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.