MTH 205-Solution-Test-01-B-SU09

MTH 205-Solution-Test-01-B-SU09 - American Universig of...

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Unformatted text preview: American Universig of Shariah Department of Mathematics and Statistics Test I 45 Name: [(9% MTH—ZOS, June 24-2009 1D #: 3.Solve the following Bernoulli differential equation. Expr ess your solution in implicit form [20 ptsl 2x3%=y(y2+3x1) :9.) 2x33” .- 3 +3.83 6?, “EH/#3111! : \33 *9 i=— 3:- = ‘21:»: :9 5323*- : if : 1L; M u =3“ 45 “9-153! =——‘—zw’=:i"3;i’ 5?) ——‘-—u.’ ._ -3 u : x 7* 2x 2.x} 4.8how the following differential equation exact and solve it. Express your solution in implicit form [20 pts] 0ny — 3)dx + (2x2); + 4)dy = 0 H -= Zj‘x —3 ===>?_"’—:‘Iflx .95 EE'léc/t N:2.x.z\3-1-L‘ __ 2.12qu3 94-. " (93%: H i} Kai :SLWXABW +13%) 7:) 99%;) :37:L *3): +343) ' fi- N :7 1(‘02‘2. 3L 1-94198: Zzzjftfi 5. Find the current in a series RL circuit with R=20 ohms and L=5 henrys, if the applied voltage varies with time according to 10 volts USISZSec 130) = 0 volts r> 2 Assume i(0)=0. [20 pts] { Hint: the differential equation that governed the problem is L + Ri’ = EU) } 9L T g3 _ Eu) cit ; g a saw _~__ _ E At+HL-2. J ogté’a. l'ld) :0 1.1.9 H lit I‘(£):-€ :3) JKE Lu)».— 26 A4: +01 lit :15 6 [bed :31ng{ -+C.‘i 4-H: 2'? Lki) : ~12: + C| C ,i “4* 0&0; {=2— LL£3:L‘\’Q\: Ji_K\———€ ) C 4, - d i 3 hi__|_é)_cze% “=9CL—7(e’l) z 3‘ "71° £>L kajitthX:J—gfl(e ~06 » / ~‘it 90) J;Li_c ) 03—562, 6.(Bonus Problem) Solve the following differential equation [10 points] (5x+3e’)dx +2xe-"dy = 0 " '3 ‘1 M M:6 flfiéizeai©4036 d) ax. _.. =2 (“Ha—Vt—deu :0 ch '5 1 as” 39' aakJ‘FTJvL "'2'- IL 32' J.%"A 313%1 flnx/ 3/1,. flkx) I e : (9., :e '2: 7‘ 3 A (pf/10¢} r: “flax/13x +Q 9/1: 3/: "' x 75 LL :: «g' “'"F’ *C’ i/é 3 5L x/‘M = , 7C /' + c x r 572. ’3) (A :1 -- _2:_——-—-- +C-X 3‘ ‘ X3!» ,5/2/ U451) ff); +CZ 1 ’34 e 2-: .— 9'5fo «3/1, 3:3 ...
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