there are two questions in the attachment with the correct answers.
i have worked through the questions, to my knowledge, however seem to be only a few steps short of reaching the actual solution on each of the questions.
please help
there are two questions in the attachment with the correct answers.
i have worked through the questions, to my knowledge, however seem to be only a few steps short of reaching the actual solution on each of the questions.
please help
1) You have $\displaystyle y_t = A \left(\frac{1}{2}\right)^t + B 2^t + 1$. Requiring that yt stays finite as $\displaystyle t \to \infty$ gives B = 0. Then use your IC.
2) Seek a particluar solution $\displaystyle y_{pr} = k r$, the l isn't need, it's in the complimentary solution. Subs into the difference equation
$\displaystyle k(r+2) - 4k(r+1) + 3kr = 4 $ and expand. This gives $\displaystyle k = -2$ and hence your solution.
For question 1a you have the complementary function and a particular solution. The general solution is the sum of these.
The condition that $\displaystyle y_t$ is always finite means that $\displaystyle B$ must be zero, and that $\displaystyle y_0=2$ then means that $\displaystyle A=1$.
For 1b you have an $\displaystyle r$ on the right hand side that should not be there.
CB