Co-integration and Error correction This is a homework question: 

$y_t = \alpha y_{t-1} + \beta_0 x_t + \beta_1 x_{t-1} + \epsilon_t , 0&lt;\alpha&lt;1, (t=1,...,T)$
where $x_t$ is an I(1) process independent from $\epsilon_t$ for all $s$ and $t$, and $\epsilon_t , t=1,...,T $ are i.i.d with mean zero and variance $\sigma^2$

Question

1) Suppose that $\beta_0 \not= -\beta_1$. Is it possible that $y_t$ 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 $y_t$ and $x_t$ are co-integrated and write down the co-integrating vector

Any help/pointers would be great.
For question 1), take the expectation of both sides, assume that the expectation of Y is the same in both periods (the definition of stationarity) and see what conditions the coefficients on X must satisfy.

For question 2), try rearranging the equation to be in terms of X and see what determines its variation.

P.S. I am still getting the hang of the mathematical notation on here, but I figure too much working out would be giving it away anyway