I am VERY confused with this question. Firstly, whenever the coefficients are variables, I have no idea what to do. I'm thinking divide both sides by x^2 based on something I think I remember but I am really not sure and if that is what I am supposed to do, I'm guessing it would be to make the equation be in some form so I can do something to it but I really need someone to give me the specifics or at least give me the exact names of the methods to use with differential equations such as these which have variable coefficients.

Secondly, what does the subscript c in the final solution stand for and what does what it stands for mean? As for what a fundamental set of solutions is, all I know is that two solutions are said to form a fundamental set of solutions if and only if their Wronskian is nonzero.

I would so greatly appreciate it if someone could outline all the steps (any tedious calculations that have no significant theoretical aspect can be omitted) for me because I am having a lot of trouble.

Thanks in advance!