Applications of the Differential Algebra Packagediffgrob2to Classical Symmetries of Differential Equations

We show how the MAPLE packagediffgrob2can be used to analyseoverdetermined systems of PDE. The particular application discussed here is to find classical symmetries of differential equations of mathematical and physical interest. Symmetries of differential equations underly most of the methods of exact integration known; the use and calculation of such symmetries is often introduced at advanced undergraduate level. Examples include cases where heuristics give incomplete information or fail in the integration of the determining equations for the group infinitesimals. The ideas presented here are thus an alternative method of attacking this important problem. The discussion is at a “hands on” level suitable as resource material for undergraduate instruction.