The Law of Mass Action in chemistry results in the differential equation fracd xd t=k(a-x)(b-x), quad k>0, quad a>0, quad b>0 where x is the amount of a substance at time t resulting from the reaction of two others. Assume that x=0 when t=0. (a) Solve this differential equation in the case b>a. (b) Show that x rightarrow a as t rightarrow infty (if b>a). (c) Suppose that a=2 and b=4, and that 1 gram of the substance is formed in 20 minutes. How much will be present in 1 hour? (d) Solve the differential equation if a=b.
