$\displaystyle \mu\in\mathbb{R},\sigma>0$ and we consider the stochastic differential equation $\displaystyle dX_t=\mu X_tdt+\sigma X_tdB_t$ with $\displaystyle X_0=x>0$. How do I show that $\displaystyle X_t=xe^{\sigma B_t+(\mu-\sigma^2/2)t}$?
$\displaystyle \mu\in\mathbb{R},\sigma>0$ and we consider the stochastic differential equation $\displaystyle dX_t=\mu X_tdt+\sigma X_tdB_t$ with $\displaystyle X_0=x>0$. How do I show that $\displaystyle X_t=xe^{\sigma B_t+(\mu-\sigma^2/2)t}$?