I posted a similar message in comp.soft-sys.math.mathematica, but didn't get any reply, so I'm trying here this time.
I'm trying to solve a linear/1st-order PDE for a function f(x,y) using DSolve. One special thing about this PDE is that it also involves two unknown arbitrary functions g(x,y) and h(x,y). What I'd like to see is an expression for f in terms g and h, in additon to x and y.
When I tried it in Mathematica, however, it seemed to take Mathematica forever to solve it. I waited a couple of hours without seeing any result, so I was forced to stop it.
Now I'm beginning to wonder if Mathematica is indeed capable of solving such a PDE at all, i.e., a PDE which involves arbitrary functions other than the one you want to solve for. For test purposes I tried giving specific values for g and h, and Mathematica returned the answer in a matter of seconds.
So, in short my question is: can Mathematica solve such PDE's?
Of course I could try running Mathematica for a very long time (like overnight) and if it still doesn't produce a solution, I could conclude that Mathematica cannot do it. But it would be nice to have a definite answer on this from someone who has more experience and knowledge about Mathematica.
Thanks in advance,