MTH 205-Solutions of Test-02-A-SU09

MTH 205-Solutions of Test-02-A-SU09 - American University...

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Unformatted text preview: American University of Shariah Department of Mathematics and Statistics Test 1 ------ -- WITH-205, July 13—2009 Name: K ea Section: ID #: artial credit for each right step. Show all your work. There will be a p d of undetermined coefficients to find the general solution of the 1. [20 pts] Use the metho non-homogenous differential equation ——-—2—— = e2" +5005): Ste‘l .fmJ fight.) I m1..1rn :0 2x \ it} ‘écm = c. +616 ) 5; J , e u x dram“ ashbic 1(1):.A6 flyng 33;} £60. are), r r n: ‘ = e I @534) Sled-x3 .ffi—Sf 5 Flgx'a-gu5r- «\- CSNIX hoétzizé $9“) = “c Panza“... 35"”: Ar (1 a" ‘3’ 1 Ac *2 nCSI-H‘L P” 1" qué'x‘wfiwx ‘3’ :léhe' ‘k 21 at $6.05): c_ 65”" Lx A8 Jqux ‘- J‘zsjmx 1553' 4.9.9521 1;. qkeu “HR 8 v7»?— aix fe'zx-yEC-DSL [ML -__-; 91A ’l-x +(-{5#2C)605L*.Kflc.k1§35 a; c C : —l' 6 -' t A 'Bglc f2— “:br‘ue i C 90 9%: ,J a“ 6 #1 C :0 f/_ 5‘- ‘fz r-" “7'5 5 g $31.1; 2.[20 pts] Use the method of Variation of Parameters to find the general solution of the non-homogenous differential equation 2 :z—Z%+2y=e‘cotx _ ~— H-K 531* w m , aime- = , “1'37"” M :17 " steam at”; -35“); tme “5ch 1-K we :' a 5mm“ Jrecbla 1x 1x ‘ -€ Irvx‘fix 4' a I” K _ Cut (:55 A “ “1(2) :—- ‘éfb % 6“ = '- J9”! ‘9 at" ch. :- ___ 507xe -.= .— 5"“t 0051 a" “7“ ‘ $14.4; ml“) T Sifg‘lfi) A“ .— Ax “(1,139 f T: J"\c§¢1 loco‘hr— *9?" x . ‘3'!)(455 : .c—e giving-x. i, lose; gra£¢1+wllex51n£ EU): ‘63:) 1 “39(x) eral solution of the differentia! equation: 3.(a) [1 Opts] Find the gen £21- “'3’ £31- LL 4 dx5 (fix—“q dx3 dx2 ‘0 "‘5 ‘qw‘H-rqm} -—3JLM" =0 .4 :so aLm-QBLY" +qmb):a m”("-q5 + we -—q\ “1(m’q)(m1+q):o éfl> m=O/O/q)-.‘:SL talk) : c. +C2d|bl 1' C} quehu)+t1;5m(3bx) (b) [10pts]Solve the initial-value problem 2 £1522 dy - x F—ngx‘+8y = 0 , y(1)=1, y(l)=0 m‘mén +370 “' L Li ‘5? Y" 5 57—)“ ‘57 VB”) 7: Cix "' Clx _ } fl " 2(3quch Ax __ "H c o k g“) C‘ «poigx K - fl #- — \ - =5) l+ ’ E (q *chf (x)=x be a solution of the following differential equation 2d2y 4. [10 pts] Let yI 2x —2—+x—-—y=0 dx dx Find a second linearly independent solution y2(x) for the differential equation using the reduction of order. 'ii” I .- i- : o + 1-: “MN V _fffx)¢§1 flJ-Ei—dz. 'yglnx ta. 1" a. it); e -.:. Ci :: '3 r: 6 ‘15 7c .. {Eman- ‘3 An ‘3 04-3 : ‘3 m ##1##” 2. l j (:25 , I _ 2 ,7/1 r-Yz 1 -112, X 0‘1 “1 [X . nix 7— 7‘: - 7t .— x}, . I 3 l '- 2. __ _. '1’:- : 7. L j; -' 3 1' '"3/1. (b)[1 Opts] Find the general solution of the following differential equation: fig: -x%=0 7:” id”) w 763 .w _a mkm")(“‘*1\Lh~ 15) - m (m-ka— 23 2..) me-i) [Vi-3') (m as 4} =43 “Kmrifiuafl (hi—«0 :o M:O/&/Q/Li L L] fin) : (3‘ Jr sz 4(ch Jrcifx 5. [20pts] When a 32 pounds weight is attached to a spring. it stretches the spring 2 feet in l 8 times of its instantaneous velocity of the object coming to rest. A damping force equa acts on the system. The weight is set in motion from the equilibrium position by a downward velocity of 1 fthec. (a) Determine the displacement as a function of time (Le x(t) ). (b) Determine the maximum displacement of the weight from the equilibrium position. N: (c) Does the weight passes the equilibrium position. if it does find the first time passes / through it. ...
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MTH 205-Solutions of Test-02-A-SU09 - American University...

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