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I got some trobule in solving the following simple-looking PDE's. Can anyone give a hint about how to solve it? thanks a lot! I guess the solution is of the form [itex]y(u,v)=A[\cos(k(u-f(v))-B]\cosh(v)-C[/itex]. But I don't know a formal way to solve.

[itex]\frac{\partial^4y(u,v)}{\partial u^2 \partial v^2} +k^2 \frac{\partial^2y(u,v)}{\partial v^2}=0[/itex]

[itex]\frac{\partial^2y(u,v)}{\partial u^2} +k^2 y(u,v) +b=0[/itex]

Boundary condition:

[itex]\frac{\partial y(u,v)}{\partial v}|_{v=0}=0[/itex]

[itex]\frac{\partial y(u,v)}{\partial u}|_{u=0,v=0}=0[/itex]

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# Simple-looking PDE

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