## On transformations of two homogeneous linear second order differential equations of a general and of Sturm forms.(English)Zbl 0643.34048

Let (ab): $$y''+a(t)y'+b(t)=0$$, $$a,b\in C^ 0(j)$$, (AB): $$Y''+A(T)Y'+B(T)Y=0$$, $$A,B\in C^ 0(J)$$ be two second order homogeneous linear differential equations. Necessary and sufficient conditions for two functions $$f=f(t)$$, $$h=h(t)$$, $$t\in j$$, so that every solution Y of (AB) the function $$y(t)=f(t)\cdot Y[h(t)]$$ is a solution of (a,b) in $$i\subset j$$ are given. These conditions are also formulated for equations of Sturm and Jacobi type.
Reviewer: J.Laitochová

### MSC:

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

 [1] Borůvka O.: Linear Differential Transformations of the Second Order. The English University Press, London, 1971. · Zbl 0218.34005 [2] Neuman F.: Teorija globalnych svojstv obyknovennych linějnych differencialnych uravnenij n-go porjadka. Differencialnye uravnenija 19 (1983), 799-808.
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