hi!
ive got three difference equations but could do with some help becuase i didnt think that they would be too long but they are my homework for this week and am slightly confused why i would get such a short homework!
a) Xn+2 - 5Xn+1 + 6Xn =0
b) Xn+2 - 5Xn+1 + 6Xn = 4
c) Xn+2 - 6Xn+1 + 9Xn =0
here the c1 = 2 and c2 = 3 so ive been taught that for a particular solution, since c1 doesnt equal c2 then
so then to try Zn = Cn
so from Xn+2 - 5Xn+1 + 6Xn = 4
it will become C(n+2) - 5(c(n+1)) + 6(Cn) = 4
and from setting n=-1 i get c-6c=4 so c doesnt equal 2 :S
where have i gone wrong?
Yes that is the full solution because it is a homogenous difference equation. Thus, there is no particular solution.
I have no idea what you did.here the c1 = 2 and c2 = 3 so ive been taught that for a particular solution, since c1 doesnt equal c2 then
so then to try Zn = Cn
so from Xn+2 - 5Xn+1 + 6Xn = 4
it will become C(n+2) - 5(c(n+1)) + 6(Cn) = 4
and from setting n=-1 i get c-6c=4 so c doesnt equal 2 :S
where have i gone wrong?
Why C_1=2 and C_2=3?
The charachteristic equation,
i mean that say r=2 and t=3 (the solutions to the characheristic equation) and since r doesnt equal t, then ive been taught to try Zn = Cn for the particular solution. then i put cn into the original equation
so from Xn+2 - 5Xn+1 + 6Xn = 4
it will become C(n+2) - 5(c(n+1)) + 6(Cn) = 4
and from setting n=0 then 2c-5c=4 so c=-3/4 and Zn (the particular solution) is 3/4n
so the general solution is