Second moment of a GBM at time two

A geometric Brownian motion $S$ starts at $S_0=1$ and has drift $\mu=1$ and volatility $\sigma=1$, i.e. $dS_t=S_t(dt+dW_t)$. Writing $\mathbb{E}[S_2^2]=e^k$, determine $k$.

$k=6$. By Ito, $d(S_t^2)=S_t^2(3\,dt+2\,dW_t)$, so $S^2$ is itself a GBM with drift $3$. Hence $\mathbb{E}[S_t^2]=e^{3t}$ and at $t=2$ this is $e^6$. (Equivalently $\mathbb{E}[S_t^2]=e^{(2\mu+\sigma^2)t}$.)