Looking for a symbolic computer algebra system software package, capable of symbolically solving systems of partial differential equations (PDEs). I am certain this can be done with Maple and (possibly) Mathematica. Could you recommend other software packages? They should be able of at least solving systems of linear and quazilinear PDEs containing first-order derivatives of the unknown functions. The coefficients can be constants or functions of the coordinates. I would like to try and see what kind of solutions one gets, when the solution is constant etc.
My preference is working with symbolic PDE solvers, but for the benefit of other readers you can also post about numerical solvers of systems of PDEs, only please make clear whether they are symbolic solvers or numeric ones.