funkt = 
      NDSolve[{u'[t] == 2 - (((u[t]))^2) + Sin[t], 
          u[0] == 2}, u, {t, 0, 15}]

Plot[
      Evaluate[u[t] /. funkt[[1]][[1]]], {t, 0, 15}]

Evaluate[u[3] /. funkt[[1]][[1]] ]

2*Sin[4]*Evaluate[u[4] /. funkt[[1]][[1]] ]

uhuu[t_] := 
      Evaluate[u[x]  /.  funkt[[1]][[1]] ]  /. 
        x -> t

uhuu[3]

2*Sin[4]*uhuu[3]