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On an involutive mapping of solutions of differential equations. (English. Russian original) Zbl 1210.34014

Differ. Equ. 43, No. 10, 1376-1381 (2007); translation from Differ. Uravn. 43, No. 10, 1346-1351 (2007).
Summary: Methods for reducing an equation to another equation play an important role in the theory of ordinary differential equations. The method suggested in the present paper is presented for second- and third-order linear homogeneous equations but can be generalized to equations of arbitrary order \(n\). An important feature of this method is that the operator \(A\) used to transform an equation to another equation coincides with the inverse of itself, \(A=A^{-1}\).

MSC:

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

References:

[1] Stepanov, V.V., Kurs differentsial’nykh uravnenii (A Course of Differential Equations), Moscow: Gostekhizdat, 1953.
[2] Kamke, E.W.H., Differentialgleichungen, Leipzig, 1959. Translated under the title Spravochnik po obyknovennym differentsial’nym uravneniyam, Moscow, 1981.
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