Its funny we have a somwhat similar question. Only the system I am trying to solve is much larger, and IVP of about 10000 ODEs. In your case, since it seems you have less than 100 ODEs range option in dsolve will work. 

SolNumericRange:=dsolve(ODEs,numeric,range=t=0..1.5)#Here by ODEs  I dentoe the sequence of your ODEs and Initial Conditions. 

This way you will have all of the solutions stored, so Maple wont need to recalculate them each time.