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# Math 238 Test 1 MATH 238

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## Popular in Appld Diff Equations I

## Popular in Mathematics (M)

This page Study Guide was uploaded by Taylor Wilson on Sunday January 24, 2016. The Study Guide belongs to MATH 238 at University of Alabama - Tuscaloosa taught by n/a in Winter 2016. Since its upload, it has received 46 views. For similar materials see Appld Diff Equations I in Mathematics (M) at University of Alabama - Tuscaloosa.

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Date Created: 01/24/16

1 8 points For each of the following differential equations find the dependent and independent variables Clearly indicate Otherwise no credit if it is linear or nonlinear lo 2 var r map a B All MULLH pLi39aPS are Fhs of ride 0 N0 Lawl vmh39vc amdL Lalo fS Pai39SeJL to a an exponent Any occunen cc of the 6538 7 I31 HM39S Prob 5 0F HAC foiom AOCX l SO KEN 5 Li neom S ii2p p PieF3 P Irich 39 17 I8 2 Del v ow 9 noti ed to am 5 EN V s NM LnaaP d 2 met l 2 8 points Determine for which values of m yx emx is a solution to the differential equation I SulaSlith ml o HM ai39vcn 1742 mmemx Offf awn 7 MLCMX 3m mx 1memx 0 AI emxm23m2 0 1 7 Com newer 1 W 3m 2 0 Factor be eWai to wowz 3 Existence and unigeness theorem Given the initial value 1 6f problem 3 fx y yx0 x0 lffand Eare both continuous functions in a rectangle R xy altxltb cltyltd that contains the point x0 ya that means quotnearquot x0 yo Then the initial value problem has a unique solution cpx in some interval X0 6 lt x lt x0 6 where 6 is a positive number Using this theorem determine whether the given initial value problem has a unique solution l attention l Do not solve P 739 PM 6 points 2 2 y14N Y z 4 mm 04 oly AX VS IV CO d39Y Uquot bg own39 gt for j Cont meow 14 FXIV 1 L X quotl o Y 7 1 I 3f xy z 3 quotX lquot2 3 ml new I14 SO Ioon 0F H42 Tho pay are mat MAJL be applying Ha 7km HM have TV km a wiqu 29 quot in HM mmvml v8 l o Fw Acme 70 4 Solve the initial value problem for the given separable differential equation 10 points d 1 4t3e 33 y 1 0 7 ow 46 at at cL gt 413 at 6 7 Se A7 2 l4 0U 7 397 g C NW Q anamp I c 0 3L0 7 6 3 04 C 2 l 7 gt 3 i C gt C 3 gt 53 Equot 2 3 A 3 7 e 3t a Tine wml39wue Aolwti39an 5 Find a general solution for y to the given linear differential equation 12 points a POO 2 d 6 d x 9X2 Eve y Hm39ng 1th balmLem ch anal y P00 39 5 fn m L39HS 0f M SkzMAoLAnamp Firm x J The cw 5 alneacky in We Stanolamci Wm Me mr i Z how Cuff 1 So we one all at to leCulal e er l nl egpat lkg Apaclroh II 390 V3 1 A 2 9 L m ll 0 ll 5 ll ll ii x fnl eanalri39n factor 39Ncrw MAlele it he and Ai39oLe of He Sl39omrkode for m I A X6 3amp1 1 1 Hat ix k 6 5 g 2397 X g GK y ch x LJ x 7 ff lxg J l Ppo ampucb Lula AL Q 1 ix Nu w te pate flo 5 3quot 33Cquot 7 m 3 x y we xq C 6 Solve the Following Bernoulli Equation for 118 points n a d 3 o y 2 C y 1 if HAE Bennovullf form dx y2 iii P001 61007quot heme fl R l l l l 2 5 1quot 1 SubWm v y y3 W MomM amok Si39JLc wv x z AV 7 I quot39 37151 mw Solve for Q dot dx 1quot a 7 clLv Ax 3 2 3 I abth htD PM V I39g l d BCY HOMHI EN 2 1 7 3 equot 6 ya 39 3X 7 1 31 y 6 No w clean 37 ch 2 7 39 l Hui CanF in FPO of 0 2 ii 373 363x U V 90 Ha ov i afnal EMquot we AIM US E0 39 iiiV 393 1A LiloSi or obm LE Dela v M in Sl amcLowcL form P00 quot3 Wm ix 9393 0 3x 7 e e 7 e 3 01 3 e x IEquot3V 36quot 3X quot quot11 6 LY 5 333 v 3 M 1 6 3 V V 3 L 1 J PPOMCquot Rule 53 e 3xv z 3 W 6 3 v 3x c 3x V 3 8 3x C 7393 63 3x C Htcarat amok fole 3 so I xco 2 of 500 Ft CL 500 7 The air in a room of volume 500ft3contains 2 carbon monoxide initially Starting at time tO fresh air containing no carbon monoxide is blown into the room at a rate ofS t3Zmin If air in the room flows out at the same rate what is the amount of carbon monoxide in the room after time t 18 points I OM HWI raft of Olfy39 5 I50 539 fl ml39n b The input rate of carbon monoxide in the room In Flcrw Pate of air Assume xt be the amount of carbon monoxide in the room at time t a Find the necessary initial condition x 0 O x CCmConlrantfon of CO in HM l39nCamx ng air 505 O z 0 AfIACC f1an air D cThe output rate of carbon monoxide in the room at time t Ourflaw hate oF ai39n Cmahan 0 Co in owl39gm39na our 2 539 MM 0F CO ward prom at rm i Sgt Cbgt 25 foSHna Y bl of am it M J N 500 IOO 1 Stay5 le39ant lolc inflow r041 of arr wrFlo W dThe mathematical model we use to solve this mixing problem is padre of and dx a Input rate of carbon monoxrde output rate of carbon monoxrde z ampX 425 Jxx X gt0Lt quot O loo gt quotquot Sefwable Cu 100 eSolve the separable differential equation in cl subject to the initial condition determined in ad to find xt ch 3E dx 39 If too gt T quot loco v27 1 X loo 7 bx T OC X00 2 nlo 1 9 6 2 ngnw ll 1 s x ll 1 6 rr 0 Q s E 1 m 5 61 v l l w 4 11 A c1 ll 639 Di 3 d O

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