\(y[x] = 
      1 + \(y\_2\) x\^2 + \(y\_3\) x\^3 + \(y\_4\) x\^4 + \(y\_5\) x\^5 + 
        \(y\_6\) x\^6; 
yp = D[y[x], x]; 
ypp = D[y[x], {x, 2}]; 

    Series[ypp + \((2\/x)\) yp + y[x]\^n, {x, 0, 8}]\)

Solve[(-1 + n) (n/2) ((1/36)) + (n/120) + 42 (Subscript[y, 6]) == 0, 
      (Subscript[y, 6])]