Determine the form of a particular solution for the differentialequation. (Do not evaluate coefficients.)

y" - 6y' + 9y =5t6e3t

So I got

yp = (At^6 + Bt^5 + Ct^4 +Dt^3 + Et^2 + Ft + G) e3t

But the answer given is(A6t^8 + A5t^7 + A4t^6 +A3t^5 + A2t^4 +A1t^3 + A0t^2)e3t

Where did they get that extra ^2and is Am-1 ....... A0 different from A + B + C in the form I had inmy answer?