Quiz 3 Key - Fall 2010

# Quiz 3 Key - Fall 2010 - Differential Equations Quiz#3 Fall...

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Unformatted text preview: Differential Equations Quiz #3 - Fall 2010 Nameﬁ%n_— Show all of your work neatly on this paper. 1. Do x3 and x4 form a fundamental set of solutions for the differential equation xzy” — 6901’ + 12y = 0? Why or why not? You must clearly show how you arrived at your answer. (3 points) a :x ‘1 x’fisz—éxmxg) 442.1!“ :0 1/ I ' ? CD Sgrﬁmx (bx)va(5xz)HZx3:0i/ 31'154’13 1333;}, 9 am r=x Q) 0-6.)“, W? a W: l X: 3x §;l:4xksx“=xb#o 2. Suppose that y1(x), yz (x), and 313 (x) are all solutions of a homogeneous linear 2nlj Order differential equation on an interval. Is it possible that these solutions could form a fundamental set of solutions? Why or why not? Be very specific. (2 points) . NO» The/“:35 {um/(M. Wax/Lo J5 a Emma/U 01%3. eﬁuaﬁm l5 ~le l 3. Suppose that the auxiliary equation of a homogeneous linear differential equation factored as given below. Determine theiirﬂjumon of’Ehe differential equation. (3 points each) : -| 1 ' =_:__¥_N'-7 x . 2/2 1.- 7x ’x/z' . X a. (m — 1)(m2 «Fm + 2) = 0 ‘7' General Solutionztl 41 :2G Smfé‘ 2. .2)‘ .u b. m3(m+ 2)2 z 0 GeneralSolution: g '3 £2, ‘1"sz x 4’ £4 6/ j}: 4. Determine the simplest form of a particular solution of the differential equation ay'” + by" + cy' + dy = 4x2 + 5 cos 3x, given that the auxiliary equation of the corresponding homogeneous differential equation is (m — 3) (m2 + 9) = 0. (3 points) yd»: Clay-3'67. + C5 (’00 3X 7- . The particular solution will have the formzyPiMWWX'l' LOOK ON THE BACK 5. Solve: y” + 2y’ + y = sinx + 3 cos 2x . (6 points) [102+ Zm+ l‘JO _x ‘ “x (“wok/O —b 3c: ('46 *+ C2X6 ‘jp= Aggy)” Bwsx + CSinZX + 'Dcoolx -9m- Em ~40WW“ *5 ‘09” 429 wax —28Sinx 4. 4cmzx— wﬂu — Sinx+30D3~V HAWJrQwSz +C€;/’K2x+bc¢ozx H -ch, 4-H) +5; :0 {ac—Hui?) "HD +qc+D23 qc'5D’ ...
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Quiz 3 Key - Fall 2010 - Differential Equations Quiz#3 Fall...

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