I am faced with the following question and would appreciate any help you may be able to offer: It is not homework, I know the first and second shift theorems and based on the other examples I have done, I know you start by taking the z-transform of the equation, then factor out X(z) and move the rest of the equation across the equals sign, then you take the inverse z-transform which usually involves partial fractions and it should yield the answer given. Cheers
Use z-transforms to solve:
$2x[k+1]-x[k]=2^k \,,\quad x[0]=2$
The answer is:
((2^k)/3)+5(((0.5)^k)/3)