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


34C20 Transformation and reduction of ordinary differential equations and systems, normal forms
34A30 Linear ordinary differential equations and systems
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