The paper compares computational aspects of four approaches to compute conservation
laws of single Differential Equations (DEs) or systems of them, ODEs and PDEs. The only
restriction, required by two of the four corresponding computer algebra programs, is that each
DE has to be solvable for a leading derivative. Extra constraints for the conservation laws can
be specified. Examples include new conservation laws that are non-polynomial in the functions,
that have an explicit variable dependence and families of conservation laws involving arbitrary
functions. The following equations are investigated in examples: Ito, Liouville, Burgers,
Kadomtsev–Petviashvili, Karney–Sen–Chu–Verheest, Boussinesq, Tzetzeica, Benney.
Differential equations and computer algebra
