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Midterm1Soln

Midterm1Soln - Name.5¢/6¢Z[ZW.S ID number MATH 2271...

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Unformatted text preview: Name:....5¢./6¢Z[ZW.S' . . . . . . . . . . . . . . .. ID number: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . January 25, 2010 MATH 2271 Differential Equations for Scientists and Engineers Winter 2010 First Midterm Exam All questions have equal weight; calculators are not allowed. Time: 50 minutes 1. Consider the equation 2233/2 — 3 + (23323; + 4)y’ = 0. (a) Show that the given equation is exact. WWI-luv} Mix/‘3) : 21d 2“ 3 Nail ; 215* Li, . We have 2% _ ‘ O N (23) 93 ' W -‘ WW WMCI‘ KNOW-5 lilac Malia”! is (ax-425:;ch (b) Find the solution that satisﬁes the initial conditiOn y(1) = 1. If possible, express y as a function of a: explicitly. We Seek 405,3) SucL :z We a FEW/33 : -” ECZDUJZ~3>A¢ g lhca _ 1” / F v 75g : Z/QgﬁngCQp'N 4} D 01 2. Find the general solution to the ODE 553/ + 23}: 3. Are there any values of :5 for Which the solution is not deﬁned? ﬂ! zﬁmffdu 2‘? //74M/ Sé/ﬁfﬂbb'ioo); peg/aft}? 79%;; = .42) 716 ‘Modatepg hMD‘gJJ/LM‘L6 eﬂuﬁl‘g‘v' "9 ’ '2 @’ I 3*7’3‘0) 37 : 2% omelet-w mam,” wam‘hdhﬁ) :5) ﬂ : CIT/~94 /@ go lw‘ng Wink“! {£11 yane‘;'£K/ I ‘ M — 2/ + 2%" : 4'3” _ _,_, f > I; fix?) 'd3 I L / _ :5; / _—_ Y ’4 ~ _ﬂL. I: ,_<7 iié 9 3'23? 1 :> 2'2: Jaw/“(7! : MW Ca <> ’ 345 I: Clio I ._a j” LIX/,avawr """"""""" '- 3, ﬁ 9,.— 313 2 . in CM ttw Mk I: MAJ Lulu» 2W. L10] 3. Solve the initial value problem (CE; \” dw 2 Et—=w—_w,' w(0)=1/2. 715 saw/(5p / )(7 i j . Z'ZZ 4,. _ J” _ J“ J” / "1" >011 Z046) I file-4P2 r 1” 24 _ Ff), XX 7 '_L x i \ _> 32/751 EVA-t ’ 3 (’1’ zit/A? :' “L (a :\ QC I / (“3327’ 3" “WCz' (I v 1‘ E ' Cl C I ” Ciewzﬂ' a . 1(1'5161' “CH; : : ;g:i [’6th Ct I I > ‘ ~ . 6J6rC (C\ x [0 r ‘4 _ I r -( ‘ > 1+.C ~ 7; ’7, Cf ’ /MNM_WW:F wwwww ﬂ TLWQ ) 3 L,” : 1‘ ] _6+ 4, L [flit 4 4. Consider the equation for an object falling near the earth’s surface in the absence of air resistance, 52': = —1Um/s2, (1)7 Where 13(25) denotes the altitude in metres at time t seconds. [5:] (a) Classify the equation (according to type, order, linear or nonlinear etc), and ﬁnd its general solution. @ ' NI/Lig {g l a 2nd (trier) hmowwugl (b) Let V denote the set of all vectors in R3 with the property that (BUS) = (Cl - 5)t2 + Cgt + C3 is a solution to equation Is V a vector space? If not, explain why, and if so, determine its dimension by ﬁnding a basis. B3 WM (4)) (81*?)"62-1—762" i“ +7 (3 is A Solid.)an 71a eéuaf/{ﬂm (M and {Wt/77 CL = 0. IT’« vs V meets all wed-M bi “(Le-- a _ to, Ca]! J V {g 4 “AN game} (ﬁr/it! ‘6‘ Jaime Mao” MA'YWV fwd ﬂak ’7 (Wm/75f [fact/1074 - / 0 \ if it > J K bi z a, 4 1/4 ‘3 \/ ®/ ‘ 42, baj at 4- ' I I O [A . 0! at ; ' (ML 43’ Kddb > . V of ‘ I i] i LWxg ‘ End of exam I ...
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Midterm1Soln - Name.5¢/6¢Z[ZW.S ID number MATH 2271...

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