the equation $a_n = 4a_{n-1}-4a_{n-2}+2^n$ have the homogeneous part of $a_n=A_1 n2^n + A_2 2^n$
but i dont know how to solve the particular part.
my method is
As $\beta(n)=2^n$
by the guessing method,
guessing the particular solution of the relation is $a_n=A2^n$
so, $A2^n-4A2^{n-1}+4A2^{n-2}=2^n$
and clearly, the the equation wouldn't hold.
how can I solve this problem?