@Carl Love Yes you a right, I use cylindrical coordinates. My original differential equation is a two dimensional PDE (the r-dimension is small compared to the other dimensions, so is neglegted). I have eliminated the theta-dependence, by using the orthogonality property of the sin and cos function (I know that the input and output on the theta dimension should be a sin or cos function). This gives me a ODE which I can solve quite simple with Maple.
When I change to cartesian, it will be very hard (impossible?) to eliminate dimensions, so I am bound to solving a PDE, which is not preferred.
I could have made a mistake in the elimination of the theta-dependence. Stange thing is that when I calculate a simply supported beam (same ODE, different BC), the result is very good. I am thinking that maybe when I compose the ODE, the assumptions I make do not apply for every BC.