I am trying to solve the following non-linear ODE numerically:

M = 5 ; g = 12/10; 
NDSolve[{-x*D[h[x], x] + 2*D[((h[x]/(h[x] + M*(1 - h[x])))*(1 - 
2*g*M*x*(1 - h[x])*D[h[x], x])), x] == 0, h[0] == 0 , h[10] == 1}, h[x], {x, 0, 10}]

where M=5 and g=1.2. The ODE is subject to the following: h[x=0]=0 and h[x=10]=1. I tried using NDSolve with no success. I very much appreciate if anyone could help with the solution over 0<x<10.