integration – Find a function perpendicular to a given function

I want to find a function $ f (x) $ such as

$ int_ {x_0} ^ { infty} f {{}} (x) bigg (-Y_1 (a : x_0) J0 (a : x) + Y_0 (a : x) J_1 ( a : x_0) bigg) dx propto delta (yy), $

in which $ Y_n $ and $ J_n $ are the nth order of the Bessel function of the second and first types respectively and $ a $ is a positive constant. Can any one help me? Any function $ f (x) $ who satisfy this equation can help me.