The discussion focuses on solving the non-constant coefficient difference equation $(x+1)y_{x+1}-(r+x)y_{x}+ry_{x-1}=0$, where r is a constant. The standard method involves rewriting the equation as $y_{x+1}= [(r+x)y_x- ry_{x-1}]/(x+1)$ and solving in blocks. An initial value for y is required, such as y(x) = x for the interval 0 ≤ x ≤ 2. For the interval 2 ≤ x ≤ 3, the solution is expressed as $y(x)= (r+x-1)(x-1)- r(x-2)/(x)$.
PREREQUISITESMathematicians, students studying difference equations, and researchers working on numerical methods for solving differential equations.