Resumo
Existem várias técnicas engenhosas para obter soluções exatas de uma equação diferencial ordinária (EDO). Surpreendentemente, elas são, em sua maioria, casos especiais de métodos mais gerais baseados na invariância da equação sob grupos de simetrias. Neste artigo, será apresentado um desses métodos tendo em vista, particularmente, EDO’s de primeira ordem.
Palavras-chave: Simetrias de Lie. EDO’s de primeira ordem. Soluções exatas.
Abstract
Exact solutions of first-order ODEs via lie point sysmmetries
There are several ingenious techniques to obtain exact solutions from an ordinary differential equation (ODE). Surprisingly, they are mostly special cases of more general methods based on
the invariance of the equation under symmetry groups. In this article, it will be presented one of these methods. focusing, especially, in first-order ODEs.
Keywords: Lie point symmetries. First-order ODEs. Exact solutions.
Referências
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STEPHANI, H.; MACCALLUM, M. Differential equations: their solution using symmetries. Cambridge: Cambridge University Press, 1989.