Question: How do i solve a ped system with the second boundary condition

i came into some questions when i wanted to solve a pde systerm as follows:

> pde := diff(u(x, y), y, y, y, y) = 0;
> sys := [pde, u(x, 0) = 0, u(x, a) = F0, (D[`$`(2, 2)](u))(x, 0) = 0, (D[2, 2](u))(x, a)-beta*(D[2](u))(x, a) = 0];
> pds := pdsolve(sys);
Error, (in pdsolve/sys/info) found functions with same name but depending on different arguments in the given DE system: u(x, a), u(x, y). It is required an indication of the dependent variables

what's the error meaning and how could i make it work, thanks~~~

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