Stochastic differential equation without diffusion

Question

I have the following SDE

$X_t=\int_0^t \sqrt{1+B_s^2}\cdot dB_s$ or

$dX_t=\sqrt{1+B_t^2}\cdot dB_t$

If I define the stochastic variable $Y_t=X_t^2$.

How can I determine the Ito equation that would satisfy $Y_t$?

Can I apply Ito's lemma?

Thanks