Question: Elliptic Integrals

I am trying to recreate a transcendental equation from a paper on buckling analysis. I have not been able to successfully manipulate equation (10) given on page 692 of the attached files into the final forms of equations (12) and (13), using the boundary conditions given in (11). Could someone take a look at my Maple worksheet and offer some suggestions that would yield an elliptic integral? Download 4865_Lo_p692.pdf
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