Spring 2006 - Zabrocki's Class - Exam 1

# Spring 2006 - Zabrocki's Class - Exam 1 - Math 20D —...

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Unformatted text preview: Math 20D — Spring 2006 - Midterm 1- Prof. Mike Zabrocki Name: _K£:\j____— Time of section: Kg: 63 v I 1. Find the solution to the differential equation y’+ {1; = cos 2t that satisﬁes the initial condition y(0) = 3. emit : ﬁt as supra t l: %:’L‘t5la}t +\~ agglﬁ— l/ Zitslnat-l—ﬁwsat't—l‘c W . ind all solutions to the differential equation .— l 0 ~ 0+;cO5(O) + C_, l; ’+‘ Itcosa’c :3 :j 1:) Cz'l/q No‘lef Not homage/lam) %=t§ff;ﬁ Hagar or 59’ amLIC and that satisﬁes the initial condition y(2) = —1. HOP‘L— \"l'5 QM 1 3 “x at 7. 9C3 t (“5 lair—“o Check M3 :36 Nx=3t ﬁb—t 575—:C, lie. 3. Find all solutions to the differential equation 7. ,___.—-——/‘\ 34:1 : 3A1 V: 3/X 3 Eli *lnvdl-V-tl/lX’lC 0M 3 0(7‘ AX 1! + A 01 2/? WV" v; d\/ _ \/ f .__‘_/.. :1 ~ .— H, a 4. On the other side of this page there are three graphs. One of them describes the direction ﬁeld of the population equation 5% = 4y(1 — y/2). Pick which one it is and explain why. QLAZO 160F330 of jail 0U We see\ ‘por a>3>0 7% ls Fos{l{\/L / 469%]:3 0A1 l9 F Old 72L 3 a: ‘ 3mg) “5 ngsq‘ltn xi @ K, a” M: a” I I .104 .7 . I I! #1-! a Ly] ' A f IX/f'leW/l \\ H. W/IJI’I/V’VA »’»JJ "W’ﬁ »»»5~0—+»g—>-¢,—o G G ‘I L ,__,,.‘,_, V» _,.._, +, 9. _,,._, .1 “‘-§‘ swuw’ u) 1/} ¢ ¢ x WXN zJHWxxx -%{.L—H; {/‘¢¢\$W¥“\\‘ (1;;wxxw. J1"! (wxx-xx awaéw— z a! yin/J“; {1144 4/14: I I f J I I 4 ; ¢ : ¢ 4 ; ¢ 4 4 ‘4': Jr‘l; , ‘V 4 4 4 ¢ 4 4 4 ¢ 1 °mns\$xx x x mm»: & £ a \3\~\‘ 6 * V \w'x ; : s H X 2" J y a a» . _. .—> 1-5 a I .6” WE: \ x \ Vx‘mw: _¥ \ "\‘\‘\\£\$‘ 'L LX LL; LLL I: -x L.“ F \xﬁi \.\\?\1\3\¥\$§\\\ I. x x L Mixyxfxumnw. LX SQ \ u s x xéxgw H z N. \; é. xvi»; :V m \ \. :w u s .,\ __\ s y x _ Ax““.a..§.>?\?~ v * s «13;» ##31 w ¥ ¥ 3: 7:! ; ¢ ;£ ; : £ \$ -03 Math 20D - Spring 2006 - Midterm 1- Prof. Mike Zabrocki Name: Time of section: 1. Find the solution to the differential equation y’ + y = 2:2 that satisﬁes the initial condition y(0) = 3. S?“de x 6 ' 6 8x5 + 811 : X28,x 6’3 : szgxdx : chx-2Xex+3.ef +C 7. 2x CK*Z%QK+ZJ+C :9 3=;L+C. =5 c:; 5; xlex—erx‘l-Zex-t \ ‘ leren l'd, equa lOIl 2. Find all solutio dt = t2 +y2- Note: homojeM-od3 Wt ) + 341, a? GU; olv V 0! ._ 3 ' 1 , OH: w“ ‘i‘ V : l : v --'-—- —- —- \ — M td’t i‘i'VZ \+V)~ #7 </\/3 /V ’t 9+; -2 -— :- 4: + i 3. Find all solutions to the differential equation )n v in c @ = _3\$2y NOJr‘iilo’f kOMOJCI/leow d1: :03 + 33/2 Noam or sepmmtla and that satisﬁes the initial condition y(2) = —l. HOPe |‘ j 58E, 4* :- O ckLC/k; 2 3x7- NX: 3X1 UL)? €xm+llj Xaj+33;c’ is {he solJ‘Hon +0 'qu5 écyw‘h‘oy“ 'l.L.=) ~%—\ 2C 1x35+33= “0i 4‘ On the other side of this page there are three graphs. One of them describes the direction ﬁeld of the population equation g}: = 4y log(2/y). Pick which one it is and explain why m 4 A Ha ;W\$\$ vs? § 1 \$ Hgy :: ‘. _ “a? §¥_\i\_ v.» ‘ w "—> 3‘ / 1 N x mu ¥ & ¥ ;. \$ I?” \r 3: X 03 7/ I; 2' If \$3-23.} x. L L 1. Wu v; 'V‘Vg A 991.114 u—F—b ...
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## This note was uploaded on 06/12/2008 for the course MATH 20D taught by Professor Mohanty during the Spring '06 term at UCSD.

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Spring 2006 - Zabrocki's Class - Exam 1 - Math 20D —...

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