Let $B$ be a standard Brownian motion. I am wondering what is the differential of the $B^2$ ?
If I apply Ito's formula I would say that the differential is equal to $2B_{s}dB{s} + 2dt$.
However, the solution says that it is equal to $2B_{s}dB{s} + dt$.
Now, if the solution is right, I am wondering how do you come to such a solution?
The solution is correct, you probably forgot the 1/2 term in ito's lemma for second derivative of brownian motion.