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

This preview shows pages 1–7. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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.) ...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern