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Linearization of second order ordinary differential equations via Cartan’s equivalence method. (English) Zbl 0671.34012

The problem of characterizing those second order differential ordinary differential equations \(y''=F(x,y,y')\) which are linearizable by a point transformation is solved using Cartan’s equivalence method. The result is nicely summarized in the Theorem: The following (local) conditions are equivalent:
(1) The equation has SL(3,R) as its infinitesimal symmetry group;
(2) The equation is linearizable;
(3) F is a cubic polynomial in \(y'\) given by \(F=A+3By'+3C(y')^ 2+D(y')^ 3\) with some technical conditions on A, B, C and D which must be satisfied.
Reviewer: W.Ames

MSC:

34A34 Nonlinear ordinary differential equations and systems
34A30 Linear ordinary differential equations and systems
34C20 Transformation and reduction of ordinary differential equations and systems, normal forms
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References:

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