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Unformatted text preview: Emmﬁl ‘* Fall 2010 o ' n n L) 32—0101 Y“ QM: x1672; swam—XL: Cay/[MD P + )L(~,—£Cao(ﬂ,nx)) + go; (ﬁnd 3: O “Sit/(011x) — woan + Co: (QM) 3" MW“) :0 ‘/ «wk? “.0: ‘4) M5: 1629+ xsmét )—cmx _
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Mt): %(5oo+{:) + 75:6???" Make sure you show all of your work neatly on notebook paper and circle your answers. Solutions without correct
supporting work will not earn credit. The problems must be in numerical order even ifthat means you need to use a separate sheet of paper for each problem. Each problem is worth 10 points. 1. 10. Verify that y : sin(ln x) is a particular solution of the differential equation x231” + xy' + y = 0. Give an
interval of definition for the solution. d 5
x—y—4y = x'ex Write an explicit solution: dx Write an explicit solution: (1 l x)dy ~— 31 dx = 0 Write an implicit solution: (323’ — ycos xyjdx + (2966”  x cos xy + By) dy = 0 Write an explicit solution: x:—: + y 2 xzy2 Write an explicit solution: % = 40:2 + 1) where x(nr/4) = 1
. . . . . tip 2 Write an impllCit solution: E = P H P The population of bacteria in a culture grows at a rate proportional to the number of bacteria present at time t.
After 3 hours it is observed that there are 400 bacteria present. After 10 hours there are 2000 bacteria present. What was the initial number of bacteria? A thermometer is removed from a room where the air temperature is 72°F and is taken outside, where the
temperature is 10°F. After 1 minute the thermometer reads 50°F. What is the reading of the thermometer after 2 minutes? How long will it take for the thermometer to reach 15°F. Consider the mixing of two salt solutions in a large tank. Suppose the tank holds 1,000 liters of brine with 10
liters entering per minute. The concentration of the salt in the inflow is 0.6 kg/liter. The solution is weli stirred
and is pumped out at 8 liters/minute. initially there are 50 kg of salt in the tank. a. Determine the amount of salt in the tank at time t.
b. When will the tank contain 2,000 liters of brine? ...
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 Fall '10
 PamelaSatterfield

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