finding out if expr has the form F(y/x^a)

Dear all,

I would like to find out if an expression is of (or can be written in) the 
general form (y/x)*f(y/x^a), with 'a' a nonzero constant. The difficulty I 
have here is the generality of the function f. You can have:
expr:y^3+1/x^(3/2); 
or:
expr:(y/x)*sin(y^2/x^4 + y^3/x^6); 

I think it reduces to this:
(after dividing by y/x,) How to find out if there is a constant 'a' for which 
a substitution H=y/x^a leads to an expression free of x and y?


Best,
NB