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P2_1030 - Math 415.01 Dr Huseyin Coskun Exam 2 Practice...

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Unformatted text preview: Math 415.01 - Dr. Huseyin Coskun - Exam 2 Practice Problems - 10230 Class (Vutha) February 14, 2011 The following list of problems is meant to serve as an extra resource for your preparations for Exam 1. This list is in by no means exhaustive, nor is it meant to predict the questions in the exam. Instead it can be used as a tool to assess how well prepared you may be, and to highlight problems that you might face. Pay careful attention to your timing and clarity of ideas — as this is something that can greatly afiect the outcome of your exam. (3.1.22) Solve the initial value problem 41/” - y = 0, 31(0) = 1, y'(0) = -5 Find B for which all solutions approach zero as t -—> 00 (3.2.8) Find the largest interval in which the given initial value problem will certainly have a unique solution. Do NOT find the solution. (t - 1)?!” ~ 3ty’ + 4y = sin“), y(-2) = 2, y’(-2) = 1 (3.3.11) If the functions yl and y2 are linearly independent solutions to y” + p(t)y’ + q(t)y = 0, prove that clyl and c2y2 are also linearly independent solutions provided c1 and c2 are not zero. (3.4.20) Find the general solution and sketch a graph of the solution and describe its behavior for increasing t. 7r 77 3/"+y=°’ 9(3) =2, y'(§)=-4 1 (3.5.18) Consider the initial value problem 9y” + 12y’+4y = 0, y(0) = a > 0, y’(0) = —1 (a) Solve the initial value problem. (b) Find the critical value of a that separates solutions that become negative than those that are always positive. (3.6.15) Find the solution of the given initial value problem 9" - 231’ + y = te‘ +4. 11(0) = 1. y’(0) = 1 (3.7.10) Find the general solution to the given differential equation 61 1+t2 y”-2y’+y= (3.8.7) ( Refer Text ) (3.9.9) If an undamped spring-mass system with a mass that weights 6 lb and a spring constant 1 lb/z'n is suddenly set in motion at t = 0 by an external force of 4 cos(7t) lb, determine the position of the mass at any time and draw a graph of the displacement versus t. (10.1.15) Find the eigenvalues and eigenvectors of the given boundary value problem. 14” + M) = 0, y’(0) = 0, 9(a) = 0 ( Note: There are no problems from sections 10.2 and 10.3 ) ® Scuba“; m yCe):<:i?)€/Vg+(w)ézyb 2- L m Mano; 44 Aetmmga 17 e“. :6, he. =) 2132:) =>- 2 PCE : it ) 4;" Oqu—onlmm <11: (2 l L4 CE):- 53E 9 L-‘l @ Q) and slums: CH. 00‘ 0‘72 0“,:ng NH 4 C403) LHS (9“) + QM) P“) + CQMQUC Q C!” 4 decoy.) : O esul\ak:a Sch—Judd WVHW C‘ONHLOJ wahL‘JL A; ‘erfgz m4 W Pew/Dd 24" MA [MK 4erqu 00%.?) Q3) @ no“ Efflkéo: qwz'i'D—Y4—410 “(1 ——I2 : J \44 —4(9)(1+) 1C9) _ “i?“ 43-2% © E‘ASOVKW‘ ~10); QézéLJr geejlfl CMaOfiCp/w age)- néQelli’fing-gt )efi': Sag State, 0.70, AQLLHOJc 523me flow/- 01: a‘ljxhfi’afiy -I 40/ SOlu‘l—O-«fil J’LQL'L W38 QbLSY‘WOWC‘S O—Q-zét + (£3): glib: O 3 3:) Q4 2g :0 3 =J e = $2: Zoré ‘ 1,; Lake, ObfyofiLv-e vWGAWmROM LC 8 Quake, 9C6); aefzéewkid. 4;, “(”07“ FOJiLCL- Pm‘mm‘ow SdHJ-Lory @xsjr Gvé55> f CAB/Qet +C WM Mw; @mkd,‘° W’Ff)(7 1:7! E;- VPCE) a. CABS-g— BLL) e‘: + C A’Uo W VP' Ce) .- e} [BM—fl 2%) + (M3+BL}] g ___ ($ka + (3M3) (5’- + (2.5) 4;] VFHCQ): Q}: [<3Atz+ C3A+6)G)L +243 ) +[ 1453+ (3 4+3) *Qz)‘: E? 1 O N :_ 1‘- J‘tA ‘ VCE)‘ C4 (LO-5 +AL 495‘“ (\fié‘ E) v m GA) [gamma 954M L1 QC): ‘hFA[ [—OC‘San/AL )4 QwJCfiAf—J] ”ICN) )—O 9) {TIA W) WA”) I 7(0):.(3 3) (ls/O VCWFO 2) C. £04 (£3 rt) 20 =) @A 11.)” Q”) ”A .1) JiA: é:“)IA:“" @421 Lb ‘—-— ...
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