Malthus and Solow - a note on closed-form solutions

Recently, Jones (2002 and Barro and Sala-í-Martin (2004) pointed out that the neoclassical growth model with a Cobb-Douglas technology has a closed-form solution. This note makes a similar remark for the Malthusian model: I develop and characterize a closed-form solution. Moreover, I emphasize structural similarities between the Malthusian and the neoclassical model if the dynamic behavior is governed by a Bernoulli differential equation.