Test 2 - MA 252—413 Test 2(July 17(Thu 2008 Z This test...

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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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