# 33b_q3_sol.pdf - MATH33B QUIZ 3 SOLUTIONS Problem 1. A tank...

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MATH33B QUIZ 3 SOLUTIONSProblem 1.A tank connected to two pipes (A and B) initially contains100gal of a salt-watersolution containing1lb of salt per gallon of water.At timet= 0, pure water enters the tank through pipe A at the rate3gal/min, and a salt-watersolution enters the tank through pipe B at the rate of5gal/min. Simultaneously, a drain is openedat the bottom of the tank, allowing the well-mixed solution to leave the tank at a rate of4gal/min.Suppose that the solution coming to the tank through pipe B contains2lb/gal of salt.Lety(t)be the amount of salt in the tank at timet. Determine the values ofa, b, csuch that thefollowing differential equation describes the balance law fory(t):y0=a-byc+t.

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Boundary value problem