Hi, In the question, equations for h(t) and k(t) are provided. It's not readily clear what the relevance of these functions are. (And they feature in the solution to part (iii)). Thanks,
h(t) and k(t) are just introduced to enable you to solve the pair of simultaneous differential equations for p1(t) and p2(t) given in the question. They don't have any particular interpretation on their own - they are just useful functions for that purpose.
