Test 1with Solutions - MA 252-NH Test 1 (June 19 (Thu),...

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Unformatted text preview: MA 252-NH Test 1 (June 19 (Thu), 2008) This test has 8 pages with 4 problems. Show Ail Your Work! Name Y1 S ' Problem 1. (3.) Verify that m 3-5—26"15$ is the solution of the initial value problem 3% -§«» 15y m 45, 14(0) 2 5. U 3 Ft)? CLQ‘JK {fig )‘i/Il‘fi‘fifl Wdiflmn 360L151 \(gtk aye: YI/u’f SO€M {jug Qfijmq'fil‘gn m% it E4 W we»?! “1’; cémé {A2 Aofiffi‘m_ g4an jmt 3M; AWME @ng gny-M, Saébffiwl in {IQ .Qfigmafififl , Problem 1. (continued) 01 differentia} equation a: + 2mg 2 O. URN») 2 (‘0) Verify that m 6"”: is a solution of the Problem 2. (a) Solve the differentiai equation 513! 2 w— 2 2 0. (ix -5- my This soiution may be either implicitly or explicitly defined. C I g- ift. ) Problfm 2. (continued) (b) Solve the initial value problem dy a; + 2553;2 = 0, y(1) = 2. This solution may be either implicitly or explicitly defined. Answer: (We?) Problem 3. (a) Find a general solution of the differential equation for a: > O. k.) ("é CM. 5 JC 2:1 “04 TE.“ Q) m. % g W figmko C C a 3:. W by if x 5.2.. C 71,): M L32“; .L E... . 1?, x x Q; m. - m Kg,“ L "fl" 6 Problem 3. (continued) (‘0) Find a general solution of the differential equation - — = f 0. +my e orrac> USPtfi) dcc Problem 4. (a) Show that; the difierential equation (2:36m w y + 63:2)dm w mdy : O is an exact equation. ‘2' w} Problem 4. (continued) (b) Solve the differential equation (211:8m — y + 6x2)da: — $013; 2 0. This solution may be either implicitly or explicitiy defined. 0 7 Pt ) ,gvgw WE Wm. m GM 2.: Sfigxexwlj +6tfi) (ix «z: 29(6va Qfichx" ‘3?)(4 213 + if?) :2 2x 61. 26.x M m ~a- Wig-#3911} “X.‘3N(?ff1)fijfg(d,‘1)= ww‘z’i’iw / _ 5‘ 1%, L5) ~= ‘21 fix-'28?" WEI WW C. 3! SOQMJWM 3.2: MW» MM ] 2161—2619(wa C [fifgiffijiéf I (We cough/«f Q Ca Iolgswged HM ‘Ce mmmwmwmwjg‘ W (5,2751; .> 21.6196“ 1 +21% C. Ohm-£24m? 1.. I ~ R fimw == Dexflbfl "QM-«g + 61.22 mafia +636“: Wm, ‘1) 53 [141) r": “I ...
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Test 1with Solutions - MA 252-NH Test 1 (June 19 (Thu),...

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