Find the solution to the following lhcc recurrence, confused

[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
with initial conditions http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/77/41b1266f6e87bb1b57dd6883644c521.png

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

 

[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).

 

[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?

 

[HallsofIvy]

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