I'm working on a problem and I've run into a differential equation that very strongly resembles the biharmonic equation but is fundamentally different: 0 = a(∂^4 ψ/∂x^4) + b(∂^4 ψ/∂y^4) + c(∂^4 ψ/∂x^2 ∂y^2). where a,b,c are scalar coefficients. Any ideas? I think these were originally solved using eigenfunction expansions so that's my first plan, but if anybody knows anything easier... I tried it in Mathematica with poor results, but DSolve tends to struggle with the biharmonic equation in Cartesian coordinates anyway.