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Unformatted text preview: MATH 1005]? Test 2 October 2572mm 1 This test paper has 5 questions and total of 30 marks. It cannot be taken from the examination
room. Only nonprogrammable calculators are allowed. Duration: 50 Minutes. NAME : STUDENT NO : PART I: Multiple Choice Questions. No partial marks. Circle the correct answer. [3] 1. If y is the solution of the initial value problem y” — 3y’ + 23/ = 0, y(0) = 1, y’(0) = 4,
then what is 31(1)? .—2€+3e2 (b) 2e+3€2 (c) 26—362 (d) 36—262 (e) 3€+262
‘3: a\e*+C1€mx 1753': Cl éxFZ CZ 81x jiolclalscwct 3753;6L9Ttm (1,34.
31(oislfté1/5CH'1CL , ,2e*+ 36M 753(05’7'8 / [3] 2. If y is the solution of the initial value problem x231” — my’ + y = 0, a: > 07 y(1) = 2 y’(1) = 6, then what is 7
(a)6+6ln3ﬂ(c)12+121n3 (d)12—121n3 (e)6—61n3
COMO”?! Euler pt /&'5 Xm ’L
, ,mﬂzo ml’mm+):osa(mpl)=O
mlm 1) 2 75m;_Ls 5’ CH” CH @nx =93; c,+c7,(&m<+l) 1 A WATH 1005F Test 2 October 2672009 1 PART II: Long answer questions. Show all your work. [3] 3(a). Find the general solution of the differential equation 3;” — 63/ + 13y = 0. ._ __ 6¥V36— 0/3] 6+45
‘m’w'gm’b ”W'WTJQJT [3] 3(b). Find the general solution of the differential equation 3023/” — 9303/ + 253/ = 0, m > 0 :O [3] 3(c). Find the general solution of the differential equation xzy” — 3xy’ + 20y = 0, x > 0. m (millgmqwo : o 75ml—4’mf102‘O m, 31.1“ We .4?!“ .,._ 25:4; (D ” ’— / “" 2 Z
Cir'1) P732! ,/\ LMATH 1005F Test 2 October 26’, 2009 j 3 [9] 4. (a) Find two linearly independent solutions of the differential equation y” — 6y’ + 9y = 0.
39: (b) Find a particular solution of the diﬁerential equation y” — 6y’ + 93/ = 2—4.
63:): :04. (c) What is the general solution of the differential equation y” — 63/ + 9y 2 DAAITiIOOSF IbstZ (nmober2é,20091 4 90’ = 2:2: + 33/
xx [6] 5. Solve the systems of linear equations @=—$+® X": ”Ls—klj 75 ﬁzzyHZJ/
: ZX’HK‘XMJ) ...
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 Spring '11
 duke

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