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

y^" - 6y^' + 9y =5t⁶e^3t

So I got

y_p = (At^6 + Bt^5 + Ct^4 +Dt^3 + Et^2 + Ft + G) e^3t

^{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 A_m-1 ....... A₀ different from A + B + C in the form I had inmy answer?