Effective procedure of point-classification for the equation y'' = P + 3 Q y' + 3 R y'² + S y'³

1998/02/05 by Руслан Шарипов, Sharipov, R. A. · 2 citations
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Numerical methods for differential equations #Differential Equations and Boundary Problems

paper · pdf · doi:10.48550/arxiv.math/9802027

Abstract

For the equations of the form y''=P(x,y)+3 Q(x,y) y'+3 R(x,y) y'² +S(x,y) y'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.

Cited by

• Umbilical and zero curvature equations in a class of second order ODE's
• Comparison of two classifications of a class of ODE's in the case of general position

Related

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• On the point transformations for the second order differential equations. I
• Differential invariants and equivalence of ODEs y''=a³(x,y)y'³+a²(x,y)y'²+a¹(x,y)y'+a⁰(x,y)
• Point-invariant classes of the third order ordinary differential equations
• Differential invariants of 2--order ODEs, I