i dont know how to solve or use mathematica to solve this 2nd order ordinary differential equations?
You could write it as $\displaystyle (a-bx) y''-y=0$ and solve it via power series. In Mathematica, use DSolve:
DSolve[y''[t]-k/(a-bt) y[t]==0,y,t]
which returns an answer in terms of Bessel functions. Might be interesting to reconcile that answer with the answer you get using power series.