A stock whose price S follows geometric Brownian motion, dS/S = dt + dB, has options that never expire. (a) What differential equation do the option values satisfy? (b) What is the most general solution of the differential equation? (c) Consider the cases of American-style call and put options of strike K that are initially out of the money. Does the general solution hold in each case? Does it hold for all values of S and t?