# Math Help - Describe the behavior after finding the gerneral solution

1. ## Describe the behavior after finding the gerneral solution

Consider the difference equation $U_{n+4} - A^{4} U_n = 0 where A>0.$ Find the gerneral solution of this equation. Describe the behavior of solution with respect to oscillation, boundedness, periodicity, and asymptotics where (1) A<1 (2) A=1 (3)A>1.

I have this problem for my homework and I dont understand what to do. PLEASE HELP!!

2. As formulated the solution of the difference equation is a sequence that is composed by four interleaved sequences each of them is writtten as...

$u_{i,n+1} = - \alpha\cdot u_{i,n} , \alpha = a^{4} , i=0,1,2,3$ (1)

... and whose solution is...

$u_{i,n}= u_{i,0}\cdot (-\alpha)^{n}$ (2)

Kind regards

$\chi$ $\sigma$