A market research firm has watched the rise and fall of many technology companies and has predicted that the variation of the proportion of future market share of three firms A, B, and C is determined by the following assumptions: Assumption 1: The variation of the proportion of participation that remains in company A is given by the assumption that 60% of the total participation remains in the company A plus 15% of the stake remains in company B plus 25% of the stake stays with company C. Assumption 2: The variation of the proportion of participation that remains in company B is given by the assumption that 6% of the total share remains in company A plus 90% of the interest remains in company B plus 4% of the interest stays with company C. Assumption 3: The variation of the proportion of participation that remains in company C is given by the assumption that 18% of the total share remains in the company A plus 15% of the stake remains in company B plus 67% of the stake stays with company C.  Also, suppose that the initial market share of the three companies is 40%, 12%, and 48% respectively. Set up a system of linear differential equations and solve it to find the share of forecast market that will remain in each of the companies after the 55 months and graphically represent the change in proportions of each company during a 180 month period.