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Biharmonic Equation with Coefficients

  1. Dec 12, 2011 #1
    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.
  2. jcsd
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