Characteristic equation: $r^{ 4} − 8r^{ 2} + 16 = 0$
Factor to find roots.$r^{ 4} − 8r^{ 2} + 16 = 0$
$(r ^{2} − 4)(r^{ 2} − 4) = 0$
$ (r + 2)(r − 2)(r + 2)(r − 2) = 0$
Our roots are r1 = 2 with multiplicity 2 and r2 = −2 with multiplicity 2.
solution
$a_{n}=(A+Bn)(2)^{n}+(C+Dn)(-2)^{n}$