First question: It does not matter as long as your initial conditions are the same i.e. y(2) and y'(2) are fine.
Second question: I have never seen that method used. Your alpha and beta parts I believe are exponents in a binomial in either your particular or complimentary portion of the answer. Method of undetermined coefficients is one of my preferred methods of solution for a second order nonhomogeneous equation though variation of parameters can work as well.
