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Quizes 1-5 with solutions

Quizes 1-5 with solutions - MA 252wNH Quiz 1(June 17(Tue...

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Unformatted text preview: MA 252wNH Quiz 1 (June 17 (Tue), 2008) Quiz 1 consists of 2 pages. Show All Your Work! Y 9. Name rint Problem. (1) Find a general solution of cagy'+93ym1 (\$>G). - (0.1) ‘ / l ‘6+ +13; ==--~ Eiqféj: if“; “W ”5* 0:? MW?” "f3? Eggpxkgﬁwc “:5 311%”? ﬁnVC WC \$1g§=§2m7€+€1me€c “3‘? ‘3“ W {ﬁreman} m LEVI/t A? zmbiiJL maﬁa! : xrép‘g 7% X3"? miﬂufziﬁz '2 (ii) Verify the solution you obtained in (i) by substituting your solution in the equation (0.1). MA 252-NH Quiz 2 (Juiy 3 (Thu), 2008) This quiz consists of 2 pages. Show All Your Work! \3" £7" Name rint 3 3. ~33 Problem 1. (1) Is the differential equation (232312 ~— 3)d:c + (2:021; + 4)dy = 0 exact? - w "7H3 3“» ' 3' - 3 ‘ Mm)?” ”AMa‘C—‘fWB N052?) “2% T+q£ \ 9M _ an; :1 £31223 Mg: ~Af}:(6 3‘33 , 53\$. (8‘6 2 J 2?: Answer: The e nation in (ii) If the equation is exact solve it 32433 W Miﬁ‘i) ““" 933 1C (2‘, ‘1} 3‘ 31972333 3M3: 37831332313363)- 3333 a; 3— 2733—22 3- ‘33”“) :3 29323“ “‘1’ M33} (gig?) ,4: (3:903 47332 £\3§'(£3‘1;£—-£3 31-3223 C Problem 2. Soive the differential equation (2)2 + yw)da: — m2dy m G. ﬂﬁﬁ _‘_ {Li/[L 32> <\ (53%“? xx 9&1 7; H U?” J ”Li J f, j a ‘ m m me WA) “)kﬂiv Kt. kn" EL 3 X - ﬂ _ M W? ‘5‘” j :3? \$7? (\$5ng [11 ::w.. A k/ U? \‘jw Com AME WHCL “023» Cm] w MA 252-NH Quiz 3 (July‘ 10 (Thu), 2008) This quiz consists of 2 pages. Show All Your Work! Name (mint) \(1 g: Problem 1. y1(a:) n cos (4:6) is a solution of the differential equation y” + 163; m 0. Use reduction of order to ﬁnd a second solution 31203). Show all your calculation. __ Do not qnote the formula. " an» m: may ("Wm M) =1 0 ‘5 =4 WWW Wm we} 00 WW) :- C ‘ﬁmw‘cwmwwmm s! ”2“]: onions) “KWWWE w A r ob f“ ‘ H w a»? m no 3% n 2%wa lﬁm‘gf M"th4x)~gu’m£<cx ‘ - I ‘ “ h J aawwacwm ) géoméexwémagﬂ . WW} ' _ w W K all}. ices, Meow—Mookarma) - "‘ 09° {mega WCWiE‘O 02903435,}; ,f 39%, 1/03“, to Mtw ; a i WMW‘X)“ momma; Problem 2. Find the general solution of the diﬁerentiai equation 12y” — 511’ -~ 2y=0. ' {Wm "' K 5 mi" dumb m” ..... .m wauumw a. «3.3. “. ’f-x. MA 252mm: Quiz 4 (July 24 (Thu), 2008) Show All Your Work! Explain how you solved the problem in an organized "way. W Problem. (i) Find the general solution of the differential equation ( {l9 PE ) 3;" —§— 4y’ + 5y 2 0. 741 “2+ armw igmwm W M 5.: iii? ii i 1:1 —~ “W” £33»- a LEM" x 2. Jr: ‘ . i w: Mﬁgﬁﬂw? m2 ﬁg; um “EX . Answer: m CQ Email“ 62% My ii) Find a particular solution of the differential equation C [0 P13) 3;" + 4y' + 5y 2 358”” by using the method of undetermined coefﬁcients. TAM a," who? =(ch4— 4W) +5A)€4X=35541 to MH’ng—gﬁ 2:.» M33: =>A==7 ' (iii) Solve the initial value problem _ S u y” + 4y’+ By = 356““, 31(0) m 3, y’(0) = - < P ) ”2,1 - X r" “,4 ”gm Q9, wox+cﬁe Max—tn [e I ’ “17‘ 42x . “21.1 - ‘m 13 \$5396 09931418 WI. -~ 2&6 m1 +g<a m2: Wow-CW7 2:3 a» o =3w’r-W w): mac; + 9‘2? 3...», WEMJWM ”‘1 ® C2,: 1’8-6‘2? x2! MA 252~NH Quiz 5 (July 29 (Tue), 2008) Show All Your Work! Explain how you solved the problem in an organized way. Name rim; Problem 1. Find the inverse Laplace transform ﬁt) =£*1{l—3+ 1 }. and Problem 3. Solve the initial value problem y' + 43; = 6—43 by using the laplace transferm. , WW2 ”E ’ .‘~ _. “‘1 a. i M 3%“ ((5%?) "” (Q (fm?) 21:8“ UM” w Meaiga 52} 0x 3%):2éﬁwéﬁ ...
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