- #1
cshum00
- 215
- 0
Hello. I am stuck with linear difference equations and i would like some help.
I was given that y(k) = y(k)homogeneous + y(k)particular and i am asked to solve the linear equation:
y(k+1) + y(k) = k
with initial condition y(0) = 0
the homogeneous solution is
y(k+1) + y(k) = 0
n + 1 = 0
n = 1
y(k)homogeneous = C(-1)^k
y(0) = 0 = C(-1)^0
C = 0
y(k)homogeneous = 0
then the particular solution
y(k)particular = Bv0*(K) + Bv1
then they tell to substitute this particular equation to the original y(k+1) + y(k) = k
and after i do so, i should get
Bv0=1/2 and B1=-1/4
However, no matter how i substitute i can't get the answer.
Maybe i am substituting the wrong thing. Can anyone show me the substitution process which leads to the mentioned result of Bv0 and Bv1?
Thanks.
I was given that y(k) = y(k)homogeneous + y(k)particular and i am asked to solve the linear equation:
y(k+1) + y(k) = k
with initial condition y(0) = 0
the homogeneous solution is
y(k+1) + y(k) = 0
n + 1 = 0
n = 1
y(k)homogeneous = C(-1)^k
y(0) = 0 = C(-1)^0
C = 0
y(k)homogeneous = 0
then the particular solution
y(k)particular = Bv0*(K) + Bv1
then they tell to substitute this particular equation to the original y(k+1) + y(k) = k
and after i do so, i should get
Bv0=1/2 and B1=-1/4
However, no matter how i substitute i can't get the answer.
Maybe i am substituting the wrong thing. Can anyone show me the substitution process which leads to the mentioned result of Bv0 and Bv1?
Thanks.