EXAM 1_M427K_FALL 2005_BECKNER

EXAM 1_M427K_FALL 2005_BECKNER - Math 427K-C — Exam 1...

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Unformatted text preview: Math 427K-C — Exam 1 Show all work. 1. (25 pts) Solve the differential equation .9” + 293v I 9:, 9(0) = 1 How does the solution depend on the initial data? How does the solution behave for large values of at? r"; 2. (25 pts) Find the solution to the differential equation my ,y(1)=\/§ I! How does the solution behave as x —> +00? Sketch the solution. 3. (25 pts) Solve the differential equation 1;” + y’ - 2y = 0, 21(0): 1, 31(0): —1 4. (25 points) Describe with both quantitative detail and qualitative features of the di— rection field plot. sumac me an. l we cam se—V' = vx é solve = V}. {3w We $0114. gha-k wag. This I? W\\\ (New US *0 mnipmcrte “H16 V " VCH‘ + de rable 90mm xtvadea—xdv) --=- (x2+2xZ-V‘)d>< xiv ( Vow Haw) =1 Lx2+ 7.va?) olx X‘VZC‘X + ‘13de W M” X} y; “old a“ We x‘s + szdx on Oheéfle and V7“. +><vdv : cw ,V2 2:“ v Vigil I om Jane \st 10 I ., 2 ————-"‘— .ng 0W6?“ dev: chm» \1 dx Wvdv :: (\+V2?c3>fi i 191/, ___ Ax k— now Boa have W \faHothS \ W2. " sfipaxcfifd ‘k- 9w cam miting 7. HM?— X Q: \Jer dd 2' ZVdV so .. 7-,. 2 —-7. (mam/mo r, :3:va Y : \ Y :—’Z_ l 2 plfuac: \+8 :61 7o 90 WOVeOJ dxshncfir-mo-is \59UL vm WW 8W Sbwhon W 0 WM} :3 0‘6“! + Clamx 0° N“ = C\ 61‘ + C264} 4:0 eomPov' c, hm 0mm! 0% 5 +0 W; Whaflamd \j‘tsc): cle" -- zeta'i“ I ljU>)""'\ CI-k'QZ :7 22325141"? \:Jé+@ Wtbyc4 :7 -\= q --’).C1 —:.7 -\:-wc\ — 7, A, «g. \ =29 % :02 0L Wgom mam ch causimg 3cm DSCHiahon 01° me graph, The/T6 Seems m be smut: marries boundgd bCereefl Hf] SEA 3 4 1.75. TY‘e cwclce or Spirals are Wax/£6 WM" \0_ ‘ W CBS-m Tn {lunchore (momswod WW Moe was or fim 00 mm” approach a cerium \Imue. \P gowook/ 41+ Jrha gmph algae. Wag 0L. mm on flap (5-? m wave mncnms D? 5W6 ...
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EXAM 1_M427K_FALL 2005_BECKNER - Math 427K-C — Exam 1...

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