I am stuck on this question

A suitable form of the general solution to y''-2y'+y=e^t+t

My work so far is

(r-1)^2=0 so r=1 so C_1*e^t+C_2*t*e^t=y(t)

Y_1=At^2e^t

Y_1'=2Ate^t+At^2e^t

Y_1''=2Ae^t+2Ate^2+2At^2e^t

plugging in and simplifying i get At^2+2A=1, however i dont know where to go from here

also for t i did

Y_2=Bt+C

Y_2'=B

Y_2''=0

so plugging in i get -2B+Bt+C=t but i dont know where to go from here, please help.