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Unformatted text preview: MA 252—413 Test 2 (July 17 (Thu), 2008) Z
This test has 6 pages with '4 problems. I $0
Show All Your Work! ‘ f 23 j g} .. Name (Printli : 32 [55 )1( Problem 1. Find the. general solution of each differential equation. O B} (a) y” + Ty’ + 123/ x O. (8 pts.) W (5%? I “Wm! zﬂriéfahw" ﬁwm
$32 ya EM Maw ﬂ «6‘35 «32% . W. MUM/ﬁrs W22“ 176 .44 %’ uS‘W
Answer: a; m if 7L6" (f
(b) y” *— Sy’ +161; 2: 0. (8 pts. )
m 5:? tzr  KMWM Wag
442— 6”; 4 My "7 0 Answer: a: = (f éqnyti“ X65”!
(C) y“ 4y’+13y= 0 ( ‘ 8 pts.) .ma Lin; +f3 '5» C9 2 _ &M(M~/) + JDM 7‘“ C. Problem 1. (cont’d) (d) 11322;”  3W + 3y = 0 (ac > 0). (8 pts.) m' 2., :
“(”7“l)“~3m+3=& ==§ mZ—M'~3m*5“0%mmtmw a ' r A  :4
44": /_. ”by,“ 3 {ﬂs‘f’l ... ﬂgfmg/J‘? Kaa/ ﬁmﬁ @Q’) r 5: V ‘L ‘2')(3 Answer: ygaz} = C C x3 (e) $ng + 3xy’ ~+ 4y = 0 (:1: > 0). (8 pts.) 2“ a:
m(mw)+3m+% r& *2 ”72am mera%m +2M+9 69 Q;
X (CICO523/4ﬂ 4 Cu. $3nﬁ/ﬁﬂ) W): ><"(C, cosaa/nx) +61 spa mm) x 1/ H
Xi Answer: cc Problem 3. (i)‘Find a particular solution yp(:c :6) of the equation y’ "—3y + 23; ~— cos(e ".3’)
(Hint: Set t— * 6 $ to compute “1(33 ) and u2(:2:) ) (14 pts.) 23g 7
46'. m2 «3m +1 1“?ch 9h: £,€X+Cla 6 3X
x X :2.
Mata QWMS ”73 € «6 H‘ 2.)? a}, (92)! :7: 2% '5”
W“ 6f, 91+?qu; '— 6')? (28 9+ Problem 3. (cont’d) (ii) (Continuation of (i).) Compute y; and yg,
the equation (E) in (i). (6 pts.) )? :: Problem 4. The population of bacteria in a culture grows at a rate proportio
to the number of bacteria present at time t. sin (i) Let It be the constant of proportionality, a:(
time t, and $9 be the initial number of bacteria. The
for 33(25) using 25, 1%, Mt), x9 and solve it. (6 pts) 15) be the number of bacteria at
11 state the initial value problem Answer 2: Solution of the initial value roblem: (ii) After one day the number of bacteria at (I) was 600. After 3 days the number
of bacteria 513(3) was 240,000. Find eh. ( Hint: compute the ratio a:(3)/a:(1)). (7 pts.) It? ”:9" [Z 952;: 4 ‘ a» ‘2 4&0 é _ ,
ZMM 1 £5“? (2 i Answer: ek «2 90C) for the continuation of Problem 4.) (See the next page Problem 4. (cont’d) (iii) Find the initial number mg of bacteria. (7 pts.) ...
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 Summer '08
 Saito
 Differential Equations, Equations

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