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Solutions Exam 1 - ME 391 Exam 1 Spring 2008 Instructions 1...

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Unformatted text preview: ME 391 Exam 1 Spring 2008 Instructions: 1. You may use an 8.5x11” sheet of formulas, theorems, hints (No example problems) 2. No Calculators are allowed 3. Show all your work clearly and with reasoning. 4. Closed book (open mind) 20 (Its a place Problem 1: Write the differential equations in Standard Form (a, b) 1b) can“, c7421: SEMX . ’ 62X 8‘ )c fl I 3x11 K XVI Uh Vi : —e. 114-6" Sin Determine if the following equations are linear (c, d, e) 1°) (1/:- X6lhl1+ ex Nor LineM %€wusé OF ’fih: Tenn Sim/k 1“) (Hui: 0 HOT LIMW [$02 17> “4’42 Trix: Sn‘powfl 1e) (1’4—Xolse") (6’19 (X “ex)b’ =0 Lil-“6M 2) Determine whether the Differential Equation 1 X +\ d ; Is Exact and Solve ("l ' ZX‘ A>‘ *- C2 ‘1 B ‘1 O M: 11731X )N=ZXl/l+| 2533‘: Zv‘ clayiczu Ema Y MUM) 9" = 32117528 ax = Xn‘z-x” Slrxlbcwflg)‘: Y(Zx«1+Dél1 ~ X‘fil‘kw lbw) a ~12,qu ; ”$411—ch (0L in have mutant) 3) Solve the Separable Initial Value Differential Equation: 6 52.3.2.1 if; : (LL11 ‘10))” UWCHZZXQ" +Z.\<LX 2(131/1 ex +XL 4“(L 4) Solve the 2"d Order Differential Equation (Reduce the order/ Determine the 'nte ratin factor . I g g ) Xi/lI'ZL1fsiLX4 ii I Viz“ ) ‘8 = 0‘ Xw ’Zw: [2X4 KAI” %(‘(A —(‘Lx3 fl_eYP(x3M’ ewacla - M ‘ :62 x: aian )—X X’Zu = YIZX Ax K1“: sz+c‘ r> u: (,x“ 7.. + clx 7.. I4 /= u: (a x4 4'C‘X v1: YLUX‘U— a‘xQAx (11/ g i 3 VF 5 x 44¢} + Q. 5) Determine whether the set {X l x1 , XE} Islrnearlyrndependenton (~00) do) 7,. 3 ,. 1. 5 Y X X2 w{x,x,x}: s Zx 3x 0 2. (0X LXVLx-bx) + (x73 3xz-0)+ (x3. (.1) ‘ (X‘5X1'Z)‘ (fl- I 'UX) , (x3.12<~0) ‘7 ZX 3 79- O ‘twacwhz‘ («C‘éClipéVa' ...
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