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"


?but it fails for some trivial cases (as does rich.hennessy's version):?

If my understanding of the rat() function is correct then this new version 
is better. I pass in the values x,y because someone might be interested in 
the more general case when x = someothervar, y=someothervar2. It catches a 
lot of cases that would be rejected without using rat().  I can?t claim it 
works in every case, but I think it is a pretty good answer for what was 
originally asked.  I can?t take credit for it, I did not think of the basic 
premise of using pdiff package.  I would not have done it that way since I 
don?t know much about pdiff.

solution(g,x,y):=block
(
    [g2,g3,g6,a],
    g2:g*x/y,
    g3:at(g2,y=1/x),
    if is(equal(g3,g2))=true then
        (g6:1,a:%r)
    else
        (g6:at(diff(at(g,y=x),x)/diff(g3,x),x=1),a:-ratsimp((g6+1)/(g6-1))),
    f:at(g*x/y,y=x^(a+1)),
    if is(equal(radcan(rat(g-y/x*at(f,[x=y/x^a]))),0))=true then 
['a=a,'f(x)=f]
)$

The end.  This is my last unsolicited post on this, sorry if I am annoying 
anyone.  Please let me know if this is good enough NB.