ALGORITHMS USING LIE TRANSFORMATION GROUPS TO SOLVE FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS ALGEBRAICALLY

We investigate the problem of finding closed-form solutions to first order, first degree differential equations g (x,y)y'(x) + f (x,y) = 0. The present work explores the application of results discovered by Sophus Lie.;of a unified framework in which to search for a solution. Statements and proofs of correctness are given of procedures that decide if an "elementary" Lie transformation group helps solve a given equation or not. Many of the elementary types of equations can be solved through these methods, in addition to types of equations solved through simple changes of variables. We evaluate an implementation of our procedures and find that in the present implementation, the group-finding algorithms do not seem competitive in speed with previously developed techniques for the.;most basic types of equations; they would best be used to when other techniques fail.;*Work supported in part by the U.S. Dept. of Energy under contract DE-AM03-76SF00034, Project Agreement DE-AS03-79ER10358. Preparation of this paper supported in part by the National Science Foundation under grant MCS ;to algorithmic solution of classes of first order equations, and as the basis.