Hello, welcome here.
Sorry for being a bit acidic today, but I don't think this is a nice way to post problems. Essentially, you a "dumping" your problem here (which seems to be from a take-home exam or a graded problem set) and then, without any further comment or attempt at a solution, expect others to solve it for you.
Yesterday I saw in passing that another new user posted a problem. It it https://mathhelpboards.com/differential-equations-17/mixing-common-drain-page-537-46-fundamentals-differential-equations-bvp-nagle-24231.html. Can you see the difference? (I am not talking about the mathematical content.) He then received help, continued to think along, and got his result verified. I think that's very nice.
So, for your case, starting with (a), what did you try and what difficulties are you facing?
Best wishes,
Sebastiaan.
