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Each problems is worth 10 points. 1. At time t = 0 a tank contains 501b of salt in 100 gal of water. Assume that water containing
i—lb of salt/gal enters at the rate of 2 gal/min and that a well stirred mixture leaves the tank at
the same rate. Set up the initial value problem that describes the process (you are not asked to
solve). What is the amount of salt after a long period of time? a ‘ ‘ i ‘
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_ i ‘ ' hr " M ‘ l t a) 1/ I 3. (10 points) solve the following initial value problem by the method of integrating factors: dy 2
— — =4t 1 =2. 4. (10 points) Separate Variables to ﬁnd the family of solutions to Elﬁ— 3‘2
dx_l—y2' ﬂ l 'j
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(1259’ 3: L1 5. (10 points)Verify that the following differential equation is exact and ﬁnd all solutions (ycos(z) + 2zey) + (sin(z) + x2ey — 3 + ma; 2 0
[Wm / I e ,r‘/(;"
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‘ / IL 9} Ii L u, [m 2+. u ismfo ﬁg“ 6. (10 points) Determine an interval in which a solution to cos(t)y' + sin(t)y = t3,y(0) = 7 400] is certain to exist. [Note that theorem requires you to put it in the form y’ + p[t)y ...
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This document was uploaded on 10/28/2011 for the course MATH 383 at UNC.
 Fall '08
 DAMON

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