Solutions between two-order differential equations.
Abstract
In this paper we will prove the following result: given the linear differential equations of order two, y'' + p_1 (x) y' +q_1 (x) y =0 , and y'' + p_2(x) y' + q_2(x) y =0 if a nontrivial solution of one of them is known, then always It will be possible to find a convenient change of variables from which we will find a corresponding solution for the other equation, this under the consideration of a certain invariant to be defined.
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References
Coddington, Earl. An Introduction to Ordinary Differential Equations. Dover. New York, 1989.
Walter, Wolfgang. Ordinary Differential Equations. Springer-Verlag. New York, 1998.
Rota, Gian-Carlo. TEN LESSONS I WISH I HAD LEARNED BEFORE I STARTED TEACHING DIFFERENTIAL EQUATIONS, Disponible en: https://web.williams.edu/Mathematics/lg5/Rota.pdf
