On the point transformations for the second order differential equations. I

Abstract

Point transformations for the ordinary differential equations of the form $y^{\prime \prime }=P(x,y)+3Q(x,y)y^{\prime }+3R(x,y)(y^{\prime }{)}^2+S(x,y)(y^{\prime }{)}^3$ are considered. Some classical results are resumed. Solution for the equivalence problem for the equations of general position is described.

AmSTeX, Version 2.1, 15 pages

Cited by in corpus (10)

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• A note on invertible quadratic transformations of the real plane
• Point classification of the second order ODE's by Ruslan Sharipov and its application to Painleve equations
• Comparison of two classifications of a class of ODE's in the case of general position
• Comparison of two classifications of a class of ODE's in the first case of intermediate degeneration
• On positive bivariate quartic forms
• Point-invariant classes of the third order ordinary differential equations
• On some equations that can be brought to the equations of diffusion type
• Umbilical and zero curvature equations in a class of second order ODE's