Are you required to show your solutions? If not, then differentiate n times (where n = number of arbitrary constants) then substitute to the choices. If both sides are equal then that would be the correct answer.
Taking for example the first item:
y = ce^2t + 3t^2
Differentiate once since there is only one arbitrary constant:
y' = 2ce^2t + 6t
Substituting these to all of the choices, you'll see y'+ 2y = 6t(t + 1) is the right answer.