Q3_1130

Q3_1130 - MATH 415.01 QUIZ 3A SHOW ALL YOUR WORK GOOD LUCK...

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Unformatted text preview: MATH 415.01 QUIZ 3A! Jan 27, 2010 SHOW ALL YOUR WORK! GOOD LUCK! NAME: 1. (6.5 pts.) Determine the critical points of the differential equation below, and classify them. i l ) —-3eroi—mp # dill/(it: ‘33Ictany/(2+y2) 3 .2 W :J 1+3?" #Bd‘a‘kog- "‘- (74\$? Ca-ng/J 11(0) : _3 _2 +0 a H; 2. (6 pts.) Show that the equation below is not exact bet become exact when multiplied by the given integrating factor. ' \$2313 + w(1 + if)?! = 0 MM!) — 1? cahititnﬁubfo "i :9“? N 5 [MB ”\A‘CS : ng— \1 X: a 1‘40 M3 '1’ ﬁx}; ﬂ/LJZ’ 52944 T .IL‘ (A ﬁg 1% + x5\nﬁi3:v L___1 ‘1) _;_— xvi V f i/ / Eli/4W V\3__(/J sz,‘ w _% /\J\ng/ ’3 MATH 415.01 QUIZ 3B Jan 27, 2010 SHOW ALL YOUR WORK! GOOD LUCK! NAME: 1. (6.5 pts.) Determine the critical points of the following differential equation, and classify them. dy/dt=ay~b\/§, a>0, b>0, 3/020 3::GmG—Rr’0 3:0 Q‘L/q [Am 5" ”42' ’3 slaw «p (bl: 0H9 4% L A~SL=~94 l Mel = “ “L365 / 1, _ a—ﬂ. “4 937: (”/A = ”:12; 2 .=- 43” O a -— 7L Bud-lame, o. 2. (6 pts.) Determine whether the following equation is exact. If it is exact. find the solution. mdm ydy W+W=O M: X N9 3 951w") 19— Q‘lb’l) 3’1 - '3 z ‘ “AIL “a I M3 ~vx _\ 30““: ‘5/2 / MD’A/x {K c‘l' W = SAX cLA‘ll"(3\7 593:5»);né'x Abs) ’1 ’L L4:A+‘3L 5L“:- lX k .. ‘3’“ Ls": ’ * ‘ L1 :3 “l l) 12‘4“” “L __ é 5;”le m3) ,_ H'l/z. : A 1 +L‘l‘3 ~ V42)? “3) \F‘T l v , 55(st Nair/23 aim .. K’ 2“ .3 @1431 1); @) bl > f: \ (x‘m‘y/L: J “'5? “((0) 9% L/(3lr0 éLGl=O “1‘3" ...
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