Solve the recurrence relation.

$($a$)a_n=a_{n-1}+30a_{n-2},$ where $a_0=2$ and $a_1=-3$

$($b$)b_n=8b_{n-1}-16b_{n-2},$ where $b_0=5$ and $b_1=4$

$($c$)d_n=3d_{n-1}+5d_{n-2},$ where $d_0=1$ and $d_1=-2$