><![CDATA[J. Eng. Math]]></source>
<year>2016</year>
<volume>98</volume>
<page-range>93</page-range></nlm-citation>
</ref>
<ref id="B3">
<label>3</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Pol]]></surname>
<given-names><![CDATA[B. van der]]></given-names>
</name>
<name>
<surname><![CDATA[Mark]]></surname>
<given-names><![CDATA[J. van der]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Frequency de multiplication]]></article-title>
<source><![CDATA[Nature]]></source>
<year>1927</year>
<volume>120</volume>
<page-range>363</page-range></nlm-citation>
</ref>
<ref id="B4">
<label>4</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Rosu]]></surname>
<given-names><![CDATA[H.C.]]></given-names>
</name>
<name>
<surname><![CDATA[Cornejo-Pérez]]></surname>
<given-names><![CDATA[O.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Supersymmetric pairing of kinks for polynomial nonlinearities]]></article-title>
<source><![CDATA[Phys. Rev. E]]></source>
<year>2005</year>
<volume>71</volume>
<page-range>046607</page-range></nlm-citation>
</ref>
<ref id="B5">
<label>5</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Cornejo-Pérez]]></surname>
<given-names><![CDATA[O.]]></given-names>
</name>
<name>
<surname><![CDATA[Rosu]]></surname>
<given-names><![CDATA[H.C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Nonlinear second order ode&#8217;s: Factorizations and particular solutions]]></article-title>
<source><![CDATA[Prog. Theor. Phys]]></source>
<year>2006</year>
<volume>114</volume>
<page-range>533</page-range></nlm-citation>
</ref>
<ref id="B6">
<label>6</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Rosu]]></surname>
<given-names><![CDATA[H.C.]]></given-names>
</name>
<name>
<surname><![CDATA[Cornejo-Pérez]]></surname>
<given-names><![CDATA[O.]]></given-names>
</name>
<name>
<surname><![CDATA[Pérez-Maldonado]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Belinchón]]></surname>
<given-names><![CDATA[J.A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Extension of a factorization method of nonlinear second order ODE&#8217;s with variable coefficients]]></article-title>
<source><![CDATA[Rev. Mex. Fís]]></source>
<year>2017</year>
<volume>63</volume>
<page-range>218</page-range></nlm-citation>
</ref>
<ref id="B7">
<label>7</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Dong]]></surname>
<given-names><![CDATA[S.-H.]]></given-names>
</name>
</person-group>
<source><![CDATA[Factorization Method in Quantum Mechanics]]></source>
<year>2007</year>
<publisher-loc><![CDATA[Dordrecht ]]></publisher-loc>
<publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B8">
<label>8</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Mielnik]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
<name>
<surname><![CDATA[Rosas-Ortiz]]></surname>
<given-names><![CDATA[O.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Factorization: little or great algorithm?]]></article-title>
<source><![CDATA[J. Phys. A: Math. Gen]]></source>
<year>2004</year>
<volume>37</volume>
<page-range>10007</page-range></nlm-citation>
</ref>
<ref id="B9">
<label>9</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Wang]]></surname>
<given-names><![CDATA[D.S.]]></given-names>
</name>
<name>
<surname><![CDATA[Li]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Single and multi-solitary wave solutions to a class of nonlinear evolution equations]]></article-title>
<source><![CDATA[J. Math. Anal. Appl]]></source>
<year>2008</year>
<volume>343</volume>
<page-range>273</page-range></nlm-citation>
</ref>
<ref id="B10">
<label>10</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Chandrasekar]]></surname>
<given-names><![CDATA[V.K.]]></given-names>
</name>
<name>
<surname><![CDATA[Senthilvelan]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Lakshmanan]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[New aspects of integrability of force-free Duffing-van der Pol oscillator and related nonlinear systems]]></article-title>
<source><![CDATA[J. Phys. A:Math. Gen]]></source>
<year>2004</year>
<volume>37</volume>
<page-range>4527</page-range></nlm-citation>
</ref>
<ref id="B11">
<label>11</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Sarafian]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A closed form solution to a special normal form of Riccati equation]]></article-title>
<source><![CDATA[Advances in Pure Mathematics]]></source>
<year>2011</year>
<volume>1</volume>
<page-range>295</page-range></nlm-citation>
</ref>
<ref id="B12">
<label>12</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Dunster]]></surname>
<given-names><![CDATA[T. M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Asymptotic solutions of inhomogeneous differential equations having a turning point]]></article-title>
<source><![CDATA[Stud. Appl. Math]]></source>
<year>2020</year>
<volume>145</volume>
<page-range>500</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
