Solving and manipulating differential equations with Maple and Mathematica. --------------------------------------------------------------------------- G. Regensburger, M. Rosenkranz Building on the introductory courses of Mathematica and Maple, we offer a general overview of how these software systems (including various packages) can be employed to solve and manipulate differential equations of all sorts. Besides going through various concrete examples, basic knowledge about the underlying algorithms will be outlined. The list of topics includes: * elementary commands for working with differential equations * symmetries of differential equations * two-point boundary value problems * method of characteristics for first-order PDEs * differential algebra for dealing with singular solutions E. Kartashova * Pre-processing and solving of linear PDEs * Pre-processing and solving of nonlinear PDEs