Let P(t) denote the price in dollars of a certain commodity at time t in days. Suppose that the rate of change of P is proportional to the difference D - S of the demand D and supply S at any time t. Suppose further that the demand and supply are related to the price by D = 10 - .3P and S = -2 + 3P.

(a) Find a differential equation that is satisfied by P, given that the price was falling at the rate of one dollar a day when D = 10 and S = 20. 

(b) Find P, given that P(0) = 1.