Thread: Linear Difference Equation

Ok I have a linear difference equation, which is as follows:
f_t - f_(t+2) = 2sin(t*(pi/2))
I am not given any conditions. All I am asked to do is solve it.

f(t) = cos[(t-1)*pi/2] + k sin[pi*(t+w)] + c , c,k,w are constants

Originally Posted by simplependulum

f(t) = cos[(t-1)*pi/2] + k sin[pi*(t+w)] + c , c,k,w are constants

I'm sorry, but that has completely confused me. I have solved the A.E. and the C.F, which turns out to be A(1)^t + B(-1)^t, but afterwards I get lost. I don't understand how you got that answer and would appreciate some more detail on how you arrived at it. Cheers

Originally Posted by LooNiE

Ok I have a linear difference equation, which is as follows:
f_t - f_(t+2) = 2sin(t*(pi/2))
I am not given any conditions. All I am asked to do is solve it.

Is an integer?

I believe t is an integer yes.

First solve which is equivalent to [tex]f(t+2)= f(t). Try a solution of the form so that and the equation becomes so that and a= 1 or a= -1. The general solution to the "associated homogenous equation" is exactly as you have.

To find a specific solution to [tex]f(t)- f(t+2)= 2sin((\pi/2)t), try a solution of the form so that so the equation becomes f(t)- f(t+2)= 2A sin(\pi/2)t)= 2 sin((\pi/2)t) and is satisfied if A= 1.

The solution is .