Question: How to solve the difference equation? x n+2 + 3x n+1 - 4x n =5 with x 0 =x 1 = 1 I know the

How to solve the difference equation?

xn+2 + 3xn+1 - 4xn=5 with x0=x1= 1

I know the general homogenous solution is xn = A(-4)n + B , because the euler's form (z2+3z-4=0) gives the root -4 and 1

However, after guessing the particular solution pn= c*n and figure out c = 1 3c(n+2)+3(n+1)-4(n) = 5

But then the general homogenous solution change to xn = A(-2)n + B + n and I don't know why this happens.

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