Computing Closed Form Solutions of First Order ODEs Using the Prelle-Singer Procedure

The Prelle-Singer procedure is an important method for formal solution of first order ODEs. Two different REDUCE implementations (PSODE versions 1 & 2) of this procedure are presented in this paper. The aim is to investigate which implementation is more efficient in solving different types of ODEs (such as exact, linear, separable, linear in coefficients, homogeneous or Bernoulli equations). The test pool is based on Kamkeʹs collection of first order and first degree ODEs. Experimental results, timings and comparison of efficiency and solvability with the present REDUCE differential equation solver (ODESOLVE) and a MACSYMA implementation (ODEFI) of the Prelle-Singer procedure are provided. Discussion of technical difficulties and some illustrative examples are also included.