1. ## Difference Equation

i have to solve Xn+1 -4Xn +3Xn-1= 36n^2
I did the first part, where i find Xn=A3^n+ B
But when i try to find the solution of the form Xn= Pn^2+ Qn+ R
it turned out weird and i cannot find the P Q R,can anyone help me?

If possible, can someone post a full answer for me? I really need an example for this kind of question.

2. ## Re: Difference Equation

Originally Posted by kanezila
I did the first part, where i find Xn=A3^n+ B
Right

But when i try to find the solution of the form Xn= Pn^2+ Qn+ R
it turned out weird and i cannot find the P Q R,can anyone help me?
The characteristic equation is $\lambda^2-4\lambda +3=0$ , that is $\lambda=1$ is a simple root . According to a well known theorem a particular solution is a polynomial $p(n)$ of degree $2+1=3$ .