I think I got the solution. I pick the second matrix given by dsolve, and then find the min/max values for the second column (corresponding to the dependent variable of interest):

for i to numelems(ArrIe) do
valIe := ArrIe[i];
numsols := (dsolve([op(subs(Ie = valIe, {de1, de2})), ics], numeric, output = Arrt))(2);

maxV[i] := max(numsols(() .. (), 2));
minV[i] := min(numsols(() .. (), 2));
end do

This is the worksheet: MaplePrimes_dsolve_min-max.mw

HTH,

jon