A system is described by the difference equation

Let the input be x$[$n$]=$ u$[$n$]$ and the initial conditions y$[-1]=4,$y$[-2]=8.$

Express the transient response as yt$[$n$]=$ c$1($d$1)$n $+$c$2($d$2)$n$.$ Let d$1$ have the largest real

part, and if the real parts of d$1$ and d$2$ are equal, the largest imaginary part.

Give the value of the real part of c$1.$