Is the small z in z Z''(z) correct?Hi, I am doing a problem and need help... I am really confused :/

Well, the problem says

"Show that the boundary conditions for =0 are and (we know that )."

comes from . This problem is about the dynamic behaviour of a hanging cable, so is the length of the cable and when it means that is at the highest point where the cable is hanging from, and is the end point, so . However, that's something that the problem tells us, so I cannot just say it is like that, I need to prove it.

So well, my first thought was to solve the differential equation, but I got to this point

I know that cannot be zero, so would not be a solution, but that does not prove why . So I guess I shouldn't be solving the differential equation.

Thanks a lot in advance for any help you can give me!