Preliminary group classification of y" = f (x) $y^2$

Abstract

Direct group classification of y" = f(x)$y^2$ fails because the classifying condition is a third-order non-linear integro-differential equation for which a closed form solution is unknown. This fact prevents a complete group classification. In this paper we resort to the method of preliminary group classification in order to perform a partial group classification of the ordinary differential equation (ode) mentioned above and obtain new classes that admit symmetry.