# 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.