I was wondering if you would point me to a book where the theory of second order homogeneous linear difference equation with variable coefficients is discussed. I am having difficulties in getting rigorous methods to solve some equations, see an example below.
In particular, given the recurrence relation
$X_{n+2} = \frac{3n-2}{n-1}X_{n+1} - \frac{2n}{n-1}X_n$,
two solutions are
$X(n)= n$ and $X(n) = 2^n$.
Is there an "elementary" way of arriving at these solutions? (i.e. without using transforms, etc.)
Thanks in advance.