SDE for X when its reciprocal is a GBM

A positive process $X$ has reciprocal $Y=1/X$ obeying $dY_t=Y_t(2\,dt-dB_t)$, with $B$ standard Brownian motion. Then $X$ obeys $dX_t=X_t(a\,dt+b\,dB_t)$ for integers $a,b$. What is $ab$?

$-1$. Apply Ito to $f(y)=1/y$: $dX=-Y^{-2}dY+Y^{-3}d[Y,Y]$ with $d[Y,Y]=Y^2dt$. This gives $dX=X(-2\,dt+dB)+X\,dt=X(-dt+dB)$, so $a=-1$, $b=1$.