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:(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Biharmonic Equation with Coefficients

Can you offer guidance or do you also need help?

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