How to solve the difference equation?

x_n+2 + 3x_n+1 - 4x_n=5 with x₀=x₁= 1

I know the general homogenous solution is x_n = 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 p_n= c*n and figure out c = 1 3c(n+2)+3(n+1)-4(n) = 5

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