Dear All,(adsbygoogle = window.adsbygoogle || []).push({});

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]

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Simple-looking PDE

**Physics Forums | Science Articles, Homework Help, Discussion**