I'm learning about stochastic processes, and I want to prove the relationship.

$$ mathop {dX_ {t}} = alpha X_ {t} mathop {dt} + beta mathop {dW_ {t}} $$

holds, where $ X_ {0} = x $.

I think the solution uses Ito's motto; However, I'm not quite sure how to get the answer. I also recognize that this is the Ornstein-Uhlenbeck process, and I believe that the solution will be a diffusion process.

I would really appreciate some help.