Error correction model

[Kaimajerus]

yt=αyt−1+β0xt+β1xt−1+ϵt, 0<α<1,(t=1,...,T) where xt is an I(1) process independent from ϵt for all s and t, and ϵt,t=1,...,T are i.i.d with mean zero and variance σ^2
Question

1) Suppose that β0≠−β1. Is it possible that yt is stationary?

2) Write down the error correction form of the model, showing the relationship between the new parameters and those in the original model. Argue that yt and xt are co-integrated and write down the co-integrating vector

Any help/pointers would be great.