function LinearDifference

%Plots solutions to the linear difference equation
%x_n=A_1*lambda_1^n+A_2*lambda_2^n as a function of n


t=5;           %total number of time steps
n=[0:1:t];      %sets n=0,1,2,...,t

A_1=1;          %Value for Coefficient A_1
A_2=1;          %Value for Coefficient A_2

%Real Eigenvalues
lambda_1=3;     %Value for the first eigenvalue
lambda_2=2;   %Value for the second eigenvalue

%Complex Eigenvalues
a=1;
b=2;
r=sqrt(a^2+b^2);
phi=atan(b/a);


%Linear Difference Equation
x_n=A_1*lambda_1.^n+A_2*lambda_2.^n;		%Real Eigenvalues
%x_n=r.^n.*(A_1.*cos(n.*phi)+A_2.*sin(n.*phi));		%Complex Eigenvalues

%Plots solutions
plot(n,x_n)
xlabel('n')
ylabel('x_n')
title('Plot of x_n as a function of n')