Integrating factors for second-order ODEs

A systematic algorithm for building integrating factors of the form mu(z, y ), mu(x, y') or mu(y, y') for second-order ODEs is presented. The algorithm can determine the existence and explicit form of the integrating factors t hemselves without solving any differential equations, except for a linear O DE in one subcase of the mu(x, y) problem. Examples of ODEs not having poin t symmetries are shown to be solvable using this algorithm. The scheme was implemented in Maple, in the framework of the ODEtools package and its ODE- solver. A comparison between this implementation and other computer algebra ODE-solvers in tackling non-linear examples from Kamke's book is shown. (C ) 1999 Academic Press.