Question: solving / simplifying a non-linear ODE

I have this non-linear ODE in q(p):

ode := diff(q(p), p) = (q(p)-a*p)/(p-a*q(p))*(p^(-b)-1)/q(p)^(-b);

for some real parameters a and b, it may be solved in exact form for the special value a=1.

Is there any hope of getting a closed-form solution or of expressing the solution in a neat way for the case 0<a<1? even some specific value of a would be of interest, e.g. a=1/2.

dsolve(eval(ode,{a=1}));
                                  1                 
           q(p) = ----------------------------------
                                             /  1  \
                                             |-----|
                                             \b - 1/
                  /  (1 - b)                \       
                  \-p        - b p + p + _C1/       

It doesn't look likely, but I thought I'd ask just in case. Thanks!