Let the Ito process $Y(t)$ and $X(t)$ have stochastic differentials
$dY(t)=\alpha Y(t)dt+\sigma dB(t)$
$dX(t)=B(t)dt+dB(t)$
with $Y(0)=1$. Determine the product of the two processes by using stochastic product rule.
I know that the product rule is $d(X(t)Y(t))=X(t)dY(t)+Y(t)dX(t)+d[X,Y](t)$, how to apply in this question?