@article{Maluendas Pardo_Gómez Gómez_2009, title={Solución de algunas ecuaciones diferenciales ordinarias mediante sus grupos de simetría}, url={https://revistas.uptc.edu.co/index.php/educacion_y_ciencia/article/view/718}, DOI={10.19053/01207105.718}, abstractNote={<p class="MsoNormal" style="margin: 0cm 0cm 0pt, mso-layout-grid-align: none,"><span style="font-family: Garamond, mso-bidi-font-family: Garamond,"><span style="font-size: small,">Mediante el algoritmo de Lie se pueden </span></span><span style="font-family: Garamond, mso-bidi-font-family: Garamond,"><span style="font-size: small,">encontrar soluciones, con su respectiva </span></span><span style="font-family: Garamond, mso-bidi-font-family: Garamond,"><span style="font-size: small,">clasificación, para las ecuaciones </span></span><span style="font-family: Garamond, mso-bidi-font-family: Garamond,"><span style="font-size: small,">diferenciales ordinarias (EDO), además, se</span></span></p><p class="MsoNormal" style="margin: 0cm 0cm 0pt, mso-layout-grid-align: none,"><span style="font-family: Garamond, mso-bidi-font-family: Garamond,"><span style="font-size: small,">puede reducir el orden de algunas </span></span><span style="font-family: Garamond, mso-bidi-font-family: Garamond,"><span style="font-size: small,">ecuaciones. Existen ecuaciones de segundo </span></span><span style="font-family: Garamond, mso-bidi-font-family: Garamond,"><span style="font-size: small,">orden que no se pueden reducir ni </span></span><span style="font-family: Garamond, mso-bidi-font-family: Garamond,"><span style="font-size: small,">solucionar, como lo son las ecuaciones </span></span><span style="font-family: Garamond, mso-bidi-font-family: Garamond,"><span style="font-size: small,">trascendentes de Painlevé, puesto que solo </span></span><span style="font-family: Garamond, mso-bidi-font-family: Garamond,"><span style="font-size: small,">admiten el grupo de simetría trivial </span></span><span style="font-family: Garamond, mso-bidi-font-family: Garamond,"><span style="font-size: small,">(Clarkson, 2005). Aquí se dan a conocer </span></span><span style="font-family: Garamond, mso-bidi-font-family: Garamond,"><span style="font-size: small,">algunos grupos de simetría que admiten diferentes EDO de primer, segundo y </span></span><span style="font-family: Garamond, mso-bidi-font-family: Garamond,"><span style="font-size: small,">tercer orden, con sus soluciones </span></span><span style="font-family: Garamond, mso-bidi-font-family: Garamond,"><span style="font-size: small,">respectivas, encontradas en su mayoría a </span></span><span style="font-family: Garamond, mso-bidi-font-family: Garamond,"><span style="font-size: small,">partir de los casos particulares, que son</span></span></p><p class="MsoNormal" style="margin: 0cm 0cm 0pt, mso-layout-grid-align: none,"><span style="font-family: Garamond, mso-bidi-font-family: Garamond,"><span style="font-size: small,">soluciones del sistema que resulta de la </span></span><span style="font-family: Garamond, mso-bidi-font-family: Garamond,"><span style="font-size: small,">anulación de la función que define la </span></span><span style="font-family: Garamond, mso-bidi-font-family: Garamond,"><span style="font-size: small,">ecuación diferencial, en la respectiva </span></span><span style="font-family: Garamond, mso-bidi-font-family: Garamond,"><span style="font-size: small,">prolongación.<span style="color: #231f20,"><span style="mso-tab-count: 1,">  </span></span></span></span><em></em></p>}, number={10}, journal={Educación y Ciencia}, author={Maluendas Pardo, Pedro Nel and Gómez Gómez, Flor Alba}, year={2009}, month={jul.} }