×

On a certain transformation of the solution set of two linear second order differential equations. (English) Zbl 0555.34029

Let q be a fixed \(C^ 1\) function and Q a fixed continuous function on an interval j. Assume there is a function \(F: j\times {\mathbb{R}}\times {\mathbb{R}}\to {\mathbb{R}}\) establishing a 1-1 correspondence between the solutions of \(y''=q(t)y\) and \(Y''=Q(t)Y\) by \(Y(t)=F(t,y(t),y'(t))\). This paper studies the question of when F has the form \(F(t,u,v)=A(t)u+B(t)v\).
Reviewer: D.Erle

MSC:

34C20 Transformation and reduction of ordinary differential equations and systems, normal forms
34A30 Linear ordinary differential equations and systems
PDFBibTeX XMLCite
Full Text: EuDML

References:

[1] Borůvka O.: Linear Differential Transformations of the Second Order. The English Univ. Press, London 1971. · Zbl 0218.34005
[2] Háčik M.: Generalization of amplitude, phase and accompanying differential equations. Acta Univ. Palackianae Olomucensis, FRN, 33, 1971, 7-17.
[3] Laitoch M.: L’équation associée dans la théorie des transformations des équations différentielles du second ordre. Acta Univ. Palackianae Olomucensis, 12, 1963, 45-62. · Zbl 0256.34005
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.