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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.