You can all ignore that I've called it C[ude]. In the real world I actually called them G_0 and K_ude.

That is not my problem. 

And it is not that I don't how to use dsolve.

But I need to solve it using commands such as:

for i from 2 to 20 do t[i] := evalf(subs(t = %, t = 396, (OD) end do; (But this doesn't work!)