DSolve[-(a*(2 + x)*y[x]^2) + 2*(1 + x)^2*y[x]*Derivative[1][y][x] - x*(1 + x)^2*Derivative[1][y][x]^2 + x*(1 + x)^2*y[x]*Derivative[2][y][x] == 0,y[x],x]