PracticeTest1_2007Fall_ans

# PracticeTest1_2007Fall_ans - Practice Test 1 Math 2171...

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Unformatted text preview: Practice Test 1 Math 2171 - Differential Equations Name: Section 006, Fall 2007 1. For each of the following differential equations, determine Whether it is separable and/or linear. (If it is separable and linear, Circle both; if it is neither separable nor linear, Circle none.) (1) ﬂ = 3m — 2y Separable dy 2 2 . (2) a; = m — y Separable Linear (3) 2—: = (m + Hemlm’ Linear dy ' ' V . (4) \$113; + 1 = 0 Separable v Linear d . . <5> sud—“Mm d , ' (6) xi = 23/ + e“ sinx Separable 2. Solve the following initial value problem dy 6x2 -——— = 7 2 = 57 d3: \/CL’3 + 1 y( ) QM] 50/Mﬁl7/l: ”05): 4/J-E7 +6 . {inﬂow/Ar bD/wﬁvn._ ya): 4% '7 . 3. Find an explicit solution to the following initial value problem de- 3\$5y2 + at E7; — 2312, y(1) = 1. by separating variables. amt/a] éo/uﬂon 1,) ﬁll) :— ; 5 l’ CL f1. - pM‘ou W woman 1 I z : M 3‘ ) //L’+)C5 4. Find an explicit solution to the following initial value problem d g 2 431+ e“ sin5x, gm) : 1, by using ”Linear Equation method 7’ as discussed in Section 1.5. . 1M. 0 @WA/ bO/HfID/I‘. 36x) : , 5L 609517!’ C e i \ l/w ‘ PAW/WIN I’D/awn; aw); (#4055206 +,e II 5. Do the following. 1 33(2~:c) dm using partial fractions. (a) Evaluate / (b) Find an explicit general solution of the following differential equation. dm_ 2% — 3:2:(2 — 51:). Here, we assume that \$0?) > 2 (Be careful). ’7; Ag“ 1;; " gt HI 6. The NC population in 1.990 was 6.629M and in 2000 [was 8.049M. Predict the NC population in 2007 and 2050 by using the Unbounded Population Model. ° FoleMIDﬂ Ill") 2/007 ’5 4-220/‘4. ' PopulM/‘(m 17) L050 [‘5 2/-2"L3M. IV 7, Given the following initial value problem: y’=y-2\$*1, 11(1):? (a) Apply Euler’s method With step size h = 0.1 to approximate y(1.4). (b) Apply Improved Euler’s method with step size h = 0.2 to approximate y(1.4). ...
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