I'm trying to do the part of this qusetion where we need to find two linearly independent solutions to (2) of the given form. Is there a nicer way to do it other than just plugging it into (2). I was thinking of trying to pick B=0 for one solution, and A=0 for another, and see if it satisfies it (since then they would be linearly independent), but that doesn't seem to work because I need two constants to match the left hand side of (2) to the right hand side of (2). Is there a nice way to do it that I am missing. Thanks!
