Question: Enforce non-trivial solutions when using dsolve

Hello Everyone,

Firstly thank you for your help everyone with answering my other question yesterday, it really helped.
Today I present with yet another issue, which is dealing with solving differential equations using the dsolve-command.

I have written a script which is defining the differential equations, (some numbers), and the constraints. However when I let it solve using dsolve, I only get a very very trivial answer, meaning f(x) = 0.
of course this is a valid answer, but not one I can work with... 
(Can I maybe give an additional information, e.g. the function type it is supposed to do this task? In the documentation there is information on setting it up as a series, but what about exponential equations?)

I have uploaded to script (very short), maybe someone knows where I went wrong?
Also, I am assuming that for solving a DE which involves a fourth order derivative I need exactly four boundary conditions, which I provided.
Things are also getting really wonky when I set Nxy to something non-zero... Then I get a solutions which involves a mysterious Z which never happened before and again all four C_x, which I assume resemble missing boundary conditions, reappear.

Any help would be fantastic! :)

Best Regards,




restart*with(DocumentTools); with(LinearAlgebra); D11 := 10000; D12 := 10000; D22 := 10000; D66 := 10000; Nx := 1000; Ny := 1000; Nxy := 0; a := 5000; b := 5000; w := sin(y)*GenFunc(x); PDGL := D11*(diff(w, `$`(x, 4)))+(2*(D12+2*D66))*(diff(w, `$`(x, 2), `$`(y, 2)))+D22*(diff(w, `$`(y, 4)))+Nx*(diff(w, `$`(x, 2)))+Ny*(diff(w, `$`(y, 2)))+2*Nxy*(diff(w, `$`(x, 1), `$`(y, 1))) = 0; RB := GenFunc(0) = 0, (D(GenFunc))(0) = 0, GenFunc(a) = 0, (D(GenFunc))(a) = 0; dsolve({PDGL, RB}, GenFunc(x))

GenFunc(x) = 0





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