Abstract
This paper is concerned with the realization of ordinary differential equation solver by using their symmetry transformation on computer algebra systems. Three standard methods of solution are compared with examples : (1)transformation of coordinate systems, (2)use of differential invariants, and(3)utilization of integral factors. Large part of symmetry analysis and the method(1)can be realized on computer algebra systems, such as constructing the equation for symmetry transformation, solving it with a trial function and transformation of variables. An algorithm is given for solving the total differential equation to obtain the first integrals for the method(2). For implementation, the rule based programming technique available in Mathematica was useful.
