How to solve non-homogenous recurrence when non-homogenous part is a Constant?

Question

$u(n)−3 u(n−1)+3 u(n−2)−u(n−3) = 17$

$U_n^{(c)} = (A +Bn+ Cn^2)*1^n$

$U_n^{(p)} = 17*1^n$

Is how far Ive gotten. I am unsure of what to do from here.

Answer 1

Hint

The characteristic equation for the homogenous part is $$r^3-3r^2+3r-1=0$$ that is to say $(r-1)^3=0$. So, the solution of the homogenous equation is $$u_n=c_1+c_2 n+c_3 n^2$$ and then, the particular solution should be a polynomial of degree $3$.

I am sure that you can take it from here.