A first order DE models the rate of change, e.g. when decay is proportional to time we have the DE: dM/dt = -K.M; this is describing that rate of change mathematically. Am I correct in saying that a 2nd order DE describes the rate of rate of change? Also, can anyone explain any application of 2nd order DEs to me? I understand it mathematically, but I am interested in how it works in practice like that decay example I pointed out above, hence this post.