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differential equations - Solve the n ODE in the loop, add the solutions to create one function


I need to solve the n ODE and create a function which is a sum of all the solutions. I wanted to use the code below, but only part (solve) and (create solution) works well. How can I store the solutions from each ODE and add them together to obtain one function ? Thank you for any help


sxf={}; (* list for solutions of each ODE *)


For [i = 1; i < 10, i++;    
  xusol = DSolve[{dx[[i]] == a[[i]], x0ui[[i]] == x0u[[i]]}, x[[i]], t] (*solve*)
  sx[t_]:= Evaluate[x[[i]] /. xusol]; (* create solution ??? *)
  AppendTo[xlist,sx]; (* store *)]

sxf = Function[t, Sum[sx,{i, 1, Ns}]]; (* sum all solutions ??? *)

Plot[sxf[t], {t, 0, tmax}] (* plot x[t] *)


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