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Test2 - MA303 TEST 2 NAME Thursday Oct 18 2007 SHOW YOUR...

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Unformatted text preview: MA303 TEST 2 NAME Thursday, Oct. 18, 2007 ' SHOW YOUR WORK. CORRECT WORK AND A CORRECT ANSWER ARE NEEDED TO OBTAIN FULL CREDIT. NO CALCULATORS. 1.(9%) Write the complex number (—1 + z’)24 in the form a + bz'. . 2.(20%) Use homogeneous and particular solutions to solve: xk+2+xk+1— 23k =6 where mo 2 O and 331 = —1. 3.(18%) Let yk denote the national income during the k—th year. Assume that yk depends on the national income during the previous two years according to the difference equation 1 yk+2-yk+1+§yk=2 for [$20. Find the general solution to this difference equation. Find the limiting value of national income, yk, as 19 becomes arbitrarily large. 4.(30%) Find the general solution to each difference equation. (a) $k+2 ~ 4$k+l + 4511]; = 2 (b) “+2 + I): = 1 l (C) $k+2 - (12);.“ +1 1‘]; = Z-k. 5.(9%) Solve the first order differential equation by separation of variables for :1:(t) > 0: dz_ 2a:t dt”a:2+1' 6.04%) For each ordinary difierential equation, find all values of A so that the function m(t) = e"t satisfies the differential equation. dx' den: (a) E+$=O (b) W_4$_0' [MR 303 T23+;] @ _____~Equ¢(:}_ 4% = A“? Ado a; ,M_ Ak._£fiv_;_Vv,fi._____;___ _.._._____-,as_f Mia; figyfl A 4 (Z 1&3? Aféfigi/Lfi W <92 ,Ai:.2_)«[-__/éc_ 461 = c, Qa)’4+ CzI‘_.“_E-(’.,{:.2)'f‘:t Wm ‘ ...
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