the P.I. should be c1.e^-t+c2.e^3t

and the A.E.=3.e^2t(t-6)

are they correct???

we get the P.I. by solving the quadratic in y' ie. D^2-2D-3=0

which gives D=-1,3

and the A.E. is calculated by separating the exponential part then........(it should be given in any text book).hope this was helpful!