Q2_1130

# Q2_1130 - MATH 415.01 QUIZ 2A Jan 20, 2010 SHOW ALL YOUR...

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Unformatted text preview: MATH 415.01 QUIZ 2A Jan 20, 2010 SHOW ALL YOUR WORK! GOOD LUCK! NAME: 1. (6.5 pts.) Find the solution of the given initial value problem in explicit form. Then,determine the interval in which the solution is deﬁned. 1%. 5 \<k«-za)¢\$_hwv “1" H723 ’ 1 3+6?” Xl'tc— “W”? l-C' ‘30): l L ’l-x\ ’ 2* C 1 1 a ._._ - , )g .. i C- 2— ‘,»‘33 \‘lj *\: y Thm§ 2"“ W I 1 ‘, , u L4 : x-L V L w w Mai/x "+4. 1L3 Lawns-l ¢9L4 j 3 : ,\ 4 x1... 'LQL *‘ﬁ‘tlz 33,2.- f } -_ 4 ‘1 A u, .\ x2“ .. ll 1 ()PUC. ‘lQ e is) » ; . . :5. = "l + \lxt'9/ .3 2. (6 pts.) State where in the ty-plane the hypotheses of Theorem 2.4.4 18 sati ﬁed in 3' (—1 y! = d‘_ _ ” l 1 / D: (51”)‘1‘3 > 1 7: balm—ems ave/bwm ﬂ : ’ (ll 41' 319/2 -'L:> b L V0 14.4”- 210 NA. L—l’131>’9 yL 5 -\3 :) @Al'Am’D‘A '- "" K 41 «Ly/2, re +1431. 4.4, 33> mi; JQL'eAr'l “a” “93% arde— gﬂmﬁh‘éz MATH 415.01 QUIZ 2B Jan 20, 2010 SHOW ALL YOUR WORK! GOOD LUCK! NAME: 1. (6.5 pts.) A ball with mass .15 kg is thrown upward with initial velocity 20 m/ sec from the roof of a building 30 m high. Neglect air resistance. Find the maXimum height above the ground that ball reaches. AV _..5 Wm v(s\._2_0 =2. Wrw 334’ .. xvi) 9: T 1 "‘ g D \j ’2 ‘1 ' in": \ ‘= A I an I a 1 -——-’v :- 0‘ ’ W\i" jl 0““ 3?” 5 E é} :3 % Vat-O Q l‘\ " ~ r - 1 \ 29331 :53 JV 0 5' \‘in 9 (204%)" Tia—vi ’ \\ ' i‘4- ‘C " T. :3: L—.———/ z/‘gL-h : 20“ ' *4” W?) . 1 r r -,7 ‘ ‘. a. ‘ . WEE} w in ‘2 L..- ,_ V k I 430' - 3° + foe _ ao‘D J“? ""T 7:31 , 35g C35 +107 :50.W 2. (6 pts.) Verify that both y1 =?— t and y2 = —t2/4 are solutions of the initial value problem a“ % ,_ —t+ (t2 +431)”2 y 2 , 31(2) = -1 Then, explain why the existence of two solutions of the given problem does not contradict the uniqueness part of Theorem 2.4.2. £W>¥Ac2 Oﬁ a Saleo'x (LA; ASL. "‘13. VaﬁJQCAQZ‘aSS/j (faa ‘0 £— QERgﬂS‘aﬁ‘ 0" {has}: 4‘3 can’it‘l’V‘J-‘j J «f “ii-1 — . i 0 ’ » l’Of «Navy/.459 ' we”, @nl‘ﬁm": x9771 é‘JZ/éw \4 M V 12 7 ( 7ALl/L 3 L I ? \'/ 7’ walk a. A t 3“ L; 21=l'+ vi. 7 'ri' %(41+A(i-4’\l L - f: : 2. v 2 a! - /—___________ - a! = 4 2.— ; ‘i 9—9-— _—_—-\ , r // Vanilla; \$L=-«l1[h 7 ‘ (£14,; 41 '1: —L V ‘0 L I 2.1- "7 31!: ‘ a I) Z W!“ L 91 :12... ’ a. 7— 5 -V v "L 3‘ l i _ 7 D U", .—— The Aeash-L anlrfmhcl “Aﬁ’pruéb. 0550-6» i: : g, +15) ‘4 ' PM. :3 ...
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## This note was uploaded on 07/26/2011 for the course MATH 415 taught by Professor Costin during the Spring '07 term at Ohio State.

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Q2_1130 - MATH 415.01 QUIZ 2A Jan 20, 2010 SHOW ALL YOUR...

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