ZillErrata2ndPrinting[1]

# ZillErrata2ndPrinting[1] - 4591X_errataSecondPrint.qxd 9:09...

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Second Printing Errata for Advanced Engineering Mathematics, by Dennis G. Zill and Michael R. Cullen (Yellow highlighting indicates corrected material) Page 47 The second equation in (5) is the result of using partial fractions on the left side of the first equation. Integrating and using the laws of logarithms gives 1 4 ln | y 2 | 1 4 ln | y 2 | x c 1 or ln 2 y 2 y 2 2 4 x c 2 or y 2 y 2 e 4 x c 2 . Page 56 Solution The equation is in standard form, and P ( x ) = 1 and f ( x ) = x are continuous on (– , ). The integrating factor is e dx = e x , and so integrating d dx 3 e x y 4 xe x q q Page 65 19. (4 t 3 y – 15 t 2 y ) dt + ( t 4 + 3 y 2 t ) dy = 0 Page 78 Example 5 Mixture of Two Salt Solutions Recall that the large tank considered in Section 1.3 held 300 gallons of a brine solution. Salt was entering and leaving the tank; a brine solution was being pumped into the tank at the rate of 3 gal/min, mixed with the solution there, and then the mixture was pumped out at the rate of 3 gal/min. The concentration of the salt in the inflow, or solution entering, was 2 lb/gal, and so salt was entering the tank at the rate R in (2 lb/gal) (3 gal/min) 6 lb/min and leaving the tank at the rate R out ( x /300 lb/gal) (3 gal/min) x /100 lb/min. From this data and (6) we get equation (8) of Section 1.3. Let us pose the question: If there were 50 lb of salt dissolved initially in the 300 gallons, how much salt is in the tank after a long time? Page 91 13. Leaking Conical Tank A tank in the form of a right-cir- cular cone standing on end, vertex down, is leaking water through a circular hole in its bottom. (a) Suppose the tank is 20 feet high and has radius 8 feet and the circular hole has radius 2 inches. In Problem 14 in Exercises 1.3 you were asked to show that the differential equation governing the height h of water leaking from a tank is In this model, friction and contraction of the water at the hole were taken into account with c = 0.6, and g was taken to be 32 ft/s 2 . See Figure 1.30. If the tank is initially full, how long will it take the tank to empty?

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