We have
Now set so we now have...
Then solve for w and we get w=3 and w=-1.
Then put this into the general equation .
Then use your initial conditions to find the constants.
I have been working on this problem but I cant find anything similar in my book. Not sure how to setup this problem.
Solve the following recurrence relations together with the initial conditions given. for , . Thanks in advance for the help.
(1) Since then
since i doesnt matter whether we have n, n+2 or n+145334544 the relation is still the same...
In general,
(2) Just solve the polynomial for w.
(3) The general equation is with the w terms being what you found in (2) and the c terms are constants you can find if you have initial conditions.
(4) The initial conditions state that and , This means that when , hence if you sub this into the equation found in (3), you get that
Then sub the other initial condition in... ... Solve this and you'll get two equations containing and . You should be able to find the c's from there and then you have the general solution.
I also just noticed that i had in my first post instead of , maybe that confused you?
To test yourself look up gamblers ruin and try to solve it. Its similar to this.