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I try to solve this PDE as below:

y''''-ky''+1=0

With boundary conditions of x=0.y=y''=0 and x=-h,y=y'=0.

k and h are constant.

The solution look like from the Fourier transforms.

There is one term in the solution which is :

beta_n is the positive roots of the equation of beta_n=tan(beta_n). n is from 1 to infinity.

I have no idea how this term come from. If someone can help me, I really appreciate it!!

Kevin

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# Help to solve 4th order ode

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