1. ## Nonhomogenous dynamical systems

Find the general solution to the following:

$A(n+1)=2A(n)+3^n-n$

and find the particular solution when A(0)=1.

I have like ten problems this way.

After all my calulations i got $A(k)=c2^k-3^k+k$
is this right? I'm lost on how to find the particular solution. Can anyone help?

2. Well, to check your answer, simply try to plug in the result you got in the given difference equation. I think your solution is not 100% correct. The general form of the solution should be $a2^k+b3^k+ck$. Plug in the given equation and compare to find a,b and c. To find the particular solution, you have to put k = 0 in the general solution. We have to get 1. So, you find the missing parameter. For example, assuming your answer is correct, and we know A(0)=1, then: $c2^0-3^0-0=1$. Therefore, $c=2$.
hope this helps