Mp = 2.435*10^18;
[Alpha] = 1.4*10^-5;
[Beta] = 6.3*10^-8;
[Gamma] = -0.013;
[Lambda]6 = 0;

zero = 10^-5;
inf = 10^9;
ref = inf - 10^-3;
[Delta] = 0.0001;
DU = Re[D[1/4 y[x]^4*([Gamma] + [Alpha]*(Log[y[x]])^2 + [Beta(Log[y[x]])^4), y[x]]];
eqn = y''[x] + 3 y'[x]/x == DU;
B = 0.070;
n = 0;
eqn0 = B + B^3/8 ([Gamma] + ([Alpha]/2)*Log[B] + [Alpha]*(Log[B])^2 + [Beta]*(Log[B])^3 + [Beta]*(Log[B])) x^2;

!(*OverscriptBox[([CapitalDelta]), (~)]) = 10;
While[
!(*OverscriptBox[([CapitalDelta]), (~)]) > 10^-10,
 initialcon1 = eqn0 /. x -> zero;
 initialcon2 = D[eqn0, x] /. x -> zero;
 sol = With[{[Epsilon] = 1/10000},
   NDSolve[{y''[x] + 3/x*y'[x] == U, y[inf] == 0,
     y'[[Epsilon]] == 0}, y, {x, [Epsilon], inf},
    Method -> {"BoundaryValues" -> {"Shooting",
        "StartingInitialConditions" -> {y[[Epsilon]] == initialcon1,
          y'[[Epsilon]] == initialcon2}}}]];
 x2sol = x^2*y[x] /. (First@sol);
 n++;
 [CapitalDelta] = (x2sol /. x -> inf) - (x2sol /. x -> ref);

!(*OverscriptBox[([CapitalDelta]), (~)]) =
  Abs[[CapitalDelta]];
 If[[CapitalDelta] > 10^-10, B += [Delta]/n*10];
 If[[CapitalDelta] < -10^-10, B -= [Delta]/n*10];]