Originally Posted by

**HallsofIvy** What you have is NOT a differential equation, it is a "finite difference" equation. Also "130e^{2x}" makes no sense because x is the function you are trying to solve for an the independent variable is n. Your solution has to be a formula for x_n as a funcition of n. You are correct that "linear finite difference equations with constant coefficients" are very similar to "linear differential equations with constant coefficients". The crucial difference is that while, if y= e^{ax} then y'= ae^{ax}= ay, with we use the fact that if x_n= a^{n}, x_{n+1}= a^{n+1}= a(a^n}= ax_n. So look for a solution of the form "Ca^n" rather than "Ce^{an}".