Effective procedure of point-classification for the equation $y^{\prime \prime }=P+3Q{y}^{\prime }+3R{y^{\prime }}^2+S{y^{\prime }}^3$

Abstract

For the equations of the form $y^{\prime \prime }=P(x,y)+3Q(x,y)y^{\prime }+3R(x,y){y^{\prime }}^2+S(x,y){y^{\prime }}^3$ the problem of equivalence in the class of point transformations is considered. Effective procedure for determining the class of point equivalence for the given equation is suggested. This procedure is based on explicit formulas for the invariants.

arXiv commentAmSTeX, Ver. 2.1, 35 pages, amsppt style

References in corpus (1)

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

Cited by in corpus (3)

• 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
• Umbilical and zero curvature equations in a class of second order ODE's