I forget about it, I mean Ordinary differential Equation in C([a,b],Rn). C([a,b],Rn) is notation for mapping of continuous functions in [a,b] into Rn, I can write f element of C([a,b],Rn) then f=(f1,f2,f3,...,fn).
what do you mean about "the solution is mapping from R into a space of...