[![enter image description here][1]][1]

I'm trying to solve the above differential equation using the shooting method.  When i set `Method -> {"Shooting", "StartingInitialConditions" -> {z[0] == 0, z'[0] == 1}` i get a solution, but it is equal to zero. I need a solution that is different of zero. When i increase the value of `z'[0]`, say to `z'[0]=1000` Mathematica stay running for a long time and i get no solution. How can i solve this?

Here is the code:

    n = 3.;
    xf = 10000.;
    s = NDSolve[
       {
        -z''[t] == (1 + (n - 2) t)^(1/(2 - n) (2 (n - 1) + 0.001)) z[
            t]^2 (Sin[z[t]+2])
        , z[0] == 0, z'[xf] == 0}, z, {t, 0, xf},
       Method -> {"Shooting", 
         "StartingInitialConditions" -> {z[0] == 0, z'[0] == 1}
         }
       ] // Chop
    Plot[Evaluate[z[t] /. s], {t, 0., 10}, PlotRange -> All]


  [1]: https://i.sstatic.net/7pPcO.png