I'm looking for examples of Helmholtz and Biharmonic equations in Cartesian co-ordinates with exact solutions, in order to compare results of my numerical solutions with it.
I was able to find quite a few examples on the internet, where the problem with boundary conditions were precisely defined. Those were, unfortunately only illustrative examples and exact solutions were not shown.
Any particular example, or a useful link to a web-page or a paper is appreciated.