# Find the solution to the following lhcc recurrence, confused!

1. Mar 25, 2006

### mr_coffee

ello ello!
I ran into this problem and i went in circles trying to figure it out. Anyone have any suggestions?
Here is what i have:
Find the solution to the following lhcc recurrence:

with initial conditions

The solution is of the form:
or suitable constants with
Find these constants.
$$r_1 = r_2 = \alpha_1 = \alpha_2 =$$

Okay so I plugged the 2 inital conditions in for the solution form and got:
1 = $$\alpha_1$$ + $$\alpha_2$$
4 = $$\alpha_1$$*r1 + $$\alpha_2$$*r2

I can't solve t hat, too many unkowns and not enough equations. I also tried to find a2,a3,a4, then putting it all in terms of a0 and a1, then i was like urnt, what now? THanks!

2. Mar 25, 2006

### Tide

You should have found specific values for the r's (4 and 3) before applying the initial conditions and you have a simple system of two equations and two unknowns (the alphas).

3. Mar 26, 2006

### mr_coffee

Thanks for the responce Tide but i'm still alittle lost.
I usually found the R's when they gave me an equation like r^2+4r+2 = 0, then just solve for r to find r1 and r2. How did u figure out r1 = 4 and r2 = 3?

4. Mar 27, 2006

### HallsofIvy

Staff Emeritus
Did you notice that while you used the initial conditions, you didn't use the recurrance itself anywhere? What happens if you plug
an= rn into the recurrance equation?