4100_F09_E1_solutions

4100_F09_E1_solutions - (' our Name: flath 4100 Exam 1 Dr....

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Unformatted text preview: (' our Name: flath 4100 Exam 1 Dr. Ciprian Gal _ Instructions: There are 5 problems. Each problem counts up to 20 points. An additional BONUS problem worth of 10 points is also added and is optional. 1. Find the general solution of the following let order differential equation: ty'+2y:sint,t>0. (if .2le [m .f 1.. 2. Solve the initial value problem: 3/” a 23;" + 53; = 0, y(7T/2) = 3, yr (7172) x 0. fig... 2a+§xo {5.3 QLQV'ac‘L Qzaa'fiba ‘ N f k" a“ QOM£lt¥fm3 1 ’73 UV): Eff: XCOBCZX) “mchg .Smfzx) WWW" ’ «kc? QXS‘EMZ x)+f2c1 eke 03( 2X”) ._..._ Hm @471 (bo‘vt 0M 1 .Xm/Z g xw‘V/‘zfl \ Ajcx): “we cam» +3 8 may) ‘/ ' 3. Solve the differential equation WWW Wan F Nsz ~— (zit-73%;) QQ’WM’L *K‘ic’fih ' My: N1 6L} +274: #3?” "#4196 f3": {VPIA‘V’D fwd; CLEch “(ea-"133w: _- I [F V115 t: N‘ X {Laymaflf U1(H_1Xjf1¢)]x M 025%“) W (45' W) “1“ N (‘1X?)“>5> "W (42%”) PM , msg/w/we [LE/“4(1) f&(élfi+bc,- ~ W “M 9‘2 1+1?“ .., (Em—Wm. M”: “ Lt’x‘: 1W" 1' — . , r 7", ‘L b + l ’ U Yfii‘iwfikfi’wa 4 a, 5 A? _ 5 “I ' ' 2" “'3 9‘1» ~ t -- :: X ' 2X WM): - L3 in 1— 2c {5 + COO «a; H"; J ((MJ Pr (buow‘i; (1‘01) L: o flu: gum Hm V) 4. The function 950?) = t is a solution of the ODE Hy” —t(t+2)y’ + (t+2)y = 0, t > 0. Find the general solution. M :2 it: x bug/“HM Sail-3?»? "\— L\I\¢i v CR L. L _‘ Q) ‘1? “‘é’f‘f‘fia \l 'V’ '1) "J;- C: 4“ GUM/W V) $16496? (a; @E+C;Le if v6 {A Edi; o GK) igm, 1Q «LawVPMmk/a "WLH-zvé Xfm gal) (1:0. @ CM «a W ejwm M m 4m “Pam 'Mfik 9% IWéM ' exg'ninlfl 4mm 3 “RM ~L¢M< WCU OVehfeow) 01Hon enmgé’ Jn‘me , ‘ Qimu $65443 air Walsh 1M :3 380'l/W talk-f 9%» ‘WQLQA umfi‘ / 3 w fie. M 4&1 3ale finfl‘zfimififi Ra Acaa’ awn?) Imimifi ’thdg QK-H: QW‘ cohm47a47‘am $4M. 6. BONUS: Suppose that the population y of a certain species of fish (such as tuna) in a given area of the Pacific Ocean is described by the equation :12 2 7. (1 _ 2) dt K 9’ where r is the rate of growth, or decline in the population, and K is the saturation level, or the environmental carrying capacity, for the species. For K = 161 X 10'3 pounds and 'r = 0.71/year, if the initial population has size yo I 0.25K, find the time for which this population of tuna will reach three quarters of the environmental carrying capacity, that is, gm. - a ' a mi? " l J - V” '~ l4 r- L 5‘ V5” K it 3}} K ...
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4100_F09_E1_solutions - (' our Name: flath 4100 Exam 1 Dr....

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