Solve the following recurrence equations using the characteristic equation.

$($a$)$

$t_n=4t_{n-1}-3t_{n-2}$ for $n>1$

$t_0=0$

$t_1=1$

$($b$)$

$t_1=1$

$t_n=3t_{n-1}-2t_{n-2}+n^2$ for $n>1$

$t_0=0$

$t_1=1$

$($c$)$

$t_n=5t_{n-1}-6t_{n-2}+5^n$ for $n>1$

$t_0=0$

$t_1=1$

$($d$)$

$t_n=5t_{n-1}-6t_{n-2}+n^2-5n+7^n$ for $n>1$

$t_0=0$

$t_1=1$

D please $($general soloution$)$