How to find values of w for which determinant of A is zero?

determinant.mw

Can we convert expression into determinant of 3 rows and 3 columns?

convert.mw

I am trying to solce eq (2) by integration. But maple integrate only 1st term in eq. Why not other two terms? 

Solve_integral.mw

Why maple give empty solutions? See ref. (12) in the attached wokrsheet. Is there anything missing when deriving Sols?

sols_tw.mw