The question is attached. How do I go about doing this? If someone does just one of them that should be enough for me to get it.

Judging via y''' - 5y'' + 6y'= 0 - Wolfram|Alpha, the answer for #1 is C since the general solution has those 3 particular solutions but how do I do it without cheating?

Any help would be greatly appreciated!

Thanks in advance!