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


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