$X_t$ is a solution of SDL
$$dX_t=b(X_t)dt+X_tdB_t.$$
What is the the drift coefficient $b(x)$ of this equation, if the square of its solution
$$M_t=X^2_t, t\geq0,$$
is a martingale?
So far, I managed to apply Ito formula to function $f(x)=x^2$ and got that
$$dX^2_t=2b(X_t)X_tdt+X^2_tdt+2X_t^2dB_t.$$
The answer for the exercise is $b(x)=-\frac{x}{2}$. In other words, as I understand it, we want to remove the regular part of the equation above to get
$$dX^2_t=2X_t^2dB_t.$$
Why?