Scholarlink

<p>We present a general method to construct first integrals for some classes of the well known second-order ordinary differential equations, viz., the Emden and Liénard classes of equations. The approach does not require a knowledge of a Lagrangian but, rather, uses the ‘multiplier approach’ [<CitationRef CitationID="CR1">1</CitationRef>, <CitationRef CitationID="CR2">2</CitationRef>]. It is then shown how a study of the invariance properties and conservation laws are used to ‘twice’ reduce the equations to solutions. In this paper, we restrict our work to the nonlinearizable cases.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

An analysis of the nonlinearizable classes of Emden-Liénard equations

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年3月14日

查看全文
  • M. Ahmed,
  • A. H. Kara

摘要

We present a general method to construct first integrals for some classes of the well known second-order ordinary differential equations, viz., the Emden and Liénard classes of equations. The approach does not require a knowledge of a Lagrangian but, rather, uses the ‘multiplier approach’ [1, 2]. It is then shown how a study of the invariance properties and conservation laws are used to ‘twice’ reduce the equations to solutions. In this paper, we restrict our work to the nonlinearizable cases.