# Homework Help: 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:
http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/3c/1e4624e0fc726276872050e3ffe28d1.png [Broken]
with initial conditions http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/77/41b1266f6e87bb1b57dd6883644c521.png [Broken]

The solution is of the form: http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/b5/d7df51334509f4e8eb7c12482421651.png [Broken]
or suitable constants http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/ba/23a25f303b1dfba5efa3cc7dbfba401.png [Broken] with http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/8d/8623a3204922fa8125ce9b843a6b9b1.png [Broken]
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!

Last edited by a moderator: May 2, 2017
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

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?