Kelly weights for two correlated stocks

Two stocks have expected excess returns of 6% and 4% a year, volatilities of 20% and 15%, and correlation 0.5. With continuous rebalancing, the expected log growth rate of a portfolio holding weights $w$ (fractions of wealth, leverage allowed) is $g(w) = r + w^\top \mu - \frac12 w^\top \Sigma w$. Find the growth-optimal weights, show they are a maximum, and compare them with the Kelly weight for each stock on its own.