math 383 mid 1

math 383 mid 1 - d”: In {- ‘1 \1 “ x 83 Mid 1. Name:...

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Unformatted text preview: d”: In {- ‘1 \1 “ x 83 Mid 1. Name: 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 ‘ all it; x a” w - ' ' /_ — g3 ‘ "1» [D ’ fl ” 5 7 a ‘ ,I‘ j r, f—M‘K“ ~-\_ I ‘ AH} a ) F St) I 7 1 E: ' I ' z I I i é, 1 4 9L” _ 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 u o :1 4 ( V - "3 1 j, -4 j ’7 —z;%t4""‘-j )' _ ’ L/ cf (3 % q3,3 _ /, ~ ) a» a ‘3 I (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‘/(;" l 1 n 1 J x (I? , J+L1V r 12/ ,4 I! ltw 97%;"- ’ n y 11/, v LI‘ N ‘ Clné 1 (:(M, e , w’f‘ I . ) ’ ‘ a ,y , ,mri x “:5 ~- q 1)) ( ’ j ‘ / 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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math 383 mid 1 - d”: In {- ‘1 \1 “ x 83 Mid 1. Name:...

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